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Development of a new automatic incident detection system for freeways using a bi-classifier approach Razavi, Abdolmehdi 1998

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D E V E L O P M E N T O F A NEW A U T O M A T I C INCIDENT D E T E C T I O N S Y S T E M FOR F R E E W A Y S USING A BI-CLASSIFIER A P P R O A C H by Abdolmehdi Razavi B . S c , Shiraz University, Iran, 1986 M.Sc . , Shiraz University, Iran, 1988 A THESIS S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y in T H E F A C U L T Y O F G R A D U A T E S T U D I E S D E P A R T M E N T O F M E C H A N I C A L E N G I N E E R I N G We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A Apr i l 1998 © Abdolmehdi Razavi, 1998 In presenting this thesis in a partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purpose may be granted by the Head of my Department or by his or her representatives. It is understood that Copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Mechanical Engineering The University of British Columbia 2324 main M a l l Vancouver, B . C . Canada V 6 T 1Z4 Apri l 1998 ABSTRACT As high as 60 to 70% of the traffic delay experienced by motorists in North America is attributed to traffic incidents. Much of this delay is caused by vehicle accidents, vehicle stalls, and other obstructions. A substantial reduction in delay can be achieved by early detection of the incidents that cause it and a prompt response to divert the traffic in the upstream flow. Since the late 60s, Automatic Incident Detection (AID) systems have been developed and implemented to help traffic management authorities. However, high false alarm rates and/or poor performance of the adopted A I D systems have caused some authorities to abandon them. The research presented in this thesis discusses the development and assessment of a new A I D system. Often after the occurrence of an incident, its "news" travels upstream and downstream through the traffic by means of two waves. Because of some practical difficulties, the information carried by the wave traveling downstream is overlooked by most researchers in this area. In this thesis, it is proposed that through an effective use of the information carried by this wave, it is possible to significantly improve the performance of an A I D system. The proposed U B C A I D system exploits the information carried by each wave independently and overcomes many of the practical difficulties by adopting a new and unique architecture. The designed architecture not only demonstrates a better performance but also has the ability to maintain the performance over a wide range of operating conditions. ii Geometric and operational data from a stretch of the Trans-Canada Highway was used to develop a simulation model. This provided a very large set of simulated data under both incident and incident-free situations. Furthermore, it provided an opportunity to examine the performance and robustness of the A I D systems over a wide range of geometric and operational conditions. The comparison of the U B C A I D method with two other existing and "in-use" systems showed that it is possible to reduce the detection time by about 40% while staying within the desired range of false alarm rates. It was also possible to increase the number of incidents detected within the first few minutes after their occurrence by as much as 2-3 fold. i i i TABLE OF CONTENTS Abstract Table of Contents iv List o f Tab les_ _____ vi List o f Figures vii Acknowledgement ix Chapter 1 Introduction 1 Chapter 2 Background 4 2.1 Incidents 4 2.2 Traffic F low Variables and Sensors 5 2.3 Incident Patterns 12 2.4 Incident-Like Traffic Patterns 15 2.5 Performance Measures 16 2.6 Calibration 18 Chapter 3 Existing A I D Methods and Practices 23 3.1 Literature Survey of Existing A I D Algorithms 23 3.2 A I D Practices 57 3.3 General Observations and Comments 64 Chapter 4 Methodology of the Study 71 Chapter 5 Simulation of Traffic Flow Under Incident and Incident-free Conditions _ 76 5.1 Simulation Program 76 5.2 Simulation Model for This Study 79 iv Chapter 6 Data Sets : 94 6.1 First Series of Data Sets 94 6.2 Second Series of Data Sets 97 6.3 Data Set Names and Structures 98 6.4 Effects of the Random Number Seed 100 Chapter 7 Development of The U B C A I D System 101 7.1 Shock Waves and Expansion Waves 101 7.2 Basic U B C System 114 7.3 Final Form of the U B C A I D System 135 Chapter 8 Discussion of Results 150 8.1 Comparison o f Performances 150 8.2 Detailed Performances 157 Chapter 9 Conclusions and Further Research . 171 9.1 Conclusions 171 9.2 Further Research 172 Bibliography 175 v LIST OF TABLES Table 2-1 - Description of Incident-Like Traffic Events that Cause False Alarms (summarized from Chassiakos, 1992) 15 Table 2-2 - Definition of the Performance Measures 16 Table 3-1 - Characteristics of the 10 Versions o f the California Algorithms (reproduced from Tignor and Payne, 1977) 27 Table 3-2 - Assessment Procedure in Stage#2 of McMaster Algorithm for Stations Where Recurrent Congestion May Occur (from Hall et al., 1993) 45 Table 5-1 - Geometric Parameters Used in the Simulation Model 85 Table 6-1 - Traffic Volumes used in the Simulation Data Sets 97 Table 7-1 - The Advantages and Disadvantages of Using Shock and Expansion Waves for an A I D System I l l v i LIST OF FIGURES Figure 2.1. A n Example of Probability Distribution Function of the Control Variable under Incident and Incident-free Condition 19 Figure 2.2. Examples for pdf of the Control Variable Showing a) Proper Choice of Control Variable b) Poor Choices of the Control Variable 20 Figure 3.1. Decision Tree for an Equivalent Form of California Algorithm#8 (reproduced from Payne and Tignor, 1978) 29 Figure 3.2. Conceptualization of Traffic Operations on a Catastrophe Theory Surface (reproduced from Persaud and Hall , 1989) 42 Figure 3.3. Flow-Occupancy Template for McMaster Algorithm (Hall et al, 1993) 43 Figure 3.4. Input and Output Features of the M L F used by Ritchie and Cheu, (1993) 48 Figure 5.1. Selected Study Site along Trans-Canada Highway 81 Figure 5.2. Link-Node Diagram and Highway Geometry for the Study Site 84 Figure 5.3. Variation of Occupancy along the Freeway for Incident-Free Cases 91 Figure 7.1. Fundamental F low Diagram and Effects of Incident 102 Figure 7.2. Effects of an Incident on Traffic Flow Variables 105 Figure 7.3. Effects of a) Demand and b) Incident Severity on Shock and Expansion Waves 108 Figure 7.4. Variations of the Lane Occupancy for a Typical Lane Blocking Incident 109 Figure 7.5. Occupancy Variations at First Upstream and Downstream Stations for a Typical Incident 110 Figure 7.6. General Scheme of the Proposed System 115 Figure 7.7. The First Prototype of the U B C A I D System 116 Figure 7.8. Some Examples from Detectors' Readings 126 Figure 7.9. Operating Characteristic Curves of Various A I D methods for the Simulated Data - " X X X A X X " Series, Lane Closure Incidents 133 Figure 7.10. Proposed U B C A I D System 136 Figure 8.1. Comparison of the D R and A D T as a Function of F A R ( X X X A X X ) 151 v i i Figure 8.2. Comparison of the number of Incidents Detected as a Function of Time Elapsed After the Onset of Incident ( X X X A X X e ) 154 Figure 8.3. Comparison of the A D T as a Function of Time Elapsed after the Onset of Incident ( X X X A X X e ) 155 Figure 8.4. Comparison of the D R as a Function of Time Elapsed after the Onset of Incident ( X X X A X X e ) 156 Figure 8.5. Detection Rates as a Function of Incident Zone, Incident Location, and Time of Day 159 Figure 8.6. Distribution of Highest, Lowest, and Weighted Average Volumes of the Study Site as a Function of Time of Day 161 Figure 8.7. Distribution of False Alarm Rates Experienced in Various Zones and Times of Day 163 Figure 8.8. Average Detection Time as a Function of Location and Time of day 165 Figure 8.9. Number of Incidents Detected and Their A D T for Each Classifier and Location within a Zone 167 Figure 8.10. Percentage Contribution of the Two Classifiers to Incident Detection 169 Figure 8.11. Percentage of False Alarms caused by each Classifier 170 A C K N O W L E D G E M E N T M y sincere gratitude is expressed to my supervisors Professor F. Sassani and Professor F. Navin for their invaluable advice and guidance during so many meetings that we had. Moreover, the fact that their support went beyond academic matters is deeply appreciated. I would also like to thank the members of my supervisory committee, Professor C. de Silva, Dr. T. Sayed, and Professor K . Bury, for their useful inputs and remarks. M y appreciation is also extended to my external examiner, Professor F. Hall from McMaster University and my university examiners, Professor D . Cherchas and Professor G. Dumont who carefully read the thesis and provided me with their helpful comments. This project was mainly funded by the British Columbia Ministry of Transportation and Highways. I wish to thank M r . Kitasaka, M r . Miska, and Dr. Zhou of the Ministry for their suggestions and support during the course of this project. I also acknowledge the invaluable help of the Ministry Library Resource Centre in obtaining much of the literature. I would also like to thank Ms . Lee and M r . Zhang who ran part of the simulation and developed a program so that I could quickly plot and compare the detector signals. Special word o f thanks is also expressed to M s . Navin who kindly reviewed and edited this thesis. M y words can not express my gratitude to my kind and caring wife, Maria who has always been there for me (even for my last minute preparations!), and to our son, A l i , who in a special way taught me other ways of looking at things. ix C H A P T E R 1 I N T R O D U C T I O N Traffic Congestion and its effects have become part of everyday life in metropolitan areas. Congestion is divided into recurrent that exists during the peak periods, and non-recurrent that frequently occurs as a result of incidents such as accidents, vehicle stalls, or maintenance activities. A n estimate by the United States Federal Highway Administration ( F H W A ) (Lindley, 1986) has reported incident-related congestion as causing up to 60% of the total motorist's delay. This value is expected to grow up to 70% by the year 2005. This is because as freeways carry an ever-increasing volume of traffic and operate at or near capacity for long periods of time, more accidents wil l occur. Also, as increased maintenance and construction on aging freeway systems takes place, more lane closures will be necessary. Moreover, incident congestion is often unexpected by drivers and may lead to secondary accidents. ' T o reduce the negative effects caused by incidents, many transportation agencies are implementing freeway incident management systems. Incident management is a coordinated and planned approach to restore a freeway to normal operation after an incident has occurred (Dudek and Ullman, 1992). Incident management has several components including: • Detection of the incident. • Verification and identification of the nature of the incident. • Dispatch of the appropriate type of response. 1 • Provision of the necessary information for drivers about the incident and alternative routes. • Implementation of control strategies (such as ramp metering) to reduce demand upstream of the incident. Incident detection is the first essential component o f a traffic management system. Caltrans 1, in a study, has determined that even under off-peak free-flow conditions, for each minute saved by early detection and removal of an incident, at least 4-5 minutes wi l l be cut from the delays. During the peak hour, a few minutes saved in restoring capacity can save hours in accumulated delay time (Roper, 1990). There are various techniques for incident detection ranging from simple motorist call systems to electronic surveillance systems. Each technique has its advantages and disadvantages (Balke and Ullman, 1993). Calls from motorists using call boxes or cellular phones, highway patrols, and other "manual" means of detection are used every day to report incidents to the traffic management centers. However, they are somewhat "spotty" in nature, and require observers to be in the right place at the right time. Often the incident is detected only after time has been lost and a problem of considerable magnitude has already developed (Roper, 1990). 1 California Transportation Authority 2 The main advantage of Automatic Incident Detection (ADD) techniques is that (at least potentially) they can overcome the deficiency of the manual techniques. A I D systems, using real-time data coming from sensory stations spread along the freeways, are electronically "everywhere" at "all times". Currently, no A I D system is being used in British Columbia. A I D has been identified as a key component in British Columbia Ministry of Transportation and Highways' South Coast Region's Traffic Management Plan (TMP) . This thesis presents the results of studies carried out as a research and development project on A I D systems for the British Columbia Ministry of Transportation and Highways. 3 C H A P T E R 2 B A C K G R O U N D In this chapter background information on traffic incidents and incident detection systems is presented. This includes definitions of the terminology and a discussion of the general concepts relevant to this study. 2.1 Incidents Incidents are defined as unusual non-recurrent events that temporarily reduce the roadway's effective capacity or increase traffic demand. Incidents, in a general sense, may be either predictable or unpredictable and include: • Unpredictable - Accidents - Vehicle breakdowns - Roadside distractions, and - Spilled loads, • Predictable, - Major events (e.g., sport events), and - Construction and maintenance activities. 4 In this thesis, the term incident is only used to refer to the unpredictable occurrences. 2.2 Traffic Flow Variables and Sensors As it wil l be discussed in the next chapter, apart from a few A I D methods that directly "see" the incident, the majority of them detect the incidents based on observed or estimated traffic variables. In this section, the main variables used in traffic flow analysis are introduced and then the variables used in A I D systems and sensors are explained. Characteristics of traffic flow in a freeway may be described by variables that are very similar to their counterpart in fluid flow. The variables can be attributed either to individual vehicles or to the state of traffic as a whole. The variables that define the state of traffic are either "point measures" or "length measures". Point measures are defined for a specific point along the freeway. These variables have to be defined for a specified time, often by a simple averaging. The length measures, on the other hand, are defined for a section along the freeway. Flow rate (q) often referred to as "flow" or usually "volume" is simply defined using ( ) the number of vehicles that pass a certain point and (T ) the time of counting as: Volume 2 is a point measure and is often expressed using "vehicles/hour". It may also be defined for a single lane in which case the unit would be "vehicles/hour/lane". The average speed of the vehicles is defined in two ways, depending on the type of "mean" that is used. The "space mean speed" or jTs is defined based on the average time taken by vehicles passing a specific length. This is a length measure and is mathematically reduced to the harmonic mean of the speed of the individual vehicles or: Us= (2T> '=1 Ut in which 11 = speed of vehicle z "Time mean speed " or jTt is a point measure in which the speed of the vehicles passing a specific point within a time period is averaged. It is calculated as: N in which U = speed of vehicle / (measured at a point) 2 In this thesis as in most of other AID literature, the term "volume" is used. 6 The units o f both mean speeds3, like the speed of individual vehicles are expressed in "miles/hour" or "km/hour". Another variable used in traffic flow theory is a length measure called "density". It is simply defined using the number of vehicles ( N ) and (L ) length of freeway on which those vehicles are spread as: (2.4) Due to difficulties in measurement of density for on-line systems, a different variable that describes the degree of the closeness of the individual vehicles is defined. This point measure is called "occupancy" and is defined as the proportion of the time that a point along the freeway is occupied by vehicles. This measure needs to be defined for a specified time period (T) and can be calculated as: (J)=YJLL ( 2 .5) in which, f = The time taken by vehicle / to pass over the point Occupancy is expressed as a percentage. Time headway (/ j ( ) is another important point measure. Headway is the time separation of one vehicle and the one following measured from a specific vehicle point (e.g., front 3 In this thesis, hereafter speed refers to the time mean speed. bumpers). Averaging this headway for a number of vehicles passing during a specific time period gives the average time headway as: A close look at the above formula shows that average headway is inverse of traffic volume. If just after a vehicle passes a point, one starts adding the headways, the numerator in this formula would be equal to total time required to pass the next (N ) vehicles. However, when measuring the headway for pre-specified time periods, considering that the passage of a vehicle would not necessarily coincide with the beginning or end o f the period, may lead to a situation where the above statement does not hold 4 . In this case the product of average headway and volume (using a compatible set of units) would be close to, but not necessarily equal to unity. The lower, the volume, the higher the deviation from unity could be. In traffic engineering handbooks, the headway corresponding to the first vehicle is defined such that the average headway remains the inverse of volume 5. Depending on whether or not this point has been considered in the calculations, the volume and average headway6 may be treated as dependent on or independent of each other. 4 An exaggerated example for illustrative purpose could be presented as follows. If during a time period of 30 second two vehicles pass a reference point, the measured volume would be 2 vehicles/30 seconds (or 240 vehicles/hour). This obviously should correspond to 15 seconds/vehicle for average headway. However, if the vehicles pass 1 and 29 seconds after the start of the period, the average headway might be calculated as 28 seconds if only one headway is considered. It may also be any value, if the headway for the first vehicle and the one that has passed in the earlier time period is also included in the calculation. 5 For the example presented in the footnote 4, the second headway is calculated by adding the first and last one-second of the period. This obviously leads to an average headway of 15 seconds/vehicle. 6 In this thesis hereafter "headway" is used. 8 There are a number o f traffic models that discuss the relationship among the variables. These models are subjects of traffic flow theories. Since none of these models has been used in development of the U B C A I D system, they are not discussed here. A general form of these models wi l l be briefly mentioned in section 7.1, when effects of the incident on the traffic flow are discussed. Although some length measures such as density could be very important when working on identification of congestion and incidents, they can not be directly measured by ordinary surveillance systems7. Therefore, their usage is impractical for the purpose of incident detection and point measures are used to identify the state o f traffic at certain points along the freeway. There are several types of sensors and detectors available for A I D systems. They include a wide range of sensing technologies including, video cameras8, infrared (Grewal, 1992) and ultrasonic sensors, (Yagoda and Buchanan, 1991) and even radar (Roe, 1991). However, the most widely used sensors in North America employ a simple technology to detect the presence of the vehicles. These sensors are called loop detectors. They use magnetic loops whose magnetic field changes depending on the presence or absence of vehicles passing over them. A computer that interrogates the loop with a frequency of a few hertz wil l receive a binary signal whose value shows whether or not the detection zone is occupied by a vehicle. 7 It is possible to estimate density using video surveillance systems, but such estimation is not used in AID systems. 8 A number of video based sensors that have been more popular outside North America will be presented in section 3.1.13. The detector sends a series of "F ' s or "0"s accordingly. This signal is processed by the computer to calculate various traffic parameters averaged during a time interval. The time intervals may vary from 1 second to 20, 30, 60 seconds, or more. The updating time for each calculated average variable could also be any value, but in most cases is 30 seconds. In this thesis, it is assumed hereafter that the sensors are of the presence detection types similar to loop detectors. Obviously, whatever information available through this type of sensors is also available from other types of sensors and this therefore does not impose a limitation for the U B C A I D system. In almost all of the A I D algorithms, occupancy is used as one of the control variables. Many A I D methods such as the California algorithms, work only based on the observed occupancy. A s stated before, occupancy is a measure of density, but unlike density, it can be obtained easily using loop detectors. It can be calculated as the ratio of number of " 1 " signals to the total number of signals in a pre-defined averaging interval. The fact that both the vehicle and the detection zone have some non-zero lengths introduces a variable bias to the measurements. Traffic volume or flow rate is also used in many A I D systems either as a control variable, or in order to enable the system to distinguish among light, moderate, and heavy traffic conditions. Volume is also easily obtained using loop detectors as the product of number of state changes in the pre-defined interval, and a constant that depends on the interval duration. Sometimes the loop spans more than one lane as in some roads in U K , (Bell and Thancanamootoo, 1988) which leads to under-counting. This is due to the possibility that two vehicles occupy the 10 detection zone at the same time. This bias depends on the flow rate and therefore should be compensated accordingly. In A I D systems, speed is an important parameter as it changes significantly in upstream of incidents. Nevertheless, unlike occupancy and volume, speed cannot be directly measured by one loop detector. However, in some traffic control and surveillance systems "speed traps" are used to obtain the speed. Speed traps consist of two loop detectors closely spaced along the same lane. The speed of vehicles can be calculated by dividing the known distance between the detection zones by its travel time. The travel time is the delay between the passage of the vehicles over the two detectors. To use this technique twice as many detectors are required, which wil l add to the hardware cost. However, at least potentially, the additional information obtained may enhance the performance of the system. Another way of estimating the average speed is to calculate it as volume divided by occupancy multiplied by some calibration factor. This calibration factor depends on the mean vehicle length and detector size and is usually assumed to be constant. However, Hall and Persaud (1989) showed that this is not always true, particularly in a transition from non-congestion to congestion which happens after the occurrence of an incident. Traffic energy is also another variable that was sometimes used in the older A I D algorithms such as in standard normal deviate algorithm (Dudek et al, 191'4). The idea comes from an analogy between traffic flow and flow of a compressible fluid. It is defined as the product of speed and volume. Sometimes speed is not measured directly, and energy can be calculated as (Cook and Cleveland, 1974): 1 1 (2.7) One may also find several other parameters that are used in the ADD algorithms, mostly a temporal or spatial difference of the above parameters. Some of these parameters are discussed in more detail in the Chapter 3, which discusses existing A I D algorithms. 2.3 Incident Patterns The impact of the incidents on freeway operation depends on many factors including • Frequency • Location • Severity • Time of day • The level of usage of the facility Incident management systems aim to reduce the congestion and delay caused by incidents. Therefore, they are more interested in early detection of incidents that cause greater impact. If an incident occurs with no lane blockage in a light traffic condition, the incident may have little effect. On the other hand, i f an incident blocks some lanes during peak demand period, the delay would be quite extensive. 12 The incidents that have greater impact on traffic also have a higher likelihood of detection by ATP systems. As it wil l be discussed in Chapter 3, most of the incident detection techniques try to find an abnormal traffic pattern developed as a result o f an incident. Therefore, it is necessary to categorize these traffic patterns. This wil l help differentiating between the cases that are "easy-to-detect" and those that are almost "undetectable" by most o f the ADD systems. Payne and Tignor (1978), divided the traffic pattern after the occurrence of an incident depending on its nature and the traffic conditions at the onset o f the incident into the following five types: 1. The capacity9 at the site of the incident is less than the volume of oncoming traffic. This is the most distinctive incident pattern for incident detection algorithms. In this case, a queue develops upstream, while a region of light traffic develops downstream. When traffic is flowing freely before the occurrence of the incident, this pattern would be clearest. A typical case occurs as a result o f a severe accident that may block one or two lanes. 2. The prevailing traffic condition is freely flowing and the impact of the incident is less severe. This pattern can be observed typically when an incident has been moved to the shoulder, or in a case of one lane blockage for which the reduced capacity due to the blockage is still higher than the upstream demand. Other than small queues close to the incident location, the traffic pattern wil l not change very 9 Capacity refers to the highest possible volume for the road. Please see Figure 7.1. 13 much. Such cases may be missed by incident detection algorithms, depending on how far the incident location is from the neighboring detector station. 3. The prevailing traffic condition is freely flowing and the impact of the incident is not noticeable in the traffic data. A typical such case can be an incident during the night, or a stalled vehicle in the shoulder under low volume conditions. Such incidents do not cause queues and therefore there wil l almost be no observable effect on the traffic pattern, thus, ordinary incident detection algorithms are not expected to detect such incidents. 4. In a heavy traffic, the capacity at the incident site is less than volume of traffic downstream. This case happens in an already congested segment of the freeway (such as the case of a secondary accident a queue that has already developed by another incident). It causes a reduction in the demand downstream and hence clears the downstream. However, clearance of downstream region usually happens slowly and there is minor or no effect on the upstream unless the accident is severe. Therefore some of the incident detection algorithms might be able to detect it but after the situation has developed for a while. 5. In a heavy traffic, the capacity at the incident site is not less than volume of traffic downstream. This case is very similar to the fourth case, but because the capacity after the incident is more than the downstream volume, it has much less effect on the traffic pattern. Generally, the effects of such an incident are local and are not expected to be detected by incident detection methods unless the downstream congestion diminishes for some other reasons. 14 2.4 Incident-Like Traffic Patterns Various traffic events may produce traffic disturbances similar to those of incidents. Such events are the major sources of false alarms by the A I D systems. These events and their description are given in table 2-1. Table 2-1 - Description of Incident-Like Traffic Events that Cause False Alarms (summarized from Chassiakos, 1992) Traffic event Description Observed pattern Bottlenecks (recurrent congestion) They are formed where the freeway cross section changes in a lane drop or addition, entrance ramp with a substantial on-ramp traffic volume, and freeway interchanges. Long lasting spatial density or occupancy difference between upstream and downstream stations Traffic pulses (in uncongested flows) These pulses are created by platoons of cars moving downstream and may be caused by a large entrance ramp volume lasting for a finite duration. A n increase in occupancy in the upstream station followed by a similar increase in the downstream occupancy Compression waves These waves occur in heavy, congested traffic, usually following a small disturbance and are associated with severe slow-down, speed-up vehicle speed cycles. Compression waves are the major sources o f false alarms. Sudden, large increase in occupancy that propagates through the traffic stream in a direction counter to the traffic flow Random traffic fluctuations They are frequently observed because of the random nature o f traffic. Short-duration, usually not high peaks of occupancy 15 2,5 Performance Measures Generally, the performance of an automatic incident detection system is measured by three parameters. Table 2-2 presents the definitions for these performance measures. Table 2-2 - Definition of the Performance Measures Performance Measure Definition Detection Rates (DR) Percentage of the incidents detected out of all incidents that occur during a specified time period. False Alarm Rate (FAR) Percentage of the false alarms out of all decisions made by the system during a specified time period10. Average Detection Time (ADT) or Mean Time To Detect (MTTD) The average amount of time required by the system to detect an incident after its occurrence11. As will be described later, the values of these performance measures of an algorithm are not fixed for a given traffic condition. They are often a function of the selected thresholds. Therefore, a better way to describe performance of an algorithm is to draw an operating characteristic curve. This curve shows the variation of the detection rate (DR) by changing false alarm rate (FAR). As it was stated earlier, performances of the AID systems are usually measured by: detection rate, false alarm rate, and average detection time. However, these three measures are not 1 0 Sometimes in off-line evaluations another definitions is used in which the denominator would only represent the incident-free part of data. On the other hand, Levin and Krause (1978), have defined FAR as the percentage of false incident messages out of all incident messages occurring during a specified time. 1 1 Sometimes the starting time is defined as its apparent time from traffic data at upstream and downstream. This needs a subjective decision and moreover the resulted figure would be less than the actual value 16 independent of one other. In most of the cases a threshold or a set o f threshold values has to be defined for the algorithm that sets its sensitivity to change in traffic patterns. Higher sensitivity for an algorithm increases its ability of detection of the less severe incidents or those that have minor effect on the traffic flow. However, this also causes an increased risk of producing an alarm when the change in traffic pattern is not due to an actual incident. Therefore, it is seen that detection rate and false alarm rate are directly related to one another. To compare various algorithms, it would therefore be logical to consider the variation of detection rate as a function of false alarm rate. The resulted curves are called operating characteristic curves. In many of the cases the abnormal traffic pattern vanishes within a couple of minutes i f not caused by an incident. Therefore, persistence checks that are used by some algorithms can filter out such patterns. This provides the opportunity of decreasing false alarm rate while maintaining the detection rate constant. However, persistence checks also increase the average detection time that in turn cause increased congestion due to late detection. The choice of the thresholds and delay time that determines D R , F A R and A D T are related to the policies o f the traffic management centers. It seems that from the operational point of view, a certain maximum for F A R should be set beyond which, it would be impractical to respond to the alarms. This will be discussed further in Section 3.3. 17 2.6 Calibration The role of calibration can be explained by means of an example. Consider a method in which only one control variable is used and only one test against some threshold value is required. It can be assumed that a high value for the control variable represents an incident condition and a low value represents an incident-free flow. To give a physical sense to this example, the control variable can be assumed to be the spatial difference between the occupancy of two adjacent stations. This example is intentionally oversimplified to clarify some points about calibration, strength, performance, and robustness of the AID algorithms. As discussed earlier, there are some incident-like traffic events that may produce similar changes in the traffic as most incidents do. On the other hand, based on incident type, location with respect to the detectors, road capacity and volume, some incidents may not produce significant changes in the measured traffic parameters. Assuming a uniform traffic flow and an incident-free condition, the occupancy of all the detector stations should be the same. This should produce a zero value for the selected control variable. However, due to the random nature of the traffic flow parameters, the zero should be replaced with a random variable with a zero mean. On the other hand, after an incident occurs and its effects are sensed at the immediate detector stations, a significant difference between their occupancy should be experienced. Therefore, under incident condition, a positive value for the mean of the control variable can be assumed. Figure 2.1 shows the probability distribution functions (PDF) for the control variable under both incident and incident-free conditions. As this figure shows, the two PDFs always have some overlap. In this simple 18 example, a single test of the control variable against the threshold is needed. No matter where the threshold is placed, there will always be a probability of missing incidents or producing false alarms. The choice of threshold will only define the trade off between these rates. For proper calibration, either a knowledge of the PDF under both conditions is required, or a trial and error approach has to be employed. u o c C D u -a "° £ c ° u u — CJ JS *-.2 X k. c TO (J > -o ~ "3 threshold looser threshold, better DFL but higher FAR ^- tighter threshold, better FAFL but lower DR incident conditi probability of missing incidents probability of giving false alarm dent dition Control variable Figure 2.1. An Example of Probability Distribution Function of the Control Variable under Incident and Incident-free Condition In this example, the proper choice of the control variable is such that the overlapping region is as small as possible (see Figure 2.2). A small overlap not only makes it more distinguishable, and, therefore, produces better performance, but it also decreases the sensitivity of the 19 performance to the calibration. To produce the best performance for this method, it should be noted that the mean and variance o f these probability functions are not constant. Not only are they functions of the detector locations, and spacing, but also functions of traffic, time, and weather condition. Therefore, ideally, a knowledge of all of these variations is required to optimally calibrate the algorithms and/or update the thresholds. I f all or.some of these variations are ignored the two PDFs used wil l have a larger overlap because o f the more uncertainty involved. Figure 2.2. Examples for pdf of the Control Variable Showing a) Proper Choice of Control Variable b) Poor Choices of the Control Variable This example can now be generalized to show that the same problems exist in all o f the A I D methods. To increase the performance and the degree that incident and incident-free conditions are "distinguishable" for the method, one may use more than one control variable (such as the California algorithm#l). Persistence checks used by some algorithms can also be assumed as additional control variables. Additional control variables increase the dimension of 20 the above visual representations of the method. I f we use two control variables along with two thresholds, we can still visualize the probability density functions as two 3D Gaussian surfaces whose overlap defines a region in 3D space. Although functions of more than two variables are difficult to visualize, one may continue to use the same concepts from Figure 2.1 and Figure 2.2. Obviously, in such cases the abscissa does not represent any specific control variable, but rather a generalization of several variables. Since the horizontal axis does not represent any specific variable, position of the threshold does not have a physical meaning. But, the movement of the threshold to the left or right can still be assumed to loosen or tighten the conditions respectively. The size of the overlap region still represents how distinguishable the two conditions are for the method. The indirect A I D algorithms differ in the number, and the type o f the control variables. They also differ in the pre-processing of control variables, how the variables are used, and their level o f sophistication. The process can be quite visible to the user or be done in a "black box" form. Sometimes the choice of thresholds may not be clear to the user, but still the concept might be applicable. As an example of the latter, the S N D 1 2 and A R I M A 1 3 algorithms have been described as dynamically updating their thresholds. However, even in this case, the number of standard deviations that form the confidence interval plays the same role as our generalized threshold does in the example. 1 2 SND algorithm is described in section 3.1.3. 1 3 ARIMA algorithm is described in section 3.1.7. 21 The size of the overlap region, that is defined primarily by the choice of control variables and the logic, defines the ideal expected performance or strength of the A I D method. The actual performance of the system, as was stated earlier, depends on the choice of thresholds or parameters, whether they are general or location specific, and whether they are updated according to the changing conditions. A robust A I D system should be able to perform well in a wide range of traffic conditions. On the other hand, generally, the required knowledge for an ideal calibration does not exist. Usually only one set of thresholds is used for all locations, and except in a few cases, no updating mechanism is used. Therefore, the performance of the system at any time and any location, depends very much on how close the system is to its optimal condition. 22 CHAPTER 3 EXISTING AID METHODS AND PRACTICES In this chapter, first a review of A I D literature is presented to explore the logic used by the existing A I D methods. Then, in section 3.2, A I D practices of a number of North American traffic authorities will be discussed. A discussion of the general findings will also be presented in section 3.3. 3.1 Literature Survey of Existing AID Algorithms During the past three decades, there has been extensive research efforts to develop or enhance A I D methods. In a literature search, about forty research groups were identified (Razavi, 1995). The A I D methods can be categorized in several ways. In this thesis, they are divided into two categories as "indirect methods" and "direct methods" 1 4. The majority of the A I D methods are of the first category, which "indirectly" detect incidents based on their impact on the traffic flow. They do so by recognizing unexpected changes in the traffic data measured by the sensors. These measurements can be done using different sensor technology, but the most popular choice in North America is inductive loop presence detectors. They provide a cheaper but slower incident detection system. Slower, because no 1 4 No specific terminology for these methods was found in the literature. These names were selected for the purpose of this thesis. 23 matter what algorithm is used, there wil l always be a lost time until the effects of the incidents arrive to the sensor locations 1 5. Another minor drawback is that most of these A I D methods can not detect the incidents in light traffic because there is almost no change in the traffic parameters other than near the incident. For the same reason, detection of incidents in light traffic is of a low priority for traffic authorities. "Direct methods" refers to a few methods that use image processing techniques to detect stopped vehicles by interpreting the scene image and finding the stopped vehicles. These methods actually "see" the incident rather than detecting it through its effects. Potentially they can be much faster than the first category in detecting the incidents. These methods also have good performance in detecting the incidents in light traffic conditions. However, they may also need closer spacing between detecting stations (cameras), which makes them more costly to provide sufficient coverage. Environmental conditions may also affect the performance of these methods. This category wil l be briefly reviewed in section 3.1.11. There has also been some research activities in development of A I D algorithms that do not belong to the "mainstream" methods. They include: • Methods designed for arterial streets; • Methods targeting detection of incidents in light traffic; and • Methods that use less conventional technology. 1 5 The UBC method presented here is of this category. However, as it will be discussed in Chapter 7 , it has the potential to substantially reduce this time lag. It does so by targeting the effects that can be sensed much earlier than those targeted by other "indirect methods". 24 For the sake of completeness, these methods are also mentioned in section 3.1.14. However, the most important group of "indirect methods" are those that are often designed for medium level of traffic volume in freeways and use data from presence detectors. Most o f these are presented in sections 3.1.1 to 3.1.12. Several methods that are of greater importance in this thesis wi l l be discussed in some detail. Their reported performance measures, however, wi l l not be discussed. This is because, as it wi l l be seen later, these measures are not necessarily compatible and comparisons made based on different sources could be misleading. 3.1.1 California Algorithms The California algorithms (Tignor and Payne, 1977) are some o f the earliest incident detection methods and are still widely used. These methods were developed by the California Department of Transportation to be used in the Los Angeles freeway surveillance systems. In the original California algorithm the occupancies at any two adjacent detector stations are compared for a significant temporal and spatial difference. Three such differences have to be tested against pre-defined thresholds as follows: OCCDF > Tx ; OCCRDF > T2 ; and DOCCTD > T3 where, /,/ + 1 = upstream, downstream stations (respectively) 25 OCC(i,t) = 1 minute occupancy at station / , for time interval / OCCDF = OCC(j) - OCCii +1) OCCRDF = OCCDF / OCC(i) DOCCTD = [OCCQ + M - 2) - OCC(i +1, f)] I OCC(i + M - 2) TX,T2,TZ = thresholds set by user At any time the system is in one of the following two states; • Incident free state, or • Incident state. A n incident wil l be triggered i f all three conditions are satisfied within the same time interval. The three thresholds are station-specific and have to be determined in the calibration stage. This algorithm was very easy to implement, but it had high false alarm rate. This was because there was no mechanism to differentiate between a real incident, and a compression wave or a short-lived flow disturbance. Therefore, the Federal Highway Administration initiated a research study to develop improved incident detection algorithms with better false alarm performances. Consequently, nine modified versions of the California algorithm were developed. They were all defined based on decision trees with states. Table 3-1 identifies the traffic features and characteristics of these algorithms, (Tignor and Payne, 1977). 26 To eliminate the false alarms due to the short-lived disturbances, a persistence check was developed by Payne et al, (1976). More states were used to enable the system to check the persistence of the disturbance for a pre-specified number of time intervals before triggering an alarm. This check decreased the false alarm rate, but obviously at the price of increased average detection time. T a b l e 3-1 - C h a r a c t e r i s t i c s o f the 10 V e r s i o n s o f the C a l i f o r n i a A l g o r i t h m s ( r e p r o d u c e d f r o m T i g n o r a n d P a y n e , 1977) A l g o r i t h m N u m b e r Fea tures used C o m m e n t s 1 O C C D F , O C C R D F , D O C C T D Essentially the California algorithm 2 O C C D F , O C C R D F , D O C C T D Essentially the California algorithm with an incident continuing state l l l i i l l i i l l l l l O C C D F , O C C R D F Same as #2, but without D O C C T D check 4 O C C D F , O C C R D F , D O C C Same as #2 but use of D O C C replaces use of D O C C T D l l l l l l l l l l l l l O C C D F , O C C R D F , D O C C T D Essentially the California algorithm with a check for persistence • • i i i i O C C D F , O C C R D F , #3 with a check for persistence O C C D F , O C C R D F , D O C C #4 with a check for persistence, best simple algorithm O C C D F , O C C R D F , D O C C , D O C C T D Has form of #4 plus check for compression wave and persistence, especially effective in "stop-and-go " traffic 9 O C C D F , O C C R D F , D O C C , D O C C T D #8 without a persistence check, especially effective in "stop-and-go " traffic 10 O C C , O C C R D F , D O C C , S P D T D F Distinguishes two traffic regimes (light and moderate) for purposes of detecting incidents The Features O C C D F , O C C R D F , and D O C C T D were defined earlier. D O C C is the downstream occupancy. S P D T D F is similarly defined in terms o f the volume divided by occupancy at the upstream station. 27 Another source o f false alarms being produced by the original California algorithm in heavy traffic, is the compression waves that occur in the stop-and-go traffic. Compression waves produce large sudden increase in occupancy, which propagates with a speed of 6 ~ 15 mph (10 ~ 24 km/h) in a direction counter to the flow of traffic. Therefore a few minutes after these waves have passed the downstream station they should reach the upstream detectors. This is the basis of check for compression waves. In algorithms #8 and #9, after a compression wave has been detected in the downstream station, incident detection process is suppressed for the following five minutes. A l l the ten algorithms were evaluated in this report using data obtained from Los Angeles and Minneapolis freeway surveillance systems by Payne et al. (1976). The algorithms #7 and #8 performed better than the others. Algorithm #7 is similar to the original algorithm with a check for persistence of the disturbance, but it uses DOCC (downstream occupancy) rather than DOCCTD. This means that rather than a relative temporal change, the downstream occupancy is tested against the proper threshold. It was based on the observation that in heavy traffic that has compression waves, the downstream occupancy rarely drops below 20% (in the Los Angeles data), whereas incidents generally produce downstream occupancies substantially less than 20%. This algorithm has been identified as the best simple algorithm (Tignor and Payne, 1977). The algorithm #8 has the advantage of a check for the compression waves, as it was described earlier. The detection of the compression waves is based on DOCCTD, the relative temporal difference in the downstream occupancy. The false alarms being produced by this algorithm or 28 #9 were essentially due to the bottlenecks and the compression wave detection was found to be effective (Tignor and Payne, 1977). The decision tree for an equivalent form of algorithm #8 is shown in Figure 3.1. Compression wave State Designates 0 Incident free 1 Compression wave downstream this minute 2-5 Compression wave downstream 2-5 minutes ago 6 Tentative incident 1 Incident detected 8 Incident continuing Figure 3.1. Decision Tree for an Equivalent Form of California Algorithm#8 (reproduced from Payne and Tignor, 1978) 29 3.1.2 Exponential Smoothing Algorithms The sudden flow-state changes observed during incidents suggest the application of short-term forecasting techniques for detecting irregularities in a time series of traffic data. Whitson et al. (1969) proposed the use of a moving average of the most recent 5 minutes of volume data as a forecast variable with confidence limits determined from the variance o f the data. Cook and Cleveland (1974) used double exponential smoothing technique to develop incident detection algorithms. With this technique, the forecast traffic variable z(x,t) is a function of the past-observed data, geometrically discounted back in time. They used a tracking signal, which is the algebraic sum of the previous estimation errors divided by the current estimate of the standard deviation. The tracking signal should fluctuate around zero because the predictions either match the data or compensate for errors in succeeding time periods. Detection is indicated by a significant deviation of the signal from zero. The mean absolute deviation - that is used as an estimate of standard deviation of the traffic data - is obtained by single exponential smoothing of the absolute values of the prediction errors, using a smoothing constant of 0.1: (3.1) where e(x, t) = Error of prediction z(x, t) - z(x, t) (3.2) a - Smoothing constant. 30 The variable forecast z(x,t) is computed by double exponential smoothing with a smoothing constant of 0.3, and the tracking signal is found as follows: TS(x,t) = y(x,t)/m(x,t-l) (3.3) Where y(x, t) = y(x, t - 1 ) + e(x, t) = Cumulative error. (3.4) A total of 13 traffic variables were investigated with the exponential smoothing algorithm (Cook and Cleveland, 1974). These variables were selected both from local (or station) and section (or subsystem) variables. In their investigation, they also included the original California algorithm and a group of five algorithms called TTI. The latter had been developed earlier by Courage and Levin (1968) at the Texas Transportation Institute as part o f the Lodge Freeway Corridor study. They concluded that the most effective detection algorithms were the exponential algorithms using station occupancy, station volume, and station discontinuity (a variable that is based on a comparison of the kinetic energies of individual lanes at a station). 3.1.3 Standard Normal Deviate Algorithm A control logic for the automatic operation of safety warning signs at three locations on the Gul f Freeway in Houston was developed by Dudek and Messer (1973). This was not an A I D algorithm, but it was responsive to stoppage waves and its ability to detect shock waves was reported as being very satisfactory. Later, in 1974, they selected a simple statistical approach to develop a station based automatic incident detection algorithm (Dudek et al., 1974) 3 1 It was assumed that a high rate of change in the control variable reflects an incident situation as distinguished from a problem caused by a geometric bottleneck. They proposed use of the standard normal deviate of the control variable for the control function. The idea was to evaluate the trends in the control variable (e.g., occupancy, energy) and to recognize when the variable changes rapidly. The SND is a standardized measure of the deviation from the mean, in units of the standard deviation and is expressed by the following relationship: x - x SND = (3.5) s Where x = value of control variable at time t, x - mean of the control variable over previous n sampling periods, 5 = standard deviation of control variable over previous n sampling periods. Therefore, a large SND value would reflect a major change in operating conditions on a freeway. Dudek et al. (1974) incorporated this simple method to the previously developed algorithm for detection of a stoppage wave (Dudek and Messer, 1973). When a shock wave was detected by the latter algorithm, the S N D technique would trigger the alarm i f the threshold was exceeded. Two operational strategies were used and evaluated. Strategy A required one 32 S N D value to be greater than its threshold while strategy B required that two successive values to be critical. This persistence check prevented some of the false alarms at the cost of a longer detection time. 3.1.4 Bay esian Algorithm Another approach to incident detection was proposed by Levin and Krause (1978) from the Illinois Department of Transportation. They developed a single feature algorithm using Bayesian statistical techniques. The traffic parameter used in their system was OCCRDF which was originally used in the California algorithms. They used mathematical techniques to find the optimal threshold, which when exceeded in four consecutive time periods, triggered an alarm. This method needs the following three databases for its implementation; • Incident data base, • Incident-free data base, and • Historical data on the type, location and effects of the incidents. The first database is needed to develop / ( Z / ( 7 , ) that represents frequency distribution function of the feature Z during an incident situation. A similar function f(Z/UQ) for incident-free situations can be developed using the second database. Levin and Krause (1978) 33 developed mathematical expressions for these functions assuming a truncated shifted gamma distribution. The probability of an incident occurring on a section, PQJf), under certain environmental and traffic conditions can be derived based on its history of capacity reducing incidents, as: average no. of incidents occuring on the study section in the time period P(U j ) = 7 \ / r" (no. of detectors in the study section) • (no. of minutes in the time period) (3.6) Clearly the probability of not having any incident is: P(U0) = l-P(U1) (3.7) For any feature value Z, (threshold), the probability of obtaining an incident signal can be expressed as follows: P(l) = P(U0))f(Z I U0)dZ + P(U, ))f(Z I U,)dZ (3.8) Where bo and bi are the upper bounds for functions f(Z/U0) andf(Z I £/,) respectively. The probability of not having an incident signal, P(0), can also be found in a similar way. Then, by applying Bayesian considerations, expressions for the following probabilities can be calculated: P(incident 11) Probability that an incident has occurred, given that an incident signal "1" was output. P(no incident 10) Probability that no incident has occurred, given that a non-incident signal "0" was output. 34 The optimal threshold (Z, ) can be obtained by maximizing the expression: P (incident 11) + P(no incident 10) (3.9) Theoretically, this optimization procedure for Zi can be repeated for / . (Z / £/,) to give a set of optimal thresholds, where " i " represents consecutive determined time intervals after the detection of an incident. However, by selecting a feature that is stable, and for which there are no statistically significant differences between the consecutive distribution functions, only one threshold value could be used. Levin and Krause (1978) selected OCCRDF among seven features, considering that OCCRDF is very stable and shows considerable difference between its values before and during the incidents. The application of the Bayesian concepts can also be extended to the case of a string o f signals. The evaluation of the probability that an incident has occurred, given an n-signal string can provide the decision-maker with more reliable information. Obviously, this comes with the price of an n-minutes delay, which has practical limitations. 3. h 5 HIOCC Algorithm The High Occupancy method (HIOCC) was developed by the Transport and Road Research Laboratory as part of their Automatic Incident Detection systems to be used in the freeways in England (Collins et al, 1979). H I O C C is a local algorithm that uses occupancy data and tries to detect presence of stationary or slow moving vehicles as a sign of an incident downstream. 35 As the name of the algorithm suggests, it identifies such vehicles when high occupancy is detected by a loop detector for a long enough period of time. In this method the occupancy is sampled with a frequency of 10 H z , and the number o f times in one second that the detector is occupied is used by the system. This is different from most of the other systems that use a period of 20, 30 or 60 seconds for averaging. This measurement whose range is 0-10 is called instantaneous occupancy. It is an indirect measure of velocity since a small instantaneous occupancy indicates that the passing vehicle has a high speed and vice versa. In the H J O C C method, the alarm will be triggered, i f for two consecutive periods or more the instantaneous occupancy becomes equal or more than the threshold value. A threshold of 10 is usually selected which means that a 100 percent occupancy for at least two seconds is needed to trigger the alarm. Like other ADD methods, the choice of threshold determines the trade off between the detection rate and false alarm rate. 3.1.6 PATREG Algorithm The Pattern Recognition Algorithm ( P A T R E G ) is another algorithm that was developed along with H I O C C by the Transport and Road Research Laboratory in U K (Collins et al, 1979). This algorithm is based on the assumption that in an incident-free steady-state flow condition, the traffic pattern observed in an upstream station, should also be observed at the next downstream station. A n estimate of the average speed in each lane can be found from the 36 measurement of the time delay of observing the same traffic pattern in the downstream station (travel time of individual vehicles). This is done using the following five steps: 1. Measure V (I), a vector containing the 40 most recent values of the upstream instantaneous flow. 2. Measure V^it), a similar vector containing the 40 most recent values of the downstream instantaneous flow. 3. Compute DU(i) = Vdwn(t)T-Vup(t-i), for i = 1,2,-40 4. Smooth DU(i) by the formula: MATCH(i) = Q • DU(i) + (1 - Q) • MATCH(i)old 5. Compute the speed by ^VT / m a x Where: D = the distance between two consecutive detector stations ^ m a x ~ t n e v a l u e at which MATCH(i) achieves its maximum The estimated speed will be compared to the pre-determined lane-specific upper and lower thresholds. To reduce false alarms due to the short-lived disturbances, the alarm is not triggered until, for a pre-specified number of consecutive intervals, the estimated speed falls outside its allowable range. 37 3.1.7 AB1MA Algorithm In 1977, (Ahmed and Cook, 1977) reported the results of their study on using the B o x -Jenkins technique to develop a forecasting model for freeway traffic stream variables. In their study, they analyzed volume and occupancy data from three freeway surveillance systems in Los Angeles, Minneapolis, and Detroit. They evaluated the performance of their proposed forecasting model against three other smoothing models: moving average, double exponential smoothing, and Trigg and Leach adaptive model (Trigg and Leach, 1967). They found that an A R T M A 1 6 (0,1,3) model could represent freeway time-series data more accurately than the other models. Later, Ahmed and Cook (1982) presented a station based methodology for the automatic detection of incidents on freeways based on the developed A R J M A (0,1,3) method. They stated that previous A I D systems had two main problems: high false alarm rates and a need for threshold calibration. They suggested that both problems are related because the threshold levels are not adjusted according to factors that cause the variations in traffic conditions. Therefore, they recommended that an accurate real-time estimation of these variations could potentially improve the performance of the A I D systems. Occupancy was selected as the key variable and a confidence interval was constructed by selecting two standard deviations away from the corresponding point estimate. The alarm was triggered i f the observed occupancy value fell outside the confidence interval. The confidence interval was defined as: ! ; + i ( ± ) = ! , ( 1 ) ± 2 C T (3.10) 1 6 Auto Regressive Integrated Moving Average 38 and Where Xt (1) = Xt - 6V,_, (1) - e2et_2 (1) - 03et_3 (1) (3.11) XM = Traffic occupancy observed at time (t +1), XM (±) = Approximate 95 percent confidence limits for XM, Xt (1) = Point forecast made at time t, et_x (1) = Forecast error made at time (t - 1 ) , 0l,02,03 = Parameters of a moving average operator of order 3, and ex. = Estimate of the standard error of the white-noise variables. 3.1.8 APID Algorithm The A l l Purpose Incident Detection algorithm (APID) is one of the two algorithms that were developed for use in the C O M P A S S traffic management system on Highway 401, in the Toronto metropolitan area. This algorithm is section based and is essentially a composite version of the California algorithms. It uses both occupancy and the speed in its calculations. The A P I D algorithm is composed o f the following major routines as described by Masters et al. (1991); • General incident detection routine (used in heavy traffic), • Light traffic incident detection routine, • Medium traffic incident detection routine, • Compression wave test routine, and 39 • Persistence test routine. The A P E ) algorithm uses OCCDF,OCCRDF, DOCCTD, DOCC and SPDTDF all used originally in California algorithms. The last one is defined using speed (SPD) as: SPDTDF = {SPD(i, t - 2) - SPD(i, t))/SPD(i, t - 2) (3.12) In A P I D , first based on an initial test of the downstream occupancy, one o f the three detection routines for light, medium or heavy traffic is selected. This gives more flexibility to the whole system, because each routine uses a different algorithm and a different set of threshold values. In heavy traffic, the general incident detection routine is used that tests the same parameters as California algorithm #4. It also checks for the persistence and compression wave, i f they are enabled. In medium traffic another routine is activated that tests OCCRDF and SPDTDF against their thresholds, and performs the persistence check. Masters et al. (1991) have not given the details of their routine for the light traffic condition. 3.1.9 McMaster Algorithms The McMaster algorithm (Gall and Hall , 1989) was developed by the traffic research group from the Department of Civi l Engineering at McMaster University. This method is based on the application of the catastrophe theory to the freeways' traffic states. It had been found earlier that speed is not always a continuous function of occupancy and volume when they are evolving smoothly with time. Often speed happens to "jump" down 40 when the traffic state goes into congestion zone. Navin (1986) suggested that this discontinuous phenomenon in traffic patterns could be explained by the catastrophe theory. Later, the traffic research group in McMaster University developed a catastrophe model for traffic data patterns. They used 30-seconds traffic data from the Queen Elizabeth Way in Ontario to quantitatively validate their model (Dillon and Hall , 1987). It was shown that data gathered upstream of incidents, while in transition to congested operation fit the catastrophe model much better than the conventional models. Figure 3.2 shows a conceptual view of the so-called catastrophe plane and data points for both congested and uncongested operation. A s it is shown in this figure, the uncongested operations are confined to a tightly defined line on the edge of the catastrophe plane. On the other hand, there is a considerable scatter in the congested operations. This is quite different from the conventional view that these operations happen on an inverted " U " shaped curve. The catastrophe model also allows the jumps to occur across the edge of the catastrophe plane while flow and occupancy change gradually. Based on their model and observations of the 30-second data on the upstream o f some six incidents, Persaud and Hall (1989) suggested that it is possible to develop a new A I D method. The key element in the McMaster algorithm is a template that is drawn in the occupancy flow plane. Figure 3.3-a shows this template which is constructed using historical data. There are three main lines in the template, which define the boundaries of the four major areas of the plane. The most important line is a curved one that divides the plane into congested and uncongested regions. This line corresponds to the imaginary edge o f the cusp catastrophe plane where the jumps may occur. In practice, historical data are used to define this line as the Lower bound of Uncongested Data ( L U D ) . The other two lines O c r i t and V c r i t , correspond to 41 the so called critical occupancy and critical volume respectively. The original McMaster algorithm was developed based on this template (Aultman-Hall el al, 1991) but, recently two further subdivisions (in areas 1 and 2) have also been added to this template (Hall et al, 1993). These further subdivisions are particularly used to enable the system to detect the incidents within a section that may experience recurrent congestion. The calibration o f this template has also been substantially changed since it was first suggested. The details of the calibration process for old and new templates are given by Persaud et al, (1990) and Hal l et al. (1993), respectively. Figure 3.2. Conceptualization of Traffic Operations on a Catastrophe Theory Surface (reproduced from Persaud and Hall, 1989) 42 a - Template for a normal station 40 60 80 100 OCCUPANCY (%) b - Template for a typical station affected by recurrent congestion Figure 3.3. Flow-Occupancy Template for McMaster Algorithm (Hall et al, 1993) The McMaster algorithm is a two-stage method. In the first stage of the McMaster algorithm the traffic state is checked using the template to see whether it is in the congested zone (areas 2, 3, or 4) or uncongested zone (area 1). I f the traffic stays in the congested zone for some consecutive 30-second intervals (usually 3), then the next stage that is the Cause of Congestion Logic ( C C L ) is activated. This delay, before the start of the next stage, is a mechanism for persistence check. The C C L logic tries to distinguish between congestion caused by an incident from one due to other causes. To do so, it also needs to check the downstream station for the traffic state using the same template. There are two other possible reasons that may cause congestion. One is the recurrent congestion near entrance ramps. For example, i f upstream is in the congested zone and downstream is in the area 4, the cause o f congestion is identified as a bottleneck. The other case happens when there is secondary congestion that represents the extension of primary congestion to the next station in a sequence. Table 3-2 presents the outcome of the C C L stage in the latest version of McMaster (Hall et al, 1993). Hall et al. (1993) also proposed usage of different templates for stations immediately upstream and downstream of an entrance ramp where recurrent congestion is often experienced (Figure 3.3-b). In this case, all the categories under area-4 o f Table 3-2 should also be changed to "congestion" accordingly. 44 Table 3-2 - Assessment Procedure in Stage#2 of McMaster Algorithm for Stations Where Recurrent Congestion May Occur (from Hall et al., 1993) Volume-occupancy Station being checked area * I-l l l l l l l l l l l l l l l l l i i i f i i i i i i i i i 4 1-1 no con. no con. con. con. con. con. Down- l l l l l l l l l no con. no con. con. incident incident incident stream l l l l l l l i : no con. no con. con. incident incident incident station l l l l l l l l l no con. no con. con. incident incident incident l l l l i l l l i no con. no con. con. con. con. con. 4 no con. no con. con. con. con. con. * see Figure 3.3-a no con. no congestion con. : congestion This method is unique both because of the model used to describe the traffic operations and because of its "two dimensional" view to classify the traffic state. The authors were among the first to address the need to achieve low false alarm rates that are operationally feasible. Hall et al., (1993) have reported good detection rates with extremely low false alarm rates. In a separate study, Forbes (1992) has proposed a modified McMaster algorithm. In this algorithm, he has used the same logic for the first stage but the second stage (CCL) has been changed to a new logic. His proposed C C L was based on the assumption that a congestion due to an incident causes a rapid change of speed as opposed to recurrent congestion where speed changes continuously. Therefore his proposed C C L included a number of tests on speed and its temporal difference. 45 3.1.10 Methods using Artificial Neural Networks Use of artificial neural networks is also one of the recent approaches toward development of automatic incident detection methods. Artificial neural networks, attempt to, imitate the learning abilities of the human brain. The concept o f neural networks was first introduced by Rosenblatt (1958). Rumelhart et al. (1986) presented the learning process and several applications of such networks. These networks have been successfully used for' many pattern classification problems ranging from engineering to financial applications. Chang (1992) from the Texas Transportation Institute developed a prototype for an A I D system that used neural networks. Two papers have also been published by (Ritchie et al., 1992, 1993) from the University o f California, who have used a similar approach to develop an A I D system. The artificial neural networks usually consist of several layers of the so-called neurons (or processing elements) that are connected to each other. Each neuron is a simple processing element that receives inputs from other neurons or outside the network and in turn produces some output. The massive interconnections among the neurons transmit the output of the neurons of one layer to those of the other layers. Each connection is also assigned a weight factor that defines how strong a message is sent to the other neuron. Contrary to conventional algorithms, there is no explicit memory for the instructions and data; everything is embeded in the connection weights. 46 The structure of neural networks, the number of layers, and the number of neurons in each layer varies based on the type of network and its application. Multi-Layer Feed-forward (MLF) networks are one of the most common types of such networks, in which the output of each neuron is only carried in one direction (forward). Figure 3.4 shows the input and output features of the M L F network used by researchers at the University of California. The three layers17 shown in this network are usually called input, hidden, and output layers respectively. The weights for each link, as well as thresholds associated with each node, are learned through a process called "training". During the training phase a large number of data patterns and expected outputs are presented to the network to find the best set of weights and thresholds which will later be used in the "recall" phase. Among various training procedures, "Backpropagation" is the one that is often favored for classification type problems where convergence time does not have to be limited or the network size is not very large. A total of 200 data sets of simulated incidents have been used in Backpropagation training of the AID system proposed by Ritchie et al. (1993). They have used another 200 data sets to test the performance of the method. 3.1.11 Methods using Fuzzy Logic Since the introduction of fuzzy set theory by Zadeh (1965), and particularly in the last decade, there has been some extensive research in using the concept and its mathematical formulation in various applications. The use of fuzzy logic has been very successful where decision-making 1 7 When counting the layers in a network, the input layer is not counted by some of the researchers. This is because the elements in this layer do not process the input signal and only pass it to the second layer, where the processing starts. 47 involves uncertainty by nature. It replaces "exact reasoning" with "approximate reasoning' in which the variables can be members of "some degree", and decisions can be true or false to "some degree". upstream occupancy at t upstream occupancy at t-1 upstream occupancy at t-2 upstream volume at t upstream volume at t-1 upstream volume at t-2 downstream occupancy at t downstream occupancy at t-1 downstream occupancy at t-2 downstream occupancy at t-3 downstream occupancy at t-4 downstream volume at t downstream volume at t-1 downstream volume at t-2 downstream volume at t-3 downstream volume at t-4 statel: incident free state2: incident Figure 3.4. Input and Output Features of the M L F used by Ritchie and Cheu, (1993) In 1994, researchers from Texas Transportation Institute (TTI) proposed using fuzzy logic to develop new A I D systems (Chang and Wang, 1994). They suggested that when comparing control variables, "crisp thresholds" could be replaced by "fuzzy membership functions". They targeted the California#8 method to modify its binary decisions with fuzzy decisions. They defined four membership functions for OCCDF, OCCRDF, DOCCTD, and DOCC variables used in California#8. These variables then could be " L O W " , " M E D I U M ' ' , and/or " H I G H " to "some degree" defined by membership functions. The rules used in the California#8 then would be transformed to fuzzy rules. A n example of a fuzzy rule is: If LastS is I N C and OCCRDF is H I G H then State is C i n e 48 Where Last _S and State are fuzzy variables, and I N C , C i n e refer to incident and continuing incident states. While methods using fuzzy logic overcome the problem of defining "crisp threshold", the problems o f defining the "membership functions" replaces the former. This often requires some subjective decision to be made by the designer. Neuro-fuzzy systems overcome this as well as cases where defining the rules also impose a problem. In Neuro-fuzzy systems, as the name implies, the learning capabilities o f neural networks are combined with the approximate reasoning capability of fuzzy logic. In some cases they are designed such that the membership functions and fuzzy rules are learned through a training process. (Hsiao et al., 1994) published a paper in which they suggested a neuro-fuzzy approach for an A I D system. They formulated problem as a classification type in which having an incident at any time could be "possible" or "impossible'. Their proposed method, Fuzzy Logic Incident Patrol System (FLIPS) identifies the optimal input-output membership functions based on training examples that are constructed from historical data. FLIPS is essentially a local or "station-based" A I D system in which the input consists of volume, speed and occupancy. The output of the system estimates the possibility of having an incident downstream of the sensor location where the traffic variables were collected. 49 3.1.12 Other "Indirect" Methods for Freeways The methods discussed so far are mainly the "better known" algorithms that are often referred to in the A I D literature. In this section, a number of other "indirect" A I D methods that were also cited in the literature are discussed. In 1980, researchers from M I T took a system identification approach to incident detection (Willski et al., 1980). They used a macroscopic dynamic model describing the evolution of the spatial-average traffic variables (velocities, volumes, and densities) to develop two detection algorithms based on Multiple Model ( M M ) and Generalized Likelihood Ratio ( G L R ) Techniques. Bottger (1979) developed a method in which the spatial forecast of traffic volumes was used as the control variable. This forecast was calculated through an analysis of the speed distribution and the traffic volume at an upstream detector station. The forecast was then compared against a threshold to decide whether or not the alarm should be triggered. Cremer (1981) also developed an incident detection method based on a simplified Kalman filter. The system used a so-called disturbance volume as the control variable against a threshold. The control variable was calculated by the use of an aggregate traffic flow model to explain the decrease of capacity during an incident. A cross-correlation technique method has been developed by Busch, (1986). In this method, it was attempted to estimate the speed of the compression waves by calculating the cross-50 correlation function of the upstream and downstream time series of traffic density. The estimated speed was then compared to a threshold to trigger the alarm. The alarm could also be triggered, i f for a certain time period, the algorithm failed to find a reliable estimate of speed. Busch and Fellendorf (1990) also developed a, so-called, general scheme for incident detection. This method was actually a combination of a number of already developed methods. After they evaluated a number of existing algorithms, (including the three previous methods, California algorithms and exponential smoothing) they used two section algorithms along with a local algorithm to build their general scheme. The previous two methods (Kalman filter and cross-correlation techniques) were used as section algorithms while an exponential smoothing technique was used as the local algorithm. Kuhne (1984, 1989) used a continuum model for freeway traffic flow in which equilibrium speed of the static-density relationship was relaxed. He then used this model to develop an A H ) method. In his method, the anticipated time development speed downstream was calculated from the development of speed, upstream. The downstream values then were compared to the actual measurements downstream for an indication of an incident. As a result of a joint project by Australian Road Research Board ( A R R B ) and VicRoads which was initiated in 1988, the A I D method ARRB/VicRoads was developed (Snell et al, 1992), (Sin, 1992). This method employed three sets of conditions to trigger an alarm. These comparisons were based on: 51 • Upstream and downstream traffic parameters (occupancy, volume and speed); • Adjacent lane traffic parameters; and • Temporal difference of traffic parameters. Another simple comparative method was developed by Chassiacos from the University of Minnesota as his Ph.D. thesis. This method called DELOS (Stephandes et al, 1992), and (Chassiacos and Stephanedes, 1993a) was based on the application of two simple, low pass filters applied to the spatial difference of the occupancies from upstream and downstream. The first filter used a 3-minute moving average to remove the random fluctuations. If the result from this filter was high enough to indicate a congestion, then the second filter that was a 5-minute moving average would be used to check the occupancy spatial difference prior to the three minute duration. This was to distinguish between recurrent congestion and congestion due to an incident. Two other AID methods were also developed at the University of Minnesota based on the information available through a video based, loop emulator called Autoscope18. These methods were called Speed Profile Incident Evaluation System (SPIES) and Autoscope Incident Detection Algorithm (AIDA) (Michalopoulos et al., 1993a, 1993b). SPIES used a pair of speed traps and compared volume-smoothed values of upstream and downstream speed for a significant difference. AIDA system, as claimed by the authors, combined the 1 8 Please refer to the section 3.1.13 for video based sensors that emulate loop detectors 52 strengths of McMaster and SPIES, as well as taking into account the temporal changes of traffic variables. A recent A I D method for homogenous freeways was developed at the University of California at Berkeley by L i n (1995) as his Ph.D. thesis. This method used the cumulative difference of upstream and downstream occupancies as its only control variable. This was then compared with a number of linear bounds that would progress in time. These bounds act as thresholds that would change with time. B y analyzing the condition under incident and non-incident situations, he showed that a finite number of comparisons were necessary to make the decisions. 3.1.13 Image Processing Techniques and Direct Methods As described earlier in section 3.1, an alternative approach to the "indirect methods" that detect the incidents' effects, rather than the incidents themselves, are provided by some methods incorporating image processing techniques. The video cameras installed along the freeways can "see" the incidents and hence transmit much better information. There has been a few attempts to use the scene image and interpret it directly to detect the incidents. Europeans have been in the forefront of research and development of such systems. I N V A L D is the name of a project that was part of the large D R I V E European program to improve road safety and transport efficiency (Keen and Hoose, 1990). Two different 'computer vision tools" were developed as part of the I N V A L D project. These two tools are: • T I T A N (Blosseville et al., 1989, 1993), and 53 • I M P A C T S (Hoose, 1989, 1991), and (Hoose etal, 1992). T I T A N was designed to detect and track individual vehicles that are moving on freeways. The information provided by the trajectory of the vehicles is analyzed to detect patterns that could be valid indications of a traffic incident. I M P A C T S uses a different approach and provides a qualitative description of traffic similar to what human operators could do. Each of these two systems have strengths and weaknesses, however, they can be used together to complement each other. Applications of an integrated system and a full scale field test called I N V A I D - I I is described by (Guillen et al., 1992), and (Guillen et al., 1993). As reported recently, Chang et al. (1993), a Japanese system has also been developed that detects incidents directly 1 9. According to this report in the Japanese A I D system, the individual vehicles are identified by subtracting the digital image from that of the background scene. The consecutive process of these subtractions would show the motion o f the vehicles, which i f stopped for a time threshold of two seconds, would be attributed to an incident. It should be noted that there are a number of other researches that use image-processing techniques for freeway surveillance systems but only to provide traffic variables 2 0. Therefore, they actually emulate loop detectors by placing virtual sensors on the road. The followings are among such systems: 1 9 The authurs of this report (Chang et al, 1993) have put the specifics of the reference in their bibliography. The author of this thesis was unable to find the actual paper that has been written by Tsuge et al. 2 0 There are some exceptional cases where a system has both capabilities such as in ARTEMIS (Automatic Road Traffic Event Monitoring Information System) (Blissett et al., 1993) 54 • Belgian system developed by Theuwissen et al. (1980) from the Catholic University of Leuven. A commercial version of it called Camera and Computer-Aided Traffic Sensor ( C C A T S ) has been developed (Versavel etal., 1989). • Traffic Research using Image Processing (TRIP), a U K project by a joint team from University of Manchester Institute of Science and Technology and University of Sheffield (Waterfall and Dickinson, 1984). A n upgraded model (Dickinson and Wan, 1989) has also been developed. • Traffic analysis Using L o w cost Image Processing (TULIP) system is the name of another British method developed at the University o f Newcastle-upon-Tyne (Rourke and Bel l , 1988). • A Japanese system called Image Data Scanner and Controller (IDSC) developed at the University of Tokyo (Takaba et al, 1984). • A video based vehicle presence detector developed by the Australian Road Research Board (Dods, 1984). • The commercially available Autoscope system designed at the University of Minnesota (Michalopoulos, 1991). 3.1.14 Other Methods There are still a number of other A I D research works that are o f less relevance to the present study. Therefore, they wil l only be briefly mentioned in this section. 55 Most of the A I D algorithms have been designed to detect the incidents on the freeways. However, a few researchers have also tried to develop methods for arterial streets. Vehicles normally move in platoons while travelling in arterial streets because their flow is interrupted. This poses a bigger challenge to the A I D method. Researchers from four universities have addressed this problem. They include: • Han and M a y (1990a, 1990b) from University of California at Berkeley, • Ivan etal. (1993) from Northwestern University, • Chen and Chang (1993a, 1993b) from the University of Maryland, and • Bel l and Thancanamootoo (1988) from the University o f Newcastle upon Tyne, later followed by Bretherton and Bowen (1991) from the Transport and Road Research Laboratory ( T R R L ) in the M O N I C A project The traffic management authorities are mainly interested in detection of the incidents under medium to heavy traffic conditions because they try to avoid the congestion caused by such incidents. However, for safety reasons, it has also been tried to develop methods that target incidents under light traffic conditions. A method by Fambro and Ritch (1980) from the Texas Transportation Institute (TTI), and one by Yagoda and Buchanan (1991) developed for the Lincoln/Holland tunnels are among these methods. The P A T R E G method discussed in section 3.1.6 has also shown its best performance under lighter traffic conditions. 56 There have also been proposals to use travel information from a number of designated vehicles to find indications of congestion and incidents. This approach needs a technology called "Automatic Vehicle Identification" (AVI) or "Vehicle to Roadside Communication" ( V R C ) . Two such methods have been proposed in papers by Hallenbeck et al (1992), and also by Parkany and Bernstein (1993). 3.2 AID Practices In this section, information about a number of existing A I D systems and related surveillance facilities in the United States and that of the Toronto area will be presented. Most of the information is the result of some site visits by Balke (1993) for a research project for the Texas Transportation Institute. Additional information has also been obtained by the author from several departments of transportation in the United States. 3.2.1 Los Angeles, California The freeway surveillance and control system in Los Angeles area covers more than 264 miles of freeways and is staffed and operates 24 hour a day. The traffic data obtained are the occupancy and volume updated at every 30 seconds interval. Distances between the detectors may range from half a mile in the core area to one mile or more in the outlying areas. Two versions o f California algorithms are being used for the whole area but the threshold values are zone specific. These algorithms are selected based on the traffic conditions. In heavy traffic (which is essentially during daylight hours), California algorithm #8 which employs a test for the compression wave is used. In lighter traffic condition, the system wil l be changed 57 to the California algorithm #5. Both of these algorithms are being used in the original form, and no new algorithm has been added. According to Balke (1993), this is because of the lack of operational experience with other algorithms. He has also stated that the operators mainly rely on the reports by the C H P (California Highway Patrol) officers and not on the incidents detected by the computer. Also, in another project, Fait (1994) has compared various means of incident detection in the Los Angeles area and has found that during the 2 months of his study only 186 of the 1698 incidents have been first detected by computer. 3.2.2 Orlando, Florida The Traffic Management Center ( T M C ) in Orlando is operated by Florida Department o f Transportation (FDOT) district 5. T M C provides surveillance over 11 miles of 1-4 freeway. A total of 387 detectors are placed in each lane of the freeway at a spacing of about 1/2 mile. A modified version of California algorithm is used for detecting the incidents. The C C T V cameras are used for verification. A new algorithm is going to be implemented that wil l compare the existing speed data with that of the historical database under specific weather condition (i.e., wet, or dry). I f it shows a substantial difference such as 10-15 miles/hour, an incident wil l be declared. T M C also has research contract with Professor Al-Deek from University of Central Florida who is working on the new algorithm. A s a result of this project, one year's worth of 30 second data has been gathered. 58 3.2.3 Chicago, Illinois Chicago metropolitan area has been one of the pioneers in traffic surveillance and control in the United States for about three decades. In the past several algorithms including the California algorithms and Bayesian method have been tried by the Traffic System Center (TSC) of Illinois Department of Transportation (IDOT) (Levin and Krause, 1979). According to Chassiakos and Stephandes (1993), the McMaster algorithm has also been evaluated in an off-line test for potential implementation. After a difficult calibration period, good detection rates but unsatisfactory false alarm rates were reported in this test. Currently the T S C uses a very simple comparative A I D method. This method uses the lane occupancy of adjacent stations in the last five minutes and compares them with some ten thresholds. A n incident is declared when the last five of the elements of upstream occupancies time series are greater than their thresholds and similarly the downstream occupancy values are smaller than their thresholds. This system inherently has a detection time of over five minutes, but it has been preferred to higher false alarm rates. Consequently, most of the incidents are detected by other means before the A I D system gives an alarm. On the other hand, Balke (1993) states that in the IDOT philosophy, A I D system is used as a secondary means of incident detection. It has been designed to help the operators in spotting the possible incident locations that have not been detected yet. It is also used as a training tool for new operators. Therefore, T S C relies on other means of detection and the experience of its operators for this purpose. 5 9 3.2.4 Minneapolis, Minnesota Management and control of traffic on five interstate and five state freeways in the Minneapolis/St. Paul area is provided by the Traffic Management Center ( T M C ) . T M C surveillance covers about 150 miles of these freeways. A t each station, loop detectors are used to measure volume, occupancy and speed in each lane (Balke, 1993) The measured values are averaged across all the lanes to obtain station averages. The data is compiled every 30 second and sent to the T M C . A modified California type algorithm had been used in the past, when T M C became operational, but because o f high false alarm rates, its use was discontinued. Operating personnel had stated that only one set of threshold values had been used when the system was operational. Therefore, during the visit by Balke (1993), no operational A I D system existed and detection of incidents was done by other means. Researchers from the University of Minnesota have also used the facilities of T M C for field tests and evaluation purposes as a result of which Autoscope system (Michalopoulos, 1991) and D E L O S algorithm (Stephandes and Chassiakos, 1993a) have been developed. 3.2.5 Long Island, New York Since 1987, New Y o r k State Department of Transportation ( N Y D O T ) has implemented a project called I N F O R M (INformation F O R Motorists) on a corridor system in Long Island. A s part of this project, an extensive surveillance system based on loop detectors has also been installed (Balke, 1993). A t first, one of the modified versions of California algorithm was used for detection of incidents. However, because o f the poor performance, particularly high false 60 alarms, the use of this system was discontinued. According to Balke, (1993), improper calibration could have been the cause of the problem. This is because, rather than using specific threshold values for each zone, only one set of thresholds might have been used for the entire system. Balke (1993) stated that the incident detection mostly depended on the experience of operators who monitored the traffic condition on a large color-coded wall map. This map showed the measured speed (for each segment of the road) with different colors, in which red meant a speed of less than 30 mph that may indicate either an incident or a recurrent congestion. Operators had to use their experience to filter out the recurrent congestion. Generally, the operators would wait until a couple of "atypical" but consecutive red lights show up, then start investigating the cause. 3.2.6 Toronto, Ontario In early 1991, C O M P A S S , a Freeway Traffic Management System ( F T M S ) started its operation on the Highway 401 in the greater Toronto area. It originally covered over 16 miles of Highway 401, with a minimum of 12 lanes that carried more than 300,000 vehicles per day. Installed detectors included both single and double loop detectors that measure speed, volume, and occupancy. At every station, occupancy and volume data were aggregated across all the lanes and then transmitted to the central computer. One of the goals of C O M P A S S was to provide a fast A I D , such that most of the lane blocking incidents can be detected within the first three minutes of the occurrence (Korpal, 1992). To do this the developed software was 61 designed to take advantage of five different algorithms at once. At first the APED (Masters et al, 1991) and D E S (Cook and Cleveland, 1974) methods were used in this system. Later switching to McMaster algorithm (Hall et al, 1993) as the primary method for the main lanes was considered. Operational use of McMaster algorithm has been started since late 1992 and the observed performance in the initial stage has been reported as satisfactory (Balke, 1993). 3.2.7Northern Virginia Virginia Department of Highways and Transportation operates a Traffic Management System ( T M S ) that provides surveillance and control over 32 miles of 1-66, 1-395, and Woodraw Wilson Bridge (Dunn and Reiss, 1991). The general idea behind this incident detection system is to detect any kind of congestion rather than those caused only by incidents. When the congestion is detected, operator identifies the cause of congestion by visual inspection o f the scene using C C T V cameras. The method used in Northern Virginia is a California type algorithm that has been developed by Sperry Systems Management. The system has been modified so in case of a detector malfunction, data from historical database as a substitute for the real-time data. The time difference of downstream occupancy (DOCCTD) used in the California algorithms is not used in this system. Balke (1993) states that the operators were relatively satisfied with the performance of the system and its calibration. They also felt that the balance of the performance measures, D R , A D T , and F A R was satisfactory. However, he also has noticed that during his visit most o f the incidents had been detected by the operators before the system could detect them. He has 62 also observed that the operators preferred to monitor the C C T V rather than the incident display screen. 3.2.8 Seattle, Washington Traffic Systems Management Center ( T S M C ) in greater Seattle provides surveillance and control on 76 miles of 1-5,1-90, 1-405, and SR-520 freeways (Dunn and Reiss, 1991). Loop detectors' data is accumulated and one minute moving average o f the volume and occupancy are then calculated. The calculated data is used on a color graphic display that uses color codes to show the level of congestion. Operators monitor this display for signs o f incident. In the past, the occupancy data was also used in a California type algorithm for incident detection. However, because o f unsatisfactory performance its use has been discontinued. Drivers who had cellular phones often would call to report an incident within 2 or 3 minutes after its occurrence, while A I D system was less reliable and could take longer. On the other hand, the algorithm had never been recalibrated since its original calibration. According to Balke (1993), it was felt that, to properly calibrate the algorithm for each freeway zone, some incident data in that zone is required. Although no A I D system is currently used in T S M C , it is believed that eventually an A I D method will be used as an important extra tool in their incident management program. 63 3.3 General Observations and Comments After reviewing the materials reported in the A I D literature, one observes the following points. • A n enormous effort has been devoted to the development of the A I D systems in the last three decades. • Despite the extensive research effort, only a few of these methods have been put in practice. • Some of the traffic management centers have given up using their A I D systems, while some others continue using similar ones 2 1. • Only in a few cases, have A I D algorithms been extensively compared with one another. • The standard performance measures reported in these cases are somewhat contradictory. To clarify the probable causes of this contradiction in results, first, one should notice that the performance measures are often incomparable and any judgment based on them could be misleading. This is because these measures are not obtained under similar situations. For example, the capability of most of the A I D algorithms to detect an incident is strongly dependent on the following factors: 2 1 For example in Seattle, Washington the traffic authorities have abandoned using their AID system that used California algorithm while In Los Angeles, California traffic authorities are using two versions of the same algorithm. 64 • Severity and duration of the incident; • Operating conditions at which the incident has occurred; • Detector spacing and the location of the incident with respect to the detectors; and • Highway geometrical factors such as: grade, lane drop, ramps, etc. Moreover, the definition of incident varies from one report to the other. For example, in some cases, a stopped car on the shoulder is not considered an incident. Also the calculation of average detection time is usually very subjective because the exact time o f the incident is not known. On the other hand, even when a research group has evaluated its method with some other methods using the same set of data, one may find large differences between the reported measures. There have been some suggestions that this might be due to different driving habits that change from place to place. Calibration could also be a major contributing factor in this regard. It is reasonable to assume that in most cases a research group is expert in calibration of its own method while it may not have the same expertise on the others' methods. A l l o f these factors have contributed to a common belief that the results of the A I D systems are not "transferable". Different reactions of traffic management centers to A I D systems, even when they are using the same system, also requires consideration. For example, all the six sites in the United States 65 visited by Balke (1993) had been using some type of California methods; three of these sites have discontinued their use. This can be attributed to two major reasons. • The author believes that the proper calibration of an A I D method is as important as the selection of the method (if not more important). On the other hand, the calibration process for many of the existing methods requires considerable time and effort, and is location specific. A considerable amount of incident data are often needed which has not necessarily been available for all sections o f a highway. This may lead to poor performance when the necessary effort has not been put into the calibration process. • It can also be assumed that the general expectation from an A I D system compared to other means of detection differs from place to place. In Los Angeles, about 11% of the incidents are first detected by the A I D system. While this may seem to be a very poor performance in other places, A I D is still used by the operators in Los Angeles as an extra means of detection. In other words, the actual performance of the A I D system on one hand, and the expected level of performance by the Traffic Management Authorities on the other, defines the acceptance or rejection of the system. Performance is traditionally measured using three quantities (i.e., D R , F A R and A D T ) . Among these measures, false alarm rate appears to be the critical one. This is because it defines how often the operators would have to react to the false alarms. I f this occurs too frequently, the operators tend to ignore the alarms among which could be true alarms due to an incident. Therefore a maximum acceptable level of false alarm rate has to be 66 set, beyond which, the system would need a re-calibration. A n example may present some idea about the necessary order of magnitudes for F A R . A n A I D system with an updating period of 30 seconds that employs 50 detector stations requires 100 decisions to be made every minute. Therefore, a seemingly low false alarm rate of 1% for such a system implies that operators would have to react to an average of one false alarm every minute. The existence and ease of use of a verification mechanism for the alarms also plays an important role. Existence of a video surveillance system with full coverage of the site would greatly decrease the time required for the verification of the alarms. A n integration of the A I D system with video surveillance is easy to implement. Right after an alarm the image from the closest camera(s) to the scene of the suspected incident would appear on the monitor. This would allow the operator to quickly respond to the alarm by either rejecting it as a false alarm, or initiating the appropriate and preplanned response. Successful implementation of such an integrated detection and verification system would also increase the level of tolerance of the operators to the false alarms. This in turn would positively affect the performance of the A I D system because a higher acceptable level of F A R leads to a higher D R and a lower A D T . A D T could be considered as the second important measure of performance. The contribution of each means of detection depends on how quickly the incident can be detected. Clearly, i f it takes too long for the A I D method to detect an incident and therefore it is detected by other means, its detection rate would be irrelevant. As an example, the operators in Seattle, who discontinued their use of A I D system would receive cellular calls starting as early as two to 67 three minutes after the incident has occurred . It takes some time to process such calls and find the location of the suspected incident or congestion. In many cases, the callers are not sure of the source of congestion and/or cannot state their exact location on the freeway. However, this shows that considering the increasingly widespread use of cellular phones, there is a certain limit for detection time beyond which the detection of the incident by an A I D system does not count. The author believes that it would be safe to assume that after the first five minutes from the onset of the incident, it has been detected by some other means. Therefore, in calculation of D R and A D T , one most probably does not need to consider beyond the first five minutes after the onset of the incident for all practical purposes. In addition, considering the above discussions, the A D T for the incidents detected within the first five minutes should preferably be under two minutes. This means, that in most of the cases, by the time the traffic management center starts receiving cellular calls, the operator has already verified the source of the congestion. Based on the above discussions, one can see that in order to have a practical scenario in which the A I D system is effectively used by the operator and is a major contributor to the overall detection system, the following steps are to be taken. • Setting an acceptable level o f false alarm rate depending on the number of stations involved, staffing level and existence of a video surveillance system; Personal Communications with Mr. Bill Legg, Washington State Department of Transportation, Seattle, Washington, August 1994. 68 • Calibrating the A I D system such that the expected F A R is about the maximum level set earlier while the expected A D T is as low as possible 2 3; and • Evaluating the D R for the first few minutes to estimate the portion of the incidents that could be first detected by the A I D system. Clearly this figure needs to lie within the acceptable range for the traffic management authorities to justify its use. The above discussion shows that many of the figures that are presented for the performance measures in the literature have no practical use. Only a slim minority of the methods is able to produce good enough detection within the first minutes with a low enough F A R . The direct A I D systems potentially can detect the incidents in a very short time. However, direct A I D systems are more expensive to implement and operate because in order to have reliable coverage, the camera intervals should be limited to 300~400 meters at best2 4. Moreover, their performance is sensitive to the lighting and weather conditions. Therefore, direct ADD systems can be used for critical locations where the frequency of incidents are higher, or the consequences are more severe, to justify the additional investment. Putting aside the direct A I D systems, one can see that other methods suffer from a single drawback that causes a considerable time delay before detection. Virtually no A I D method 2 3 In most AID methods, there is more than one threshold or parameter to be set. In other words there is more than one degree of freedom involved in calibration and the resulting performance This means that at least theoretically it is possible to maintain a FAR while ADT can vary within a limited range. 2 4 At first, it may seem that the same type of cameras needs to be installed to provide enough coverage for verification purposes. However, two points in this regard are important to notice. One is that the spacing between adjacent cameras used only for verification purpose, could be 2-5 times of what is needed to directly detect the incidents. Second is that the technical requirements to optimize the function of cameras for detection 69 would activate the alarm unless the congestion caused by the incident has been sensed at the closest upstream sensory station. This is while in many cases, a persistence check also adds to this delay because the persistence check is often activated after the congestion has been sensed in the upstream sensor location. The actual time delay, as discussed in Chapter 7, depends on many factors but on average is two or more minutes. Considering the previous discussions about the importance of detecting incidents within the first 2-3 minutes, it is easy to see that existing A I D methods are very limited in achieving an effective operational performance. This study has tried to improve the expected operational performance by targeting this very limitation. In Chapter 7 there are more discussions about this limitation of A I D systems and how the method presented here overcomes it. and verification are not necessarily the same: Particularly considering that for verification the cameras often need pan, tilt, and zoom capabilities, while for direct detection, a stationary view of the scene is preferred. 70 C H A P T E R 4 M E T H O D O L O G Y O F T H E S T U D Y The outline and methodology of this study will be presented in this chapter. The details o f each step wil l be discussed in the chapters that follow. As was shown in the literature review, it is not possible to compare the performances of various ADD methods directly. This is because the reported performance measures are not reasonably consistent with each other. This lack o f transferability is mainly because geometric features, incident severity, and many other parameters that affect the performance, have not been identical in these cases. Therefore, to have a reasonable assessment of the ADD method developed in this thesis and for other ADD methods, it is necessary to compare them based on identical data sets. The incident severity, its location, and the geometry o f the highway affect the performance o f the method. It is possible to observe a good performance from a method under certain conditions and yet have another method outperform the first under different circumstances. Therefore, it is necessary to select the data sets to cover a wide range o f operational and geometric conditions so that the results are a better representative of the performance of each method. This would allow an assessment of the robustness of the ADD systems, and whether they can maintain their performance when used under varying conditions. 71 During the course of this study, real data from the sensors were not available and, therefore, it was decided to use simulated data. Care was taken in every step from selection of the simulation program to assigning the model parameters so that the simulation model was as close as possible to the real traffic operation of a selected study site. Furthermore, the number of simulated data were selected much higher than what is usually reported in the A I D literature to ensure that a high confidence can be attributed to the results. Simulated data, by nature, is a representation of the real data. N o matter how good the modeling, there is never a guarantee that the representation is an exact replica of the system. Despite the validity of the above statement, it is very important to notice that there is nothing in the simulation model that could be assumed as biased towards or against any of the A I D methods. Therefore, the generated data should pose the same challenge to all o f the methods. Consequently, although it is possible for the performance measures to be different from what could be obtained from real data, there is no reason why the order that A I D methods perform should be any different25. B y using simulated data, there are some added advantages, particularly in the investigative stages of the study. One such advantage is that the number of incidents can be as high as desired. It is also possible to put the incident anywhere that is desired and under any 2 5 This particularly can be stated most confidently when there is a sigriificant difference between the results of two competing methods. As it will be shown in section 8.1, such a significant difference is observed in the results (i.e., DR in the first 2-3 minutes after the occurrence of incident or FAR) of the method proposed here and two other existing methods. 72 circumstances. It also provides the flexibility in designing the data sets to keep a number of factors constant while only changing one. This provides the opportunity to better analyze the results and identify contributing factors in the analysis. A few of the existing methods had to be selected whose performance could be compared with that of the U B C - A I D method developed in this study. However, due to the lack of consistency in reported performances, it was not possible to identify the best existing algorithms. Therefore, to select methods for comparison purposes, the following two preferences were considered: • Methods that have been operationally used and evaluated; and • Methods whose exact or close reconstruction based on the published information was possible. Among the many existing methods, only a few have been operationally used. Various versions of the California methods are among the most widely used ADD methods. Traditionally, they have often been selected for comparison purposes in literature. The original developers evaluated California#7 and California#8 as the "best simple" and "most effective in stop-and-go traffic" algorithms respectively (Tignor and Payne, 1977). These two versions of the California methods were selected in early trials of the U B C - A I D system. The McMaster Method, which has been favored and used in recent years by the Ontario Ministry of Transportation on the Queen Elizabeth Way and Highway 401, was also selected 73 for comparison purposes. This method, with its unique approach, has shown a good detection rate with a very low false alarm rate. The method could be reconstructed but its calibration is somewhat difficult. Neural network approach developed by Ritchie and Cheu (1993) and the neuro-fuzzy approach by Hsiao et al, (1994) were two recent methods that were also considered because of their merits. However, since reconstruction of both methods required knowledge of some parameters (e.g. momentum and learning rate for the neural network) that were not available, they were not used in this study 2 6. However, their approaches wil l be discussed later. A basic form of the U B C ADD method was developed and its performance as well as performances of the selected algorithms (i.e., California #7, #8, and McMaster 2 7 ) were tested. The results of the first series of tests showed that California #7 was under performing the California#8 consistently. This meant that for all ranges of conditions, California#8 performed better. Therefore, later, the rest of the tests only continued with the other two methods. The results o f the first series of tests showed the feasibility o f idea behind the U B C ADD system as well as showing some difficulties. The final form of the U B C ADD system then was developed and tested with new and expanded series of data sets. The data sets were used to 2 6 However, these approaches as well as other indirect AID methods are not expected to outperform UBC AID methods because of the limitations that will be discussed in Chapter 7. 2 7 It should also be mentioned that initially Double Exponential Smoothing (DES) method (Cook and Cleveland 1974) was also programmed and tested but very early results showed that its performance are by far worse than the others. Therefore, even the tests with the first set of data series for this method were abandoned. 74 compare the performance of the proposed system with the performance of the California#8 and McMaster methods. A detailed analysis of the results also provided a comprehensive view of the robustness of the proposed system as the conditions change. 75 CHAPTER 5 SIMULATION OF TRAFFIC FLOW UNDER INCIDENT AND INCIDENT-FREE CONDITIONS To assess the performance of the U B C A I D method and compare it with the performance of California#8 and McMaster, a simulation of traffic flow under incident and incident-free conditions was necessary. In this chapter first the simulation program selected for this purpose will be discussed. Then the steps taken to build a simulation model based on the selected program will be explained. 5.1 Simulation Program Traffic simulation programs can be categorized based on their level of detail into either macroscopic or microscopic. Macroscopic simulation programs use traffic flow theory to model relations among flow parameters such as density, speed, etc. Microscopic simulation programs generate a higher degree of detail by modeling the behavior o f individual vehicles. For the purposes of this study, it was necessary to use microscopic simulation, because it was required to generate detector signals, as they would be collected in the real world. T R A F family of simulation programs contains the most comprehensive and powerful simulation packages thus far developed for the United States Federal Highway Administration ( F H W A ) . The T R A F series include both macroscopic and microscopic simulation components 76 for a range of applications including freeways, urban networks, and rural roads. FRESEVI, the freeway microscopic simulation component was selected for this study. It is the enhanced version of its predecessor, ENTRAS simulation program. In F R E S I M , individual vehicles are assigned characteristics such as position, speed, acceleration, etc. These characteristics change in response to other vehicles and geometric conditions as the vehicles move along the freeway. The freeway geometric conditions that can be directly represented in F R E S I M , which are more important in this study, include: • One to five through-lane freeway mainlines with one to three lane ramps, • Variations in grade, radius of curvature, and superelevation, • Lane additions and lane drops anywhere on the freeway, • Freeway blockage or capacity reducing incidents (rubbernecks), and • Auxiliary lanes, which are used by traffic to begin or end the lane changing process, and to enter or exit the freeway. However, a shortcoming in F R E S I M is that it is not possible to directly model the effect of reduced lane width. There are also a number of operational features that are incorporated in F R E S I M (Federal Highway Administration, 1994). Those features that were important in this study include: • Comprehensive lane-changing model, 77 • Comprehensive representation of the freeway surveillance system, • Representation of six different vehicle types, including two types of passenger cars and four truck types, each type having its own performance capabilities such as acceleration, etc., • Heavy vehicle movement, which may be biased or restricted to certain lanes, • Differences in driver habits, which are modeled by defining ten different driver types ranging from timid to aggressive drivers, and • Vehicle reaction to upcoming geometric changes. The user may specify warning signs to influence the lane changing behavior o f the vehicles approaching a lane drop, incident, or off-ramp. Vehicle type, driver type, turning movements, and other attributes are assigned to each entity, as they are about to enter the freeway system. F R E S I M uses pre-defined distributions and a random number generator to assign these attributes. To replicate the inherent randomness of the real world, a number of other events such as lane changing, gap acceptance, etc. are also simulated, based on their probability of occurrence. F R E S I M uses the "Car following rules" to determine a vehicle's acceleration/deceleration as a function of the distance and speed of the leading vehicle and its driver type. After each time increment, new states wil l be calculated for every vehicle in the system. At the beginning of the simulation, the freeway system is empty. During a so-called initialization period, the 78 freeways segments are filled with vehicles and simulation continues until the interaction of the vehicles with each other and with the system geometry reaches an equilibrium point. Obviously, the random nature of the system does not allow the system to reach an absolute steady flow. However, after a few minutes 2 8, the input and the output of the system would be close enough so that one can assume that equilibrium has been attained. In this study, it was necessary to generate traffic parameters such as occupancy, volume, and speed with double loop detectors as i f they were generated by real sensors. The surveillance systems that can be simulated in F R E S I M include single loops, double loops, and Doppler radar. They can provide the necessary data averaged over any required time period. Considering the capabilities of F R E S I M , it seemed well suited for this study. However, the output files generated by F R E S I M are often very long and in a report-like format. A small program was written to extract the required traffic parameters from the output files generated by F R E S I M . 5.2 Simulation Model for This Study To build the simulation model for this study using F R E S I M , the following steps were taken: • Selection of the study site, • Obtaining the required parameters, and 2 8 This refers to the simulated time. 79 • Selection of the detector locations. The following sections discuss each step of building the simulation model. 5.2.1 Study Site The main objective of the simulation part of the study was to generate a large number of incident and incident-free data sets. This was to be done so that a wide range of conditions, including operational and geometric variables could be provided for this study. Therefore, the first step was to select a study site, such that it included as many geometric variations, on-ramps, and off-ramps as well as bottlenecks in a relatively short length (3-4 km). A site, about 2-km east of the Grandview on-ramp in the eastbound lanes of the Trans-Canada Highway (TCH) in Burnaby, British Columbia, was suggested by the Ministry o f Transportation and Highways. The safety branch of the Ministry at the time was considering this site for installing detector stations because of its high frequency o f incidents. In this study a larger portion of the T C H was selected that covered, as a part, the length that was originally suggested. The total length of the selected site is 3,640 m. It starts from 290 meters west of the Boundary off-ramp (just after the Lougheed Highway underpass) and extends to 1290 meters east o f Willingdon Street on-ramp as shown in Figure 5.1. This section provides a higher variation in grade, curvature, and superelevation. It also includes a total of five ramps of which a total length of 1340 meters is considered as part o f the study 80 site. They include Boundary off-ramp, Grandview on-ramp, Willingdon off-ramps (South, North), and Willingdon on-ramp. Figure 5.1. Selected Study Site along Trans-Canada Highway 5.2.2 Required Parameters To build the input data sets for the simulation model, two main groups o f data had to be found or assumed. 81 • The parameters that represent the geometry and traffic operations of the study site which should remain constant during the simulation (e.g., geometrical parameters of the location); and • The parameters that wil l change from case to case and represent the variations that are the subject of the study (e.g., location, severity of the incidents). In this and the subsequent section, the first group o f data is discussed. The second group wil l be discussed when data sets are being explained. F R E S I M uses a link-node arrangement to describe the geometric and operational parameters of the freeway. Links represent one-directional segments of the roadway that have reasonably constant geometric features. Nodes represent locations in the roadway where geometrical features change significantly (e.g., ramp merges, changes in curvature). In order to build the link-node diagram, five points along the T C H that represent the tips of the on- and off-ramps were identified. However, to identify other points the following parameters were considered as well; • Grade, • Superelevation, and • Curvature. 82 These parameters change continuously along the highway. To select node locations, these values had to be obtained as a function of the distance traveled from a base point along the highway. The Ministry's Photolog 2 9 system was used for this purpose, and in every frame (20-meter s apart) each of the above parameters was recorded. The road scenes from the Photolog system were also used to find exit signs, and starting or ending points of the lanes for the ramps, etc. This highly detailed data, along with survey maps, was then used to identify major points of change for curvature, grades, or superelevation to be used as nodes. However, the Photolog system was not available for the ramps. Therefore, only the survey maps were used to estimate the grade and the radius of curvature. Consequently, a total of 19 nodes were selected along the freeway, and some other 14 nodes were selected to represent changes on the ramp links. The Link-node representation o f the study site and its geometry are shown in Figure 5.2. The estimated geometric parameters used in the simulation model are presented in Table 5-1. Although the program is designed to work with both systems of units, in the available version, the metric system had not been enabled by FRESEVl providers. Therefore, in this thesis a mixture of both units can be seen. Photolog system consists of a number of laser videodiscs that contain pictorial information and engineering details of the highway system. 8 3 I A-Link-Mode Diagram | CSOeC) Boundary Off-ramp Grandwiew on-ramp Trans Canada Highway 3640 meters of Eastbound 290 m wrest of Boundary off-ramp to 1290 m east of WUHngdon on-ramp B » t t * J Willingdon off-ramp (S) <£H) Willingdon off-ramp (N) Willingdon on-ramp Det#4 Detector Stations Node Number Incident Locations |a?)w] Note: Link lengths, incidents' and detectors' locations are to scale. Curvatures are not shown Angles are not correct - D e i ? * Figure 5.2. L ink -Node Diagram and Highway Geometry for the Study Site 84 Table 5-1 - Geometric Parameters Used in the Simulation Model Link Odometer starting node 1 .ength (m)w Grade (%) Superelevation (%) Radius of Curvature (ft) I "> I0Q0 inn +1 -1 1190 190 +1 +1 1700 1 4 1180 70 +1 +1 1700 4 5 1450 100 +1 0 1700 5 fi 1550 110 +1 -1 6 7 1880 110 -1 -4 _ 7 X 2010 110 -1 +2 1100 8 9 2140 180 0 +1 1100 9 10 2120 450 -2 -1 10 11 2770 170 0 -1 _ 11 12 2940 100 0 -1 12 n 1240 200 0 0 _ n 14 1440 220 0 -1 _ 14 IS 1660 80 0 -5 _ 15 16 1740 120 0 -1 _ 16 17 4060 250 +1 -1 _ 17 IS 4110 200 0 -4 _ IX 19 4510 220 -2 -4 2400 1 11 170 -fi 74S 31 12 _ 40 0 _ 55 91 97 _ 1 so -fi 92 91 _ 150 -5 _ 150 91 9 100 0 _ 1 1 1 1 1 100 +1 470 111 112 _ 100 +1 _ 150 n P I _ 50 0 75 121 122 _ 110 0 _ 50 122 121 _ 80 0 _ 114 111 _ 80 0 111 112 _ 50 0 90 112 111 _ 110 0 _ 131 13 - 50 o - 150 The free flow speed was another parameter that had to be specified for each link. This was set to 50 mph (80 km/hr) considering the posted speed on the highway. Among the ramps, only the Willingdon off-ramp (N) had a posted speed of 30 km/hr. For most of the ramps, this parameter was selected as 37 mph (60 km/hr). The exceptions were due to the following point. F R E S I M does not allow the radius o f curvature to be smaller than some specified value. However, for example, the Willingdon off-ramp (N) has a highly curved ramp segment that is 85 not within the allowable range. A closer examination of the effects of the curvature and superelevation shows that they are used to find some safe upper bound for the desired free flow speed. Therefore, in such cases, after calculating this bound, it can be entered directly as the desired free flow speed. This bound is calculated in F R E S I M manual (Federal Highway Administration, 1994) as: V = Jl5R(e + f) (5=1). Where V =Upper bound for vehicle speed, mph R = Radius of curvature, feet e = Rate of roadway superelevation, feet/foot / = Coefficient of friction for a given pavement condition The traffic operation and the percentages o f trucks and heavy vehicles are also required for the simulation model. A 6% value was used in this model. This was estimated based on the actual counts from a tape recording at the site. Furthermore, it was observed that most of the trucks were biased to the lane #1 3 0. This means that they wil l only use the second lane when passing another vehicle, after which time they return to the first lane. In F R E S I M , this bias of the heavy vehicles can be incorporated. In FRESIM, through lanes are counted from right to left. Therefore, in this thesis lane#l, or first lane refers to the rightmost through lane. 86 Traffic volumes entering each entry node or diverting off the freeway through off-ramps are also part of the necessary data for the simulation. However, since the purpose of this study is to evaluate the effects of the changing conditions and since these volumes are changing by time, they are discussed later in the next chapter where data sets are presented. In addition to the parameters discussed above, there are a number o f other parameters such as the duration of time periods and time increments, etc. that can be arbitrarily selected. Still, there are a number of other parameters, which can optionally be defined when building the simulation model. There are some default values for such parameters that wil l be used in cases where the user does not provide additional and more accurate data. Almost none o f such parameters is usually available. Some typical cases are as follows: • Driver type distribution and car-following sensitivity factors; • Various vehicle types and their specifications (e.g., length, jerk value); • Maximum acceleration for each range of speed; • Coefficients of friction for various pavement types; • Lag to accelerate/decelerate; • Time to complete a lane change; • Lane changing probability; and • Percentage of cooperative drivers. 87 These parameters clearly show, at least potentially, how comprehensive the simulation model can be. However, when these parameters are not available, the default values have to be used. The degree of sensitivity of the results to most of these parameters is unknown at present. 5.2.3 Detector Locations Locating the surveillance systems is one o f the major steps in defining the simulation model for the study on A I D algorithms. After a search in the literature, only a few cases were found where the effects of the detector spacing on the performance of some specific A I D methods had been studied (Goldblatt, 1980). However, no general guideline concerning location of the detectors, particularly with respect to ramps, was found. Since the traffic close to the ramps is less uniform it is reasonable to suspect that placing the detectors too close to the ramps may have an adverse effect on the reliability of the measured data. However, the question remains that even in such a case, how close is too close, and whether this applies equally to both off-ramps and on-ramps. One may imagine that the reliability of the A I D detection system wil l greatly depend on the randomness of the measured traffic data. In other words the more uniform the incident-free data are, the higher the possibility of detecting an incident and the lower the possibility of producing false alarms. Therefore, any added disturbance other than the normal randomness of the traffic parameters will contribute to a less favorable situation for the A I D algorithms. Around the on-ramps the vehicles (mainly in the first lane) have to slow down to 88 accommodate the merging vehicles, while merging vehicles are also trying to find a gap and then accelerate to the main stream speed. This causes an obvious disturbance to the flow and increases the occupancy. In contrast, the area around the off-ramps should be much less disturbed because no merging is involved. In this thesis, the standard deviation of the occupancies recorded over time, at any given point, is suggested as a good quantitative measure. To use this measure in studying the effects of the ramps on the uniformity of the traffic flow, a very large number of simulated detectors are necessary to collect traffic data along the freeway oyer time. To do this, 60 detector stations were defined along the freeway. The detector station #1 was arbitrarily selected 100 ft downstream of the starting node. The other stations were placed 200-ft (61-m) apart along the freeway. F R E S I M handles a maximum of 37 stations at a time. Therefore, coverage of the whole freeway with detectors was done in two complementary parts, with detector number #31 in common as a check. Each complete set was simulated for a number of cases for 15 minutes without any incident. Consequently, a detailed picture of the changes in traffic parameters were generated. The resulting average and standard deviation of the recorded occupancies for two o f the simulated cases are presented in Figure 5.3. In the first case, only the passenger cars were present, while in the other case, 6% of the vehicles were assumed to be trucks and heavy vehicles biased to the first lane (as were used in the generation of the main data sets). 89 Referring to Figure 5.3, first, the occupancy changes of the first lane for the case with trucks is considered. As expected, in the upper diagram, six plateaus can be identified that correspond to the six zones of varying lengths whose volumes wil l be constant (e.g., between Boundary off-ramp and Grandview on-ramp). The height of these plateaus increases or decreases based on whether there is an upcoming on-ramp or off-ramp respectively. However, in the area close to the Grandview on-ramp, the average occupancy is much higher than expected. This starts some 100 feet upstream of the on-ramp node, and continues for another 700-900 feet. A similar, but less strong jump in the occupancy, can also be seen in the area around the Willingdon on-ramp. This can easily be explained, based on the reactions of the drivers of both merging vehicles and those on the first lane of the freeway. 90 Boundary off-ramp Grandview Wi l l ingdon Wi l l ingdon Wi l l i ngdon on-ramp off-ramp (S) off-ramp (N) on-ramp 1 X I / Lane-1,6% Trucks Lane-2,6% Trucks Lane-1, no Trucks Lane-2, no Trucks i i i i i i i i i i i i i i i i i i i i i i i i t i i i i > i i i i i ) i i i i i i i i i i i i Detector Station (#) Figure 5.3. Var ia t ion of Occupancy along the Freeway for Incident-Free Cases However, a more interesting parameter to consider is the standard deviation o f the occupancy in the lower diagram. It shows a somewhat constant level of variation for occupancy that is due to "normal" traffic fluctuations. Almost within the same areas that there were jumps in the average occupancy, one can observe the jumps in the standard deviation as well. This is an important factor to be considered when placing the detector stations for A I D purposes. It gives some quantified measure of the expected reliability of the data. A high variation of measured occupancy under normal traffic condition will contribute to high false alarm rates. 91 The Grandview on-ramp carries almost twice as much traffic as does the Willingdon on-ramp. Interestingly, this is also reflected in the magnitudes of the jumps for these two on-ramps both in the lower and the upper diagram. A s expected, the occupancy in the second lane is much more uniform than the one in the first lane. In addition, it is interesting to compare the case having no trucks with the previous one. Although the same jumps can be seen in this case as well, they are substantially weaker, and a shorter length of the freeway is affected. This shows how sensitive the data wil l be to the percentage of the trucks and heavy vehicles. This can be attributed to the limitations in the maneuverability and performance of heavy vehicles. These tests also confirmed that off-ramps do not introduce any significant change in the normal level of variations. They only reduce the average occupancy level. Since any such simulation program uses random numbers, its output is unavoidably at most an isolated case of what could have happened in real life. This is true no matter how well the simulation program and the model used are. Therefore, meaningful decisions have to be based on a statistically significant number of experiments. In this case, also a number of tests were done to make sure that the idea and its premises are valid. Based on these tests, proper locations for the detector stations can be found from Figure 5.3. For this study, the spacing between the detectors was arbitrarily selected to be constant and an integer multiple of the 200-ft used in the earlier tests. Using a distance, of 2200-ft (670-m), 92 one can place six detector stations along the selected segment of the freeway. A s shown in Figure 5.3, the detector stations 4, 15, 26, 37, 48, and 59 were selected as the six detector locations to be used in the main simulation model. This selection puts one of the stations (#4) within the region where the auxiliary (deceleration) lane for the Boundary off-ramp extends. However, this is not expected to affect the reliability of the data for A I D purposes, but it means that the measured volumes may not correspond to any specific point in the freeway 3 1. They neither correspond to the volume of the flow before, nor to the volume after the off-ramp. This is because some of vehicles that are going to exit the freeway will not pass the sensor. 93 CHAPTER 6 DATA SETS A large number of data sets were necessary so that the A I D methods could be tested under both incident and incident-free conditions. During the course of this study, many such data sets were generated and used. Two main series that were used wil l be discussed here 3 2. 6.1 First Series of Data Sets To generate a large number of incident and incident-free data sets, a smaller number of incident cases can be simulated in which the recorded detector data before the occurrence of the incident represent the incident free-data sets. Similarly, those after the occurrence of the incident represent the incident data sets. A ten-minute window of the recorded data was selected for each incident case when the incident starts just after the fifth minute and continues to the end of the simulation. The detectors record the average volume, speed, headway, and occupancy every thirty seconds. As it was mentioned earlier, it is desirable to study the performance of the A I D algorithms under various conditions. This provides an opportunity to examine the robustness of the A I D A smaller number of intermediate data sets were also generated and used when various options for the UBC AID method were being explored. 94 methods. To cover a wide range of incident cases under various conditions, the following parameters can be varied: • Incident location (location along the freeway, closeness to the upstream or downstream detectors, lane); • Incident severity; and • Time, or traffic volume. Incident location can be represented in three ways as mentioned earlier. The effects of the geometry, on-ramps, and off-ramps in the performance of each A I D algorithm can be taken into account by placing the simulated incident in each detection zone. In our case, where we have five detector stations this gives us five possible zones for simulating the incident. Furthermore, the performance of each algorithm may depend on the closeness of the incident to the detectors. In other words, it may depend on whether the incident is closer to the upstream detector, the downstream detector, or the middle of the zone. To consider this, any number of locations could have been chosen within each zone. In this study, to keep the total number of combinations manageable, three locations per zone were selected. The effects of the incidents happening in the first lane on the traffic are certainly different from those in the second lane. Therefore, two choices of lanes were considered for each location along the highway. 95 The severity of an incident is also a major factor in its effect on the traffic and therefore the possibility of its detection. To study this, three degrees of severity were considered in generating the data sets. The highest severity was a full blockage in one lane and a rubberneck factor of 10% in the other lane, plus a capacity reduction downstream of the incident. The second and third degrees of severity were a capacity reduction of 90% and 80% in the specified lane, respectively. The traffic volume and percentage o f inflow and outflow o f the freeway and its ramps wil l change significantly with time of day. To consider this change in the present study, the required data for volumes have to be treated as a variable. Since the time window is not very large, the change of traffic volumes during each simulation can be neglected. However, each case can be assumed to happen at a different time of day. A total of ten times for a typical weekday was selected to be used in the generation of the data sets. To obtain the necessary values, the most recent hourly counts from the study site were obtained from the Ministry of Transportation and Highways. The values representing the volumes over the weekdays were averaged to obtain the typical weekday traffic volume on an hourly basis. The figures representing traffic volumes for the 8 t h to the 17 t h hour of the day are shown in Table 6-1. Those representing 9 t h , 11 t h , 13 t h, 15 t h, and 17 t h hours were used in the first set of data series. Considering the five different parameters discussed above, one can find a combination of 450 incident cases as: (5 zones)(3 location / zone)(2 lanes)(3 levels of incident severity)(5 times of day) 96 Table 6-1 - Traffic Volumes used in the Simulation Data Sets Volume of T C H (East Volume of Volume o f Volume of Volume of Volume of Time Bound) Boundary Grandview Willingdon Willingdon Willingdon Between off-ramp on-ramp off-ramp off-ramp on-ramp 1 st Ave. & (S) CN) Boundary 08 3750 697 1143 670 205 449 09 3549 593 1065 744 238 442 10 2687 413 839 529 178 434 1 1 2379 428 867 397 140 490 12 2652 460 1006 395 154 574 13 2598 412 1070 414 164 638 14 2988 465 1130 450 178 690 15 3184 528 1154 490 227 688 16 3208 506 992 482 199 617 17 3063 593 910 483 199 531 6.2 Second Series of Data Sets A s wil l be discussed in Chapter 7, after preliminary tests with the first series of data sets showed promising results, a new expanded series was considered. The new series required a larger number of data sets so that 50-60,000 incident /non-incident decisions could be made based on them. Furthermore, the implementation of U B C AID required some extra 15 minutes worth of data before making the first decision. This series was generated using the same general structure but with the following changes: 97 • All of the hourly volume data from 8 a.m. to 5 p.m. were used to represent 10 times of day (twice as many as the first series); • Each case was simulated for 35 minutes in which the incident occurs at t=25 min; and • Only lane blocking incidents were simulated and the two other levels of severity were not used. 6.3 Data Set Names and Structures The data sets in both of the series were named in a structured manner. This allowed the characteristic of each incident case be represented in a concise coded format33. The coding structure is as follows: • Three locations per zone are called: "U", " M " , and " D " to represent the locations closer to the upstream detector, in mid-span of the zone, or closer to the downstream detector. They are located on 1/6, 1/2, 5/6 of the spacing (2200 ft, or 670 m) from the upstream detectors. This provided a uniform distribution of the incidents irrespective of the geometry of the freeway (see Figure 5.2- B). • The zones were numbered by their upstream detector station number; i.e., "1", ... "5" (see Figure 5.2 - B). In addition, by selecting small codes, it is possible to use these names as the file names on the computer as well 98 • The lanes were numbered as "1", and "2", in which "1" refers to the rightmost lane. • Three levels of severity were called: "A", "B", and " C " , in which the order is from highest severity to the lowest. In the second series of incident cases only severity level of "A" was simulated. • Times during a day were designated by the 24 hour notation as: "09", or "17". • To distinguish the second extended series of data sets an "e" was added to the end of the name structure. As an example, the case "U31A13e" refers to one of second series in which the incident was located close to the upstream point of the third detection zone (i.e., 1/6 of detector spacing after detector station #3). It occurred in the first lane and with a high degree of severity. The assumed time of the day at the beginning of the simulation was around 13:00 or 1:00 p.m.34. To reduce the overall time spent on the simulation, and for easier handling o f the data sets, a batch o f thirty incident locations for any combination of the incident severity and time of day was processed using one data file. To manage this and as a wild character for other purposes, the character "X" was replaced in any position of the name structure where it referred to all the possible combinations. Therefore "XXXB09" represents all the thirty incident cases of the first series with medium severity occurring about 9 a.m.. 99 6.4 Effects of the Random Number Seed Another parameter that can optionally be set in F R E S I M is a random number seed that is used in the generation of the random number series. This number may not seem important for most of the users. However, in this study, using the same number for all the incident cases has an important implication. For example, considering the 90 incident cases represented by " X X X X 0 9 " , one can see that all the conditions are exactly the same for the first five minutes. It is only after the occurrence of the incident that each individual case wil l result in a different sequence of events. Therefore, the incident-free databases consisting of the first five minutes are not independent of each other and lack the required randomness that one expects to generate with simulation. Although, even by putting aside this part of the data, some incident-free data wi l l remain useful, it would be more reasonable to use all o f the simulated data. To overcome this problem, the random number seed within each of the mentioned 90 cases should be different (while they can remain the same when the time of day is changed). The F R E S I M can input an eight-digit number whose default value is 00007581. In this study, the four leftmost digits were arbitrarily selected to be changed sequentially. Since the vehicle counts provided by the Ministry are labeled as 1st hour, 2nd hour, etc,, they rather represent the situation that is closer to 12:30, 1:30, etc. However, since the time is not directly being used in this study this is of no significance and has no effect on the validity of the results. 100 CHAPTER 7 DEVELOPMENT OF T H E UBC AID SYSTEM In this chapter, first the traffic flow before and after the occurrence o f an incident wil l be discussed. It wil l be shown that as a result of an incident, the characteristics of the flow are changed upstream and downstream of the incident through propagation o f two waves. It wil l also be shown that part of the useful information carried by these waves has been overlooked in other methods. Based on the discussion that follows a concept for the proposed system wil l be introduced. After testing the general feasibility of the proposed system, using its basic version, the final form wil l be presented. 7.1 ShockWaves and Expansion Waves To analyze the state of traffic before and after the occurrence of an incident the so-called "fundamental flow diagrams" can be considered. The state of traffic in a macroscopic sense is often described by flow rate, density, and speed through a set of diagrams each showing the relationship between two of them. Figure 7.1 shows one of diagrams in which an inverted " U " curve represents the relationship between flow rate and density. Various shapes and formulas for this curve have been proposed by traffic engineering. However these shapes and formulas are not discussed here and the general shape shown wil l only be used to discuss some concepts and characteristics of the traffic flow before and after the occurrence of an incident. The concepts and characteristics presented here are valid irrespective o f the curves selected. 101 Density Figure 7.1. Fundamental Flow Diagram and Effects of Incident The "space mean speed" (u s ) can also be found for any point on the flow-density curve as the slope of the connecting line between the origin and the point in question. The space mean speed is calculated from division of flow by density. The value for density may range from zero (empty road) to a maximum called "jam density" (fcj ). The maximum flow rate that is possible for a road is called "capacity" (q ) and the density at which this occurs is often J max termed the "critical density" (kc)- The flow takes a zero value under two conditions; empty road and traffic jam where the speed is zero. The highest possible speed is called "free flow speed' and can be represented by the slope of the tangent to the curve at the origin. 102 The critical density divides the curve into two distinctive regimes. The first part of the curve in which an increase in demand is accommodated by an increase in density and flow rate is called "free flow". In this regime, the speed remains close to the free flow speed, while in the second part of the curve, 'Torced flow", speed is very sensitive to density. The second regime represents the condition under which the drivers are too close to each other to drive "freely" and an increase in density would substantially reduce their speed. In this regime the further a point is to the right the higher the degree of congestion would be. It can be seen that an efficient use of the facility is achieved when the flow rate is close to the capacity without entering forced flow regime. The effects of an incident on the traffic flow can be discussed using Figure 7.2. When an incident occurs in a highway operating under free flow condition, the capacity within a limited segment of the highway would be reduced. The flow-density relationship in this section is represented by the dashed curve in Figure 7.2-a. The traffic operation outside of this limited segment still follows the original curve but its volume could be controlled by the capacity at the incident location. If this capacity were less than the demand (volume prior to the incident) as shown by point "U", the volume in the immediate area upstream and downstream of the incident would be decreased to the capacity at the incident location. This requires a change in density that differs on two sides of the incident. The occurrence of an incident reduces the effective demand downstream of its location and hence the condition would proportionally change to a lower density represented by point "L". 103 While there is a difference in the density of points " U " and " L " , their speed difference is minor, i f at all different35. On the other hand, the condition on the upstream clearly would no longer allow free flow traffic and a high-density area wil l be formed in which the speed is significantly reduced. This is represented by a jump from point " U " to point " H " in the diagram. There is also a significant reduction in the speed upstream as a result of lost capacity. The difference between the arrival and departure rate of flow causes the vehicles to be accumulated behind the incident location and this causes the high-density area to progress in the opposite direction of the traffic flow. The edge of this area moves backwards and is called the "shock wave". In the same sense, the difference between the flow rates at the incident location and that of the "undisturbed flow" represented by " U " causes the low-density area to progress forward in the direction of the traffic. The front edge of this area that causes an "expansion" of the gaps between vehicles is termed the "expansion wave 3 6". The speed of the shock wave can be analyzed using Figure 7.2-b. In this figure, the backward progression of the high-density area is shown in which after a time increment of At the length of this area has increased by A £ . The increase in the number of accumulated vehicles during At in the freeway segment shown can be found as: Number of vehicles entered- Number of vehicles exited or, 3 5 This is unless the operating condition prior to the incident is very close to the capacity. 3 6 In the literature, the term "shock wave" has also been used for this wave. However, the author prefers the term "expansion wave" both considering the effect it has on the traffic and being consistent with the terms used in compressible fluid flow. 104 a) Density b) Traffic Flow Direction kjj 'ML Shock Wave Direction Incident Location kH C) Exp. Wave o o € u f— Det. St# i+1— f-4-Incident Location Det. St# i — d) Occj+i Occj Voli+ Volj Spdi i Spdj * L . —r— + a ^ e E i 1 r i i i i I L + +2 Shock.x 'Wave T 1 1 r I I I + *5 Time Figure 7.2. Effects of an Incident on Traffic Flow Variables 105 In which qu and qH denote flow rates for undisturbed and high-density areas respectively. On the other hand, the same increase in accumulated vehicles can be expressed using densities of the undisturbed and high-density area (ku and Considering that only the density in the length Al has changed, the mentioned increase can be calculated as: Therefore, the speed of the shock wave can be calculated as ikn ku) This also corresponds to the slope of the cord connecting the points " U " and C C H " as shown in Figure 7.1. It is also noticeable that the slope of this cord is negative and is consistent with the fact that shock waves move in the direction opposite to the traffic flow. In a similar way the speed of the expansion wave can be calculated as: (ku ~kj) Where qL and are flow rate and density for low-density area. This speed can also be interpreted as the slope of the cord connecting points " U " and " L " in Figure 7.1. This geometric interpretation also shows that speed of the expansion wave, the speed of the vehicles before the incident, and that o f the downstream are all almost the same and equal to 106 the free flow speed, unless the condition is too close to capacity. It can easily be seen that the speed of the shock wave is much lower than that of the expansion wave because while the numerator in both formulas are the same, the denominator for the shock wave is much larger. The "news" of an incident is carried by the shock and expansion waves to the detector stations. The time taken for this news to be sensed depends on the speed of the waves and the distance between the incident location and the closest upstream and downstream stations. While the incident location could be anywhere within the spacing between two adjacent detector stations on average one can put it in the middle of that spacing. One such example is shown in Figure 7.2-c in which progression of both waves is shown. It is notable that the lines representing shock wave and expansion wave are parallel to the cords "UFT' and " U L " of Figure 7.2-a respectively. In Figure 7.2-d the signals measured by upstream and downstream detectors are shown. Clearly, the magnitude of changes in occupancy and speed sensed by the upstream detectors are much larger than those by downstream detectors. However, these changes in upstream signals occur with a much larger delay as expected. The strength and the speed of the shock wave depend on the capacity to demand ratio before the incident and the severity of the incident. A s shown in Figure 7.3-a a higher demand or lower capacity to demand ratio causes a higher speed for the shock wave. However, the figure also shows that the capacity to demand ratio has little or no effect on the speed o f the expansion wave. Figure 7.3-b shows that a more severe incident that causes a larger reduction of capacity generates a stronger shock that moves faster. The strength of the shock relates to 107 the jump in density that is caused by it. In this case, also the severity of the incident has almost no effect on the speed of the expansion wave, which remains close to the free flow speed. \ a) o P3 I y / / j / II I """*"•» ^ X ^ "**" *** ^ X . i ' b, Density wRate / / YBI 7/ " // * I / II ' *** X . **• X . >. \ V . V . \ X x. \ >. \ X V - "" /' \ f ™' * V * " — — N \ •*•» x \ ** -_ x X - » N X "* «^ v X . *• X ** -_. **• X *•«_ v, X —. \ \ *** ^ X . Density Figure 7.3. Effects of a) Demand and b) Incident Severity on Shock and Expansion Waves 108 The cases and effects discussed so far excluded the normal traffic fluctuations and non-homogeneity in the roadways. It also used simplified models where the jumps or drops in traffic parameters occur instantaneously. However, in reality signals sensed by the detectors contain noise, are not uniform, and are less abrupt. A more realistic view of the changes in traffic parameters as could be sensed by detectors is presented in Figure 7.4. It shows the occupancy readings from a series of six detector stations along the study site before and after the occurrence of a lane-blocking incident. The typical changes of the occupancy and the progression of both waves can be seen in this figure. In this example, the speed of the expansion wave is about 4-6 times that of the shock wave. F i g u r e 7.4. V a r i a t i o n s o f the L a n e O c c u p a n c y fo r a T y p i c a l L a n e B l o c k i n g I n c i d e n t 109 To compare the magnitude of the changes due to the arrival of the shock and expansion waves with magnitude of the normal fluctuations, the readings from two immediate detector stations are plotted in Figure 7.5. To do this comparison, the conditions before and after the arrival of the waves are averaged to find an imaginary stationary level for each case. One can see that the occupancy jump due to arrival of the shock wave is distinguishable from those normally present in a signal. This is while the occupancy drop due to arrival of the expansion wave is not much larger than those caused by existing noises. In fact, one may be mislead by a random drop that occurs in the upstream occupancy at t=480s as a sign of arrival of an expansion wave. 0 J ^ — - I 1 1 1 1 — I 1 1 , 0 90 180 270 360 450 540 630 720 810 900 Time (s) St#3 and St#4 represent upstream and downstream respectively (reproduced from Figure 7.4). (s) Lines represent stationary conditions before and after the arrivals of the corresponding waves. Figure 7.5. Occupancy Variat ions at First Upstream and Downstream Stations for a Typica l Incident 110 The above discussions about shock and expansion waves and their important implications if used as indications of an incident in AID systems are summarized in Table 7-1. Table 7-1 - The Advantages and Disadvantages of Using Shock and Expansion Waves for an ADD System Advantages Disadvantages Shock wave The magnitudes of the changes sensed in occupancy and speed are much larger and more distinguishable from random fluctuations. The changes are more abrupt and do not damp out as the shock wave progresses. This helps making more reliable decisions The speed of the shock wave is a function of the severity of the incident and the capacity-to-demand ratio. The shock waves move much slower and there is a long delay before their presence is felt at upstream station and consequently a high ADT. Expansion wave The speed of the wave is almost independent of the incident severity and capacity-to-demand ratio. The expansion wave moves almost as fast as the vehicles downstream of the incident that could lead to early detection of the incident. The speed almost does not change and the occupancy drops are not much larger than the random fluctuations in volume'7. The changes may damp out as the wave progresses. The changes are also sensitive to presence of ramps. This may lead to higher FAR. Considering that passage of a shock wave is much easier to detect than that of an expansion wave, the AID methods have always focused on detection of shock waves. Therefore, as mentioned earlier local or station based algorithms depend on detecting congestion that occurs after the arrival of the shock wave. Double exponential smoothing and the neuro-fuzzy method by Hsiao are among these local methods. The expansion wave produces the same drop in volume as does the shock wave because the volume needs to be continuous to satisfy the fundamental conservation law. I l l A s opposed to "station-based" algorithms, in "section-based" algorithms the information from both upstream and downstream is used. Some of these methods are called "comparative" in which a comparison of the upstream and downstream is used. California methods and A P I D are among these methods. In comparative methods, mainly a strong enough difference between the occupancy of upstream and downstream is counted as an indication of an incident. Therefore, considering that changes in downstream are small, the mentioned difference only could be sensed after the shock wave has passed the upstream detector station. A close look at other algorithm shows that one way or the other the congestion needs to be present before the alarm is triggered and i f downstream condition is also checked it works as a supplementary check. Among "section" algorithms, there are only t w o 3 8 seemingly exceptions for above statement: The neural method by Ritchie (1992) and the Australian neural method by Rose and Dia (1995). In both of these cases, the traffic parameters of upstream and downstream are both fed to a neural network whose task is to classify the inputs as an incident or non-incident pattern. However, knowledge of how the weights are calculated during the training period and the training sets reveals that the effects of the shock wave would easily outweigh those of the expansion wave. This causes the network to be less sensitive to the changes in downstream (if McMaster may also be assumed to be of this category since it uses the downstream information as well, but it does it after the congestion has been detected and persisted in the upstream station. See page2 of paper by Hall etal. (1993). 1 1 2 at all). Therefore, in these cases too, the incident would remain undetected until the shock i • 39 wave passes the upstream station . Based on the above discussions one could conclude that despite the diversity of the approaches used by indirect A I D methods, they share a common characteristic that acts as an important drawback. This characteristic is that the potential for an earlier detection by using the information carried by the expansion wave has been ignored. Therefore, the detection occurs only after the congestion has already developed. This as discussed in section 3.3, substantially reduces the operational effectiveness of using ADD systems. To target this very drawback, the method developed in the present study, uses information carried by both waves. The potential reduction in detection time can be analyzed by considering the characteristics of the two waves. I f both waves shared the same speed and strength, the detection time could be reduced by half because the incident "news" had to travel only half the distance. Given the higher speed of the expansion wave an even further reduction of detection time could be expected. However, the lower strength o f the expansion wave reduces the reliability of the decisions made based on it and therefore the full potential can not be realized. The degree to which the A D T can be reduced mainly depends on the degree that the "news" carried by the expansion wave can be reliably utilized. In the following sections, the basic concept and the details of the proposed U B C A I D system wil l be presented in which it is tried to take advantage of both waves in a reliable manner. This can also be concluded from examining the reported detection times of both methods. 113 7.2 Basic UBC System As was shown earlier, a substantial reduction of detection time can be expected if the information carried by both shock and expansion waves are exploited. It was also mentioned that changes made by expansion waves were either neglected by existing AID methods or were examined in such a way that they were outweighed by dominant changes caused by shock waves. This hints that the effects caused by each wave have to be analyzed independently. This would allow each wave to be treated differently and according to its own characteristics. The logic of the proposed AID system can be described using Figure 7.6. It consists of the following three stages: • Preprocessing • Classification • Decision making In the core of the proposed system, there are two classifiers each dedicated to analyzing the condition as to whether a shock wave or an expansion wave is present at a sensory station. At first however, the signals from each sensory station may be preprocessed in a way that is most suitable for each classifier. The decision whether or not to trigger an alarm would be made after the outputs of the two classifiers - as evidences of the occurrence of an incident - are examined at the third stage. This structure allows upstream and downstream signals to be analyzed independently while the result of the analysis can then be combined. 114 Decision making O O [ 1 ; Classified 1 ! '_ ! r 1 I Classifier#2 ! i ' o Preprocessing Figure 7.6. General Scheme of the Proposed System After a number of initial tests, using the general structure proposed above, a basic version of the proposed system was developed. This basic version, shown in Figure 7.7, was mainly used to study the feasibility of applying the strategies discussed earlier. In the following sections, various stages of this basic version will be discussed. 7.2.1 Input Features and Preprocessing The study site has two lanes and therefore for each detector station there will be two sets of detectors. Assuming that measurements of occupancy, speed, volume and headway are available for each detector set, there will be eight main measurements as potential input per 115 station40. As mentioned in section 2.2, among these measurements all but the headway have been used in the existing AID methods. The headway can easily be obtained from the signals of "0" and "1" from the detectors in a similar way to the other measures. The time between two consecutive transitions from "0" to "1" will be the headway between consecutive vehicles. Shock wave Detector Expansion wave Detector Smoothing by Moving Average Upstream Measurements Downstream Measurements Figure 7.7. The First Prototype of the U B C A I D System 4 0 Since the point mentioned in section 2.2 about headway and volume has not been considered in FRESIM, the average headway and volume are treated as independent of each other. 116 When selecting the inputs for a classifier, often, but not necessarily always 4 1, it is avoided to use inputs whose information content would be redundant. Among the four variables stated, this condition might apply to volume and headway depending on how the headway is calculated. A n examination of the F R E S I M showed that the product of headway and volume (with a compatible set o f units) is close but not necessarily equal to unity. Therefore the two variables are not fully redundant and this would be truer for smaller values o f volume. There are a number of ways to use the measured values for each lane. In other ADZ) methods usually the measurements are averaged over the adjacent lanes, This has the drawback that it reduces the sharpness of the resulted change when the waves arrive at the station. This is because the effects are usually stronger and arrive sooner in the same lane that the incident has occurred. Therefore using individual measurements increases the chances of early detection. In the first set o f trials, the classifiers were used for each lane rather than for each station. This provides a chance to not only detect the incidents sooner, but also to specify which lane contains the suspected incident. This second factor is not very important and can be found through other means. The first factor is important but comes at a price of doubling the number of decisions made per unit time for a two-lane freeway. Doubling the number of decisions potentially doubles the number of expected false alarms as well. Therefore, in the basic version, the mentioned features for both lanes were used together for both of the classifiers. Using these eight features, one decision per station was made for each classifier. In addition 4 1 In the proposed UBC AID system, as will be discussed in section 7.2.2, neural networks are used for classification. When used as function approximations, neural networks show better performance to model addition or subtraction compared to multiplication or division. Consequently, depending on the underlying factors, a neural network used for classification may also show a different performance when some input 117 there were instances when a substantial difference between values of same feature (e.g., Volume) measured in two lanes was a further indication of the existence of an incident. A s mentioned earlier, when the expansion wave reaches the detectors, downstream measurements wil l experience minor and less abrupt changes. These changes are generally in the same order of the present signal noise. This means a lower signal to noise ratio that makes it hard for the classifier to distinguish between a temporary change due to normal traffic fluctuations and the one that is caused by an incident. For this version, a moving average with span of two periods was used to smooth the signals prior to feeding them into the downstream classifier. A moving average of the two periods smoothes the signal by substantially reducing the magnitude of the noise but it may also delay the detection. This is because the magnitudes of the changes due to the arrival of any of the waves would be halved in the first period. When considering the shock waves the upstream signals experience more abrupt and larger changes in the measured parameters. This makes it easier for the upstream classifier to distinguish between a change due to the arrival of a shock wave and a change due to noise. Therefore, there is no need to use smoothing for upstream signals and potentially delay the detection of an already slow-moving but strong shock wave. In case of the expansion wave however, the reliability of the signal demands using a moving average filter to smooth out noise, even though it may come at the cost of a delayed detection. This is particularly justified when features are inverted before using, despite the fact that they carry the same information. 1 1 8 noting that the expansion wave although weaker moves much faster, and in a majority of cases, the first sign of arrival may be observed after one sampling period. 7.2.2 Upstream and Downstream Classifiers Neural networks as discussed in section 3.1.10, have been successfully used for many classification problems. Their ability to handle noise and even missing data makes them ideal for various applications. They are also inherently nonlinear, and therefore they have a higher chance to perform reasonably well for nonlinear problems. This is in contrast to the statistical methods that are mathematically sound but suffer from some linear and constraining assumptions. As shown in Figure 7.7, in the basic version, a three-layer feed-forward neural network was used for both classifiers. Each classifier had eight input nodes for the previously mentioned input features. The hidden layers and the output layers had five and one node, respectively. This combination for the classifiers was selected after a number of trials that showed a better performance. As was mentioned earlier, in neural networks, the weights associated with each link connecting two nodes are set during a process called training. During this process a set of already classified patterns, called "training data set", along with their desired outputs are fed into the network. The weights are then adjusted during consecutive trial and errors such that the error, or difference between the desired and actual outputs, is minimum. After the training 119 stage is completed, a pattern fed to the input nodes in the so-called recall stage can be classified by the network 4 2. Backpropagation method is widely used in training of feed-forward neural networks. The details of this training process are explained by Rumelhart et al. (1986). Backpropagation produces a good classification performance but the training process is very slow for large networks. However, the approach of the present method only requires a small network that does not require extensive training time. Furthermore, the idea in the present A I D system is to train the network off-line and only the recall wi l l be done on-line. Since recall does not require any trial and error and only needs a few calculations, it would only take a fraction of a second to classify data patterns of an operational site. Another important point to consider while training is that a prolonged training or a small ratio of training patterns to the link numbers can produce what is often called over-fitting or over-training. The main reason to present a sample o f patterns for training is to enable the network to generalize from that sample to the original population where that sample has been selected. Obviously using a sample with too few patterns, or a non-randomly selected sample produce a bias towards a specific region of the population. The same problem may arise when either there are too many weights to be adjusted or the network is excessively presented with the training sample. Consequently, i f after the training, the network is tested with another sample from the same population, it wi l l show a substantially larger error. 4 2 The feed-forward neural networks are used in many applications other than the classification as well. However, since in this thesis they are used for classification purpose the sentences above refer to specific role. 120 In the present case a 6-to-l ratio for the number of patterns to the weight (and biases) provides a good condition for the network. Early stoppage of the training can also be used to reduce the risk of over-training. Often there is a "test data set" whose error is calculated along with that of the training set. However, contrary to the training set the error o f the test set has no direct effect on the calculation of the network weights. As long as both errors are decreasing, the training may continue but an increase of test error signals the critical point for stopping the training process. Each of the two classifiers was trained by a randomly selected pattern set of X X X A 1 1 set of the simulated data. They were also tested during the training process by the other half of the same set of data. In each case the outputs for patterns that represented the condition prior the occurrence of the incident were labeled as "0". In a similar way the outputs for the rest of the patterns were labeled as "1". 7.2.3 Decision Making Block The outputs of the classifiers are fed into the decision making block whose task is to examine the evidence and trigger the alarm i f necessary. In the basic version, this block consists of two thresholds and one " O R " gate. Although in the training set incident and non-incident patterns are represented by " 1 " and " 0 " values, the outputs of network can be any number (e.g., in the range -0.1 to +1.1). The larger the number, the higher the resemblance of the pattern to an incident situation is expected to be, and vice versa. However, no other conclusion can be made about the output of such a 121 network. For example, a probability can not be attached to the output value directly . Therefore, mostly a simple threshold defines whether the pattern belongs to a class or not. This threshold, for a two-class problem is often selected to have a value of 0.5. A threshold value of 0.5 tends to provide an unbiased misclassification for each of the classes involved. However, although this might be good for problems with "symmetric" classes, its use is not justified for the problem at hand. The main reasons for using biased thresholds are as follows: • As it will be shown in section 7.2.4, a substantial number of patterns would be "mislabeled" as incidents. They represent the measurements at the time after the incident has occurred, but before the effects of the incident have been sensed by the detectors. This mislabeling is somewhat unavoidable because defining the exact time when the incident effects reach the detector is not always possible, whether in the simulation data or in the real situation. • In the simulated data, the number of incident and non-incident patterns have been selected to be equal. In reality however, the incidents happen rarely and therefore incident patterns are much less available than the non-incident patterns. One can either select the same number from the non-incident data to keep the balance, or use an appropriate weight to compensate for the imbalance. Otherwise a biased threshold would be necessary. The probabilistic Neural networks are exceptions in the sense that each of their outputs are assumed to be the probability that a pattern belongs to a specific class. 122 • Most important of all is that the consequences of the two types of misclassifications are not the same. The tolerance for a false alarm should be much less than the opposite error that happens when an incident has been missed for one interval. The ratio of the former to the latter might be in the order of 1 to 100 or lower. On the other hand, this threshold can be effectively used as a calibrating parameter. Although in the present form it does not assign a confidence to the output of the network, it is certain that a higher output means a higher confidence. Therefore, by increasing the threshold one can increase the expected confidence before accepting the network's decision as true. Considering the earlier discussions it is obvious that a higher threshold for the downstream classifier should be used to compensate for its lower expected reliability. In the first prototype the outputs of the classifiers after passing through their thresholds are combined with an " O R " gate. The result wil l be an alarm i f the output of any of the two classifiers is more than the respective threshold. B y using an " O R " gate the false alarm rates of the two classifiers wi l l be summed. Therefore, it is necessary to adjust the thresholds such that the false alarm rate is in the acceptable region for the operator. However, the benefits of using an " O R " gate are more than its drawbacks. Consequently, larger number of incidents wil l be detected and the average detection time wil l be reduced because there is no need to wait for the effects of the incidents to reach the detector locations at both sides. 123 Another factor to consider is whether to use any persistence check to reduce false alarms due to short-term fluctuations of the traffic parameters. Using smoothing for signals fed to the upstream classifier or selecting higher thresholds for each of the classifiers are alternative ways of tackling the problem. After a number of trials, it was found that using the persistence check unnecessarily adds to the detection time. While by smoothing and proper calibration one can get a better A D T for the same F A R . Therefore, using smoothed values for downstream measurements and higher values for the thresholds were the measures that were taken to alleviate the effects of short-term perturbations and achieve desired reliability. 7.2.4 Training Data Sets To evaluate the basic version o f the proposed system, the first series of data sets were used in which for each case an incident had occurred five minute after the start of simulation 4 4 within a 10-minute time window. The four main measurements were recorded once every 30 seconds for each individual detector. B y putting together sequential readings of the immediate detectors at either side of the incident, one can get twenty patterns per incident case for each classifier. The first ten of these patterns have been labeled as non-incident and the other ten as incident. The true number of incident labels for each pattern set should always be less than ten, but this practice was due to lack of an exact knowledge of the onset of the arrival of waves (particularly the expansion wave). A closer look at what happens after an incident will clarify 124 this and some other points. Figure 7.8 shows volume and occupancy readings as a function o f time from four selected examples. The incident in all o f the cases has occurred at T=300 seconds. A l l o f the charts have been drawn with the same scale to make it easy to compare readings of one example with another. The first readings are from the upstream detector about 560 meters away from the incident. Although the incident has occurred at 9 a.m., it has taken about 4.5 minutes for its effects to be sensed by the upstream detector. Therefore, the incident from the point of view of an observer at upstream detector position has occurred at t=570 seconds, and only the last two of the patterns should have been labeled as incidents. A similar incident that occurs at about 11 a.m. may not be sensed and is undetectable by other methods within the first 5 minutes of the incident. Fluctuations in the volume and occupancies are also noticeable, as they are quite typical of what is expected during normal traffic. This is a straightforward case as far as labeling the onset o f the arrival of the shock wave is concerned. This refers to the start of simulation after some "start up period" in which the vehicles fill the road until equilibrium of the inflow and outflow is achieved for all of the links. 125 2000 -r 1750 1500 0) 1250 E 3 1000 O > 750 500 250 0 a) Upstream of Incident Case D11A09 Volume Occupancy / / / / / » / ^ — -60 120 180 240 300 360 T i m e (sec) 420 430 540 80 70 60 50 40 30 20 10 0 600 b) Downstream of Incident Case D11A09 Volume (smoothed) Volume Occupancy (smoothed) Occupancy 80 70 60 50 40 30 20 10 0 240 300 360 Tim e (sec ) 600 2000 1750 1500 0,1250 | l 0 0 0 £ 750 500 250 0 c) Upstream of Incident Case U31A11 volume 60 120 180 240 300 360 T ime ( sec ) 420 480 540 80 70 60 40 §• 308 20 10 0 600 d) Downstream of Incident Case M22A15 (lane#1) Volume (smoothed) Volume Occupancy (smoothed) Occupancy 240 300 360 T i m e (sec ) 420 480 540 T 80 70 60 50 o 600 Figure 7.8. Some Examples from Detectors' Readings 126 The second example shows the readings from the first downstream detector of the same incident. It shows both the actual readings and those smoothed with a moving average. Since the incident is very close to the detector (about 110 meters away), it is reasonable to expect the arrival of the expansion wave in less than half a minute. However, the presence of a temporary higher volume just before the incident makes it hard to assume so until one or two more periods have passed (particularly when looking at the smoothed curve). This case is a clear example of the common problem of identifying the onset of incident effects from downstream signals. The importance of the smoothing is also evident from this figure, as the amplitude of the normal fluctuations is comparable to the changes due to the incident. However as a drawback, it can be seen that the smoothed signal both lags and is damped by the time the expansion wave has arrived at the detector. The next case shows an example where it is even harder to decide about the onset of arrival of the shock wave. The incident has occurred close to the upstream at 11 a.m. At t=360 seconds there is a substantial decrease in volume that is an indication of a shock wave. However, as conflicting evidence, the occupancy has also decreased. It is not until after the following period that the occupancy increases substantially, which is also coincident with a moderate increase in volume. Only at t=420 seconds the volume and occupancy have both changed in the expected (i.e., opposite) direction at the same time. This has been probably caused by a random decline o f traffic volume just prior to the arrival of the shock wave. N o matter what the cause is, it is very difficult to decide when to declare the pattern as incident. 127 The last example shows an unusual case where a "legitimate" false alarm is almost unavoidable. The readings are from a downstream detector that is located in the first lane when an incident occurs some 330 meters away in the second lane. The volume and occupancy readings at t=270 seconds are unusually low, and further during the last 30 seconds before t=300 no vehicle has passed the detector. This causes even the smoothed curve to become very low and signals a false alarm. Another surprising change is also observable long after the incident has occurred (and continued). The volume and occupancy at t=510 and 540 seconds reach the same levels as before the incident as i f the incident has been cleared. These examples show that defining the first time period when the effects of incidents are observed is a subjective and nontrivial task 4 5. Therefore, although it was carried out for all o f the upstream detector patterns, its result was not used in re-labeling of the patterns. Rather, it was used to estimate limits for detection rate and average detection time. These limits can not be passed by other A I D methods that work based on capturing the shock wave. A visual check of the " X X X A X X " series shows that in only 86-89% of the cases the effects wi l l be sensed on the upstream detector within the first five minutes after their occurrence. The average time that is necessary for the shock wave of these incidents to reach the upstream This is even harder to do in case of real traffic data. Obviously the better the boundaries of the classes are defined the better the expected performance of the network would be. However, as long as the decision is made in a consistent way, it should not have a significant adverse effect on the performance. This is clear both from the results of the tests done in this work and from the historically proven performance of the neural networks when dealing with noise and missing data. An additional important factor to consider is that in the problem at hand for each classifier there are only two classes the bias toward each can be adjusted by thresholds in the decision making block. 128 detectors is estimated to be about 2.1-2.5 minutes. These figures give very good indications on the performance bound, as wi l l be seen in section 7.2.5. 7.2.5 Testing Other AID Methods and Intermediate Results Although the main purpose of testing at this stage was to study the feasibility of the idea, a general comparison of the performance of other selected A I D systems with same data also provides useful information. In this section after discussing strategies used to calibrate other methods, the intermediate results will be presented. Calibration of California #7 and Claifornia#8 methods require adjustment of three and five thresholds respectively. After trying a number of suggested values from the user guideline (Payne and Knobel, 1976), it was observed that California#8 that has a check for compression waves was consistently outperforming the California#7. This means that for similar level of A D T the F A R for the California#7 was higher. Therefore, the rest of the fine-tuning was only continued with California#8. To find the best performance possible by the California#8 method, special effort was put into fine-tuning of this method. The three performance measures have to be prioritized; the key measure chosen as was discussed earlier is F A R . Then given an acceptable range or value for F A R , the adjustment of the threshold should continue until the best values for D R and A D T are found. Often this fine-tuning means finding the values such that any small change in one direction increases the F A R , while change in the other direction either doesn't improve the 129 other two performance measures or deteriorates them. Therefore, the following strategy for fine-tuning of the California#8 was used: 1. Select an acceptable number of false alarms as the lower bound. 2. Use the suggested values for the thresholds 3. Run the program for all o f the data sets and continue changing (tightening) the thresholds to arrive at the selected level of F A R . 4. Change each of the thresholds in the direction of relaxing the conditions implied by the threshold 4 6 and rerun the program. 5. Each time after step 4, recheck the previous thresholds for possibility of further relaxing the threshold and retaining the same level o f F A R . 6. Increase the number of acceptable false alarms i f necessary and repeat from step 3. Following the above steps one can find the best performance possible for the given set of data. However, these values may be thought of as the limiting upper bound for the performance. This is because everything was adjusted knowing the feature values for all o f the patterns. There is no guarantee that the same thresholds wil l be the best when new patterns are checked. Therefore during calibration, rather than a fixed number of false alarms from a limited (even though large) number of cases, one needs to use an expected F A R from the recorded data at hand. 4 6 Sometimes this means increasing the value and sometimes decreasing it. This can be decided either by examining the related condition in the decision tree or simply by trial and error. Since in this method the changes in performance measures are a monotonic function of the thresholds, therefore this strategy is very easy to be used for California methods. 130 A similar calibrating and testing approach was taken for the McMaster method. After a number of trials of the original proposed logic (Gall and Hall , 1989) using the calibration process suggested in (Persaud et al, 1990), the modified template from a later paper (Hall et al, 1993) was built and tested. Since the latter showed better performance for the test cases, the rest of the fine-tuning was only pursued with the modified template 4 7. The calibration process for the McMaster algorithm consists o f defining the mentioned template in the volume-occupancy space as shown in Figure 3.3. This template has four areas, two of which are divided in turn into two sub-areas. To calibrate the McMaster algorithm, one has to define the boundary curve and lines between these areas and sub-areas. The main curve is the parabolic line (with three parameters) that defines the lower bound of the uncongested operations. Generally, the performance is very sensitive to the parameters of the equation of this curve. The calibration was carried out following the same general strategy while using three periods of persistence check as suggested in the literature. In both methods, a station specific calibration in which calibration is done for each station or zone independently is expected to enhance the results. After a number of trials, it was observed that the D R for both methods might only increase less than 1% while the A D T may decrease by about 5% and 10-15% for California#8 and McMaster methods, respectively. 4 7 There are two versions for the modified template as shown in Figure 3.3-a and b. The first one is used for a normal station while the second one is suggested for stations affected by recurrent congestion. In the study only the first template was used since the way to define curve LQDF was not clear for the author. However, the 131 However, the performance measures presented here are based on a global calibration to make the condition the same as for the proposed system that only uses one set of thresholds. Before discussing the performance measures reported in this section, the following points should be noticed: • The detection rate is calculated over the first five minutes after the onset of incident. • When counting false alarms for the proposed system at this stage only the decisions before the occurrence of the incident in the same zone were considered 4 8. For other methods however, the alarms before the occurrence o f the incident or those after its occurrence but on the downstream part of the incident location were counted 4 9. In both cases, the denominator represented only non-incident decisions. The A D T and D R o f California #8, and McMaster algorithms along with those of the first version of U B C prototype have been plotted as a function of false alarm rate. Figure 7.9 shows these plots for the " X X X A X X " series of data. Two lines are plotted for U B C results in each graph. The lines marked as " U B C , U " shows the results for a condition that only author does not expect this to make more than a minor difference in the tests performed here considering that only in a small number of test cases recurrent congestion may occur around station#3. 4 8 This was because at this stage there was no mechanism to avoid the alarms from propagating to neighboring zones. 4 9 Since these methods seems to be more vulnerable to false alarms in upstream of the incidents, this was done to make the resulted performance measure more comparable with those of the proposed method at this stage. However, complete comparison should only be made on the results presented in Chapter 8 where all of the conditions have been applied equally to the final version of UBC AID system and the other methods. 132 upstream classifier is used and the other line represents the results when both classifiers are used. The former is plotted to be compared with the performance bound found visually. Q < 2 5 2 1.5 1 0 5 0 — — California#S — . —McMaster — - _UBC, U UBC, U&D 0.05 0.1 F A R (%) 0.15 0.2 100 — 95 £ 90 K Q 85 4-80 — — California#8 — . —McMaster — - - U B C , U UBC, U&D 0.05 0.1 F A R ( % ) 0.15 0.2 Figure 7.9. Operat ing Characteristic Curves of Various A I D methods for the Simulated Data - " X X X A X X " Series, Lane Closure Incidents The A D T for the upstream classifier lies in the range that was found by visual check o f the time taken for the effects of the shock wave to be sensed at the upstream detector location (2.1-2.5 min). In other words, the time spent by the system to be convinced that the changes 133 in the upstream parameters are due to an incident is almost zero. On the other hand, when using the downstream classifier as well, the A D T is about 0.6 min below the bound found by visual check. This implies that the idea of utilizing the reliable portion of the downstream information to detect incidents before their congestion reaches the nearest station is indeed feasible. The plots for average detection time also shows that California #8 and McMaster algorithms provide very close results. It is also easy to see that there is about half a minute difference between when the presence of the shock wave has been sensed and when these methods have triggered the alarm. It is possible to reduce this difference by applying the station specific calibration, particularly for the McMaster method, but even though small, there wil l always be a difference. The other part of Figure 7.9 shows the detection rates within the first five minutes. A similar explanation holds for these plots as well. The U B C upstream classifier lies in the 86%~89% range. Introducing the downstream classifier pushes the detection rates up by about 10%. This is because the shock wave of these cases takes more than five minutes to reach the upstream detector station while the expansion wave that has reached the downstream station was strong enough to trigger the alarm in the U B C system. The California#8 and McMaster methods show close results with one another, and with the bound found by the visual check. These graphs show the performances for cases where the incident has blocked one lane of traffic. However, the incidents from " X X X B X X " and " X X X C X X " series that represent less 134 severe incidents were also tested with all o f the methods as well. The results were similar to those of " X X X A X X " series in the sense that only the proposed system could pass the bound found visually but with a smaller margin. This on one hand confirms the feasibility of the idea for the less severe incidents and on the other hand, however, it shows that the expected contribution of the downstream classifier wil l fade away for less severe incidents. This is because the more severe the incident is, the stronger the changes due to arrival of its expansion wave will be. Fortunately, traffic management authorities obviously put a higher priority on early detection of more severe incidents. 7.3 Final Form of the UBC AID System The basic version of the proposed system only showed the general feasibility of using expansion waves independently as indicators of incident to detect them more quickly. It was only tested in the same zone as the incident because there was no mechanism to avoid alarms when the incident was in the neighboring zones. Further computer experiments also showed that a number of modifications are necessary to enable the system to use the detector signals efficiently and maintain its performance under various conditions. Therefore, after a number of trials the final form of U B C A I D system was designed and tested. Figure 7.10 shows the proposed U B C ADD system in the final form. The modifications made to each of the three stages are discussed in the following sections and the results will be discussed in the following chapter. 135 7.3.1 Preprocessing As shown earlier by the histograms in Figure 2.2, to provide an opportunity for making reliable decisions, control variables based on which the decisions are made should be selected as distinguishable as possible for incident and no-incident conditions. To increase the reliability at least two groups of problems need to be overcome: • The temporary fluctuations present in the control variables. • The variation present in the control variables as a function of time or location of the detectors. 136 The first problem was addressed in the first version of the proposed system by smoothing the downstream signals. This would reduce the width of the bell shape histograms and thus shrink the overlap region. In the case of upstream signals, this was not necessary because the histograms are farther apart and therefore the benefit does not justify the inherent delay that comes with smoothing. The second problem refers to what could be called 'robustness", that is the ability to maintain the reliability for a wide range of operating conditions. I f one considers the incident-free histogram for a certain detector in a short period (e.g., 15 minutes), the mean would be different when considering the same histogram in another period. In both cases however, a small standard deviation is expected for such a histogram. Obviously, the histogram drawn for the same location for the period of one day, would show a mean that is somewhere in between the typical means during that day. However, the standard deviation would be many times larger than the former ones because of the variations during the day. The similar widening of the histogram is expected i f one considers various locations. In other words, when the system is showing good performance in one zone, it could produce an unnecessarily high number of false alarms at some other zones or miss incidents somewhere else. There are two ways to solve the problem: • To use time and location specific calibration. • To select control variables such that they are as independent as possible from time and location. 137 The first solution has been suggested and used by many researchers. However, this not only requires much more effort to be put into calibration, it also requires incident data for all locations and times that are not always available. This would be more of a problem for methods that use statistical means or neural networks. The neural networks owe much of their ability to handle noise to the large amount of representative data exposed to them during the training process. When a sufficiently representative database exists or in the absence of other alternatives, this might be a path to follow. The second solution requires selection of the control variables such that they are affected and adapted to the changes of traffic variables. In first version, the traffic parameters were used directly (although smoothed) as input features to the networks. In the final form of the U B C A I D system however, the ratios of traffic variables to their estimated normal values have been used as the input features. The estimated normal values should represent, as close as possible, the expected values of the traffic variable being measured by the specific detector for that specific time under non-incident condition 5 0. One way to estimate these is to average the historical values for the location and time of day. This method has been used by some researchers mainly to replace the measured values in case of a faulty reading by a sensor. This method, although an option, is not necessarily a good one because a number of factors can substantially and adversely affect its expected reliability. Among such factors, one may consider the effects of the day of the week, day of the year, special occasions, and weather conditions. This is clearer when one 138 notices that about one false alarm in a thousand decisions is all that can be allowed. A better estimation would be one whose value is updated along with each measurement. In this study, a moving average of the last 15 minutes (updated every 30 seconds) was used as an estimation of the normal values. The flow of information in the preprocessing stage can be easily followed from Figure 7.10. The signals from each of the detectors are first stored in a database. The signals are then fed to a smoothing stage in which a one-minute moving average is used to smooth the signals. Both the smoothed and non-smoothed 5 1 signals along with the normal values calculated from the data contained in the database wil l be fed to the next block. In this block, for each zone the input features of the two classifiers are calculated by dividing the selected smoothed and non-smoothed signals by their respective normal values. The outcomes of this block are two sets of non-dimensional numbers whose values should be close to unity for normal conditions. In cases where the sensory measurements are missing or not valid, it is also easy to substitute a value of unity for the missing features. It should be noticed that this process is in addition and not related to the process of "normalization" or "scaling" of input features for most neural networks that is for a different purpose. This includes recurrent congestion. 5 1 Obviously for every detector station the smoothed signals are used when the decisions for the upstream zone is being made and non-smoothed values are used when the downstream zone is considered. Please notice the difference between downstream zone and downstream detector. 139 Among the eight possible data candidates to be fed to the classifiers, in a two-lane highway, only six have been used for each classifier. The selection of the signals for each classifier is discussed in the following section. 7.3.2 Classifiers The classifiers in the final form of the proposed system are different from those o f the basic version in the number of input features, in the training patterns, and in the size (as a result of the former). The differences and the reasons for them are discussed in this section. Among the four measured traffic parameters used in the U B C A I D system, not every one carries the same information content as to whether or not there is an incident. One could either use all o f the available features or select the ones that are truly being used and put aside the ones that are providing little information to increase the efficiency of the computations. In some cases, selection of more than enough features may also indirectly have an adverse effect on the results in some instances. This is because with an increase in the number of inputs the number of dimensions in the pattern space is increased. If not every part of such a space is adequately represented by the training patterns the outcome o f the network for patterns close to that neglected part in the recall stage could be very wrong. On the other hand, eliminating an input that may contain the necessary information, even i f it is in some of the cases, would deteriorate the resulted performance. 140 Genetic Algorithms (GA) have been used to both find the optimal set of inputs and to design neural networks. Genetic algorithms, inspired by the evolution and survival of the fittest provide optimization tools for many problems where conventional techniques are not applicable. G A is different from traditional optimization methods mainly because it works with coded parameters and it starts from a random population o f candidate solutions. Every individual of this initial population, or as it is called "first generation", is represented by a numerical string called "chromosome". To create the next generation, first, pairs of individuals are selected and proportionally represented based on their performance, or "fitness" as termed in G A . The selected parents reproduce the new individuals that share partially the genetic information of each of their parents. This process is done through "crossover" in which the new chromosomes are derived from splits of the parents' chromosomes. With an often-low probability some o f the chromosomes get "mutated" in which a "gene" is randomly changed. The process is repeated for the next generation while it is expected that each generation brings about better solutions or "fitter individuals". Although random selection has an essential role in this method, the information as to what the best solution should be is transferred and reinforced through higher probability that the "fitter" has to be genetically represented in the next generation. Comprehensive details of G A are presented by Goldberg (1989). The full deployment of G A to design optimal neural networks and their inputs required extensive computational power and time. However, G A was used for subsets of data and the results showed the relative importance of the input features for each case. Based on the results of these experiments, the following parameters were selected as the input features: • Speed, occupancy, and volume for detection of shock waves. 141 • Headway, volume, and occupancy for detection of expansion waves. These selections make sense noting the different role traffic parameters may play during detection o f shock and expansion waves. As discussed earlier, there is some redundancy in the information carried by volume and headway signals. When detecting shock waves, speed, and occupancy are primary features while volume and headway are of less importance and only one of them need to be used. On the other hand, while detecting expansion waves the headway and volume are as important or more important than occupancy while speed is not important. The latter because speed barely changes as a result of an expansion wave as shown in Figure 7.2-d. The speed of the vehicles after passing an incident would not be higher than speed of vehicles prior to the incident unless there has been some congestion prior to the occurrence of the incident. The other difference between the first version and the final form of the proposed system lies in the training patterns to fix a problem with the former. As stated earlier the tests of the first version were done only in the same zone as o f the incident. For example i f one considers only the upstream classifier as trained in the first version, after the alarm is triggered in the zone of incident, it may also be triggered for the neighboring upstream and downstream zones. The alarms in the neighboring upstream zones are caused by natural progression of the shock wave to the upstream and wil l be discussed in the following section. However, the alarms in the downstream are caused as a result of confusion of the shock wave and expansion wave by the upstream classifier. 142 It was mentioned that during the training process of a neural network i f the pattern space is not adequately represented by the training patterns, the output o f the network for patterns not represented could be very different from expected output. This particularly applies to the portions of such a space that require the network to extrapolate. Representing only normal and after shock traffic patterns to the upstream classifier and labeling them, as two classes would leave the condition of after arrival o f the expansion wave at the mercy of the network. Therefore, in some cases the condition after arrival of expansion wave may appear closer to that o f after arrival of shock wave rather than normal traffic. When training the networks the training patterns are divided into three groups as follows: A . Normal traffic B . After shock wave C. After expansion wave To train the first classifier, The first and third groups ( A & C) of data are used as the first class (absence of shock wave) and second group (B) is used as the second class (presence of shock wave). To better reflect the role of the classifier its name is changed to "Shock Wave Detector" as shown in Figure 7.10. The second classifier named as "Expansion Wave Detector" is trained in a similar way. In this case, the first and the second groups ( A & B) are used as first class (absence of expansion wave) and the third group (C) is used as the second class (presence of the expansion wave). In both cases the output for the first class is selected as "0" and for the second class as "1" . 143 7.3.3 Decision Making Block T h e decision making block shown in Figure 7.10, has the same role as it did in the first version but with some added conditions. These conditions are necessary to filter out as many false alarms as possible while enabling the user to set the thresholds loose enough to gain advantage o f the early indications o f incidents. A s mentioned in the previous section, the problem encountered when using the basic form o f the proposed system was having false alarms in the neighboring zones o f where incidents had occurred. These false alarms could be divided into the following two groups: • False alarms due to confusion o f waves by the classifiers (shocks detected in downstream zones or expansion waves detected in upstream zones). • False alarms due to progression o f waves to the neighboring zones (shocks detected on the upstream zones or expansion waves detected in the downstream zones). T h e main causes for the first group o f false alarms were the training patterns and as discussed in the previous section these can be easily fixed by proper selection o f the training patterns. However , the second group o f false alarms, as will be shown here, is a natural by-product o f using an " O R " gate. 144 This problem could be explained using the typical incident shown in Figure 7.4. A close look at this figure shows that the expansion wave arrives at stations #4 and #5 roughly about 0.5 and 1.5 minutes after the occurrence of the incident. It also shows that the shock wave arrives at stations #3 and #2 roughly about 1.5 and 4:5 minutes after the onset o f the incident. Therefore assuming that the specified thresholds are passed at these times, and using an " O R " gate between the outputs of the two classifiers, the incident would be detected in 0.5 minutes in zone#3. However, 1.5 minutes after the onset of the incident there would be a false alarm in zone #4 because of the output of the expansion wave detector for station #4. Similarly, 3 minutes later there would be another false alarm in Zone #2 because of the output of the shock wave detector for station #2. Both of the false alarms could be simply avoided by using an " A N D " gate, but then the detection of incident would have been delayed by one minute. Since the core concept of the proposed system was to save on detection time by using the first evidence that is strong enough and not to wait for further indications, using " O R " gate is essential. This however, could be temporarily changed to avoid the false alarms caused by progression of waves. This requires a condition to switch the " O R " gate to an " A N D " gate after the source of an alarm has been verified by the operator. This switch needs to be done for a limited neighborhood and maintained active for some time to ensure that it covers the progression of the waves. The switching only affects the detection time for secondary incidents that may occur in the neighborhood of the first incident. Although this at first may seem a disadvantage but even using the " A N D " gate the U B C method should achieve on average about the same detection 145 time as the other methods. This is clearer considering that higher speed of the expansion wave allows them to reach the detector station sooner. Most importantly, the effects on the overall A D T wil l be insignificant, because after all, incidents are rare events and even more so are secondary incidents. Other than the two groups of false alarms discussed above there are at least another group of them that require adding a number of if-conditions to the decision making block to avoid them. These false alarms occur mainly in, but are not limited to, cases where an expansion wave is not detected in an incident zone and its progression causes an alarm in the downstream zone 5 2 . Considerable time and effort were spent on analyzing and finding mechanisms to avoid this and similar types of false alarms. A n examination of the cases with this false alarm shows how they could happen. Given the random nature of traffic it is always possible that an expansion wave could be weakened temporarily by normal fluctuations. On the other hand, it is also possible that the effects of the same wave are strengthened by normal fluctuations when it arrives at the next station. The combination of these two events is not very likely but still may cause an unacceptable level of false alarm rate. This becomes clearer when noticing that about one mistake in every thousand decisions is all that is allowed when it comes to triggering the alarm. It should also be mentioned that although in majority of cases the source of the expansion wave was an Obviously if the detection first occurs in the incident zone, the alarm would be verified and consequently the switching to "AND" gate would be applied and false alarm would be avoided. 146 incident, in the rest of them the expansion wave was there for no apparent reason other than normal disturbances present in traffic. A n increase in the threshold level may seem a solution at first, but experiments showed that doing so to bring the F A R to an acceptable level, would considerably reduce or even eliminate the advantage expected by using U B C A I D method. After a number of trials a double threshold approach proved to be an effective way of avoiding most of these false alarms with minimal effects on A D T or D R . In this approach, a higher threshold rfH E represents the value above which there is enough certainty that an expansion wave exists. The other (lower) threshold fL E represents the value under which there is enough certainty that either normal condition or a shock wave exists. The values between these two thresholds represent a gray zone where none of the above statements can be made with adequate certainty. To attribute an expansion wave to an incident in zone /', both of the following conditions must be met EWDOM>Tu,E a n d EWDOi<TL,E Where, EWDOi= Output of expansion wave detector for station / (upstream of zone /) EWDOM ^Output of expansion wave detector for station i+1 (downstream of zone /) The first condition is similar to that used for the basic version while the second one ensures that no expansion wave is present in the upstream station. This is because after the occurrence 147 of an incident, traffic parameters only should be at about either normal or congested levels in the upstream of incident. Any indication of the existence of an expansion wave upstream of the zone would cause the rejection of a potential alarm. It can be clearly seen that a double standard is effectively used when dealing with expansion waves on each side of the zone being examined. A similar approach could also be substituted for the single threshold used in the basic version for shock waves. The two conditions to be met for the shock wave detector outputs are: SWDO,>TH,S A N D SWDOM<TL,S Where, SWDOi= Output of shock wave detector for station i SWDOM "Output of shock wave detector for station /+ / TH S TLS = High and low thresholds for shock wave detector respectively The above measure is also helpful when considering false alarms caused by the slowly developing compression waves and recurrent congestion. Although the latter is mainly taken care of by using the expected normal values, there are cases in which the above measure reduces F A R . Then an " O R " gate is used between the results of above conditions unless the condition for switching the gates is active in the zone. It may appear that by using the above conditions the 148 switching would not be necessary, because the alarms should not be caused by progression of waves anyway. However, experiments showed that, depending on the threshold, this is not always true and some cases escape checks (mostly in the downstream direction). Experiments also showed that it would be more beneficial to use A N D gate than select tighter thresholds. This is easy to understand when considering that any change in threshold has some, even i f low, cost while effects of using an " A N D " gate only occur in very rare occasions. It should be emphasized again that due to the random nature of the traffic no matter what conditions are selected there would always be extreme cases of false alarm and/or missed detection opportunities. The above measures were aimed at avoiding false alarms with higher probability or frequency of occurrence. It was also tried to keep the number of thresholds or parameters to a minimum. Consequently, the proposed system only requires two pairs of thresholds to be set. These thresholds need to be set after the classifiers are trained with a diverse set of training patterns. Since each classifier works independently the two pairs of shock and expansion wave thresholds act independently. This allows the user to set the thresholds by examining the expected performance measures while changing them in pairs. 149 CHAPTER 8 DISCUSSION OF RESULTS In this chapter the results of the final form o f the proposed A I D system is presented. First the results wi l l be compared to those of the California#8 and McMaster method for the second set of data series to show the advantages o f the proposed system. Later, robustness of the proposed method wil l be discussed when more detailed results are presented. 8.1 Comparison of Performances Because of the multi-criteria nature, the performance of the A I D systems can be compared in various ways. Individual figures that are sometimes published in the papers only reflect instances of the performance and are not very useful. A better way often adopted in the literature is to draw operating characteristics as discussed earlier. It consists of drawing detection rate and average detection time as a function of false alarm rate. In this section after presenting the characteristic curves, new ways of comparing the performance wil l be explored in which a different insight wil l be gained. The detection rate and average detection time are shown in Figure 8.1 as a function of false alarm rate for the U B C and other two methods. A n important point to consider when interpreting the results is that in these diagrams, the F A R is used in a pseudo-independent variable sense. The calibration parameters and thresholds are the real independent variables 150 that are set by the user. The values of F A R as well as D R and A D T will be calculated for each run of data. The critical role of the F A R puts it in the abscissa of the diagrams, but it is possible to arrive at more than one value of D R or A D T for a single F A R . This is of course, because there are more than one threshold or parameter involved. Therefore the operating characteristics curves show roughly an "envelop" for the achieved performances by connecting the best results in each case. 100 95 90 Q 80 75 70 - - - California#8 — —McMaster UBC 0 0.03 0.06 0.09 0.12 0.15 FAR (%) 4 3.5 3 c 2.5 * 2 < 1.5 1 0.5 0 - - - California#8 — —McMaster UBC 0.03 0.06 0.09 0.12 0.151 FAR(%) Figure 8.1. Comparison of the DR and ADT as a Function of FAR (XXXAXX) 151 The top part of Figure 8.1 shows the detection rate after 10 minutes from onset of incident for the range of F A R that is of interest. In this range of F A R , the California#8 has achieved a higher detection rate than McMaster and U B C methods. A visual check of the signals shows that in about 97% of the cases the shock wave has reached the upstream detector station within the 10-minute time window while the rest has left no significant effect on signals. Therefore, the California#8 has detected almost all of the detectable incidents while U B C method has detected 2~4% less incidents. The seemingly inferior results of U B C method may appear inconsistent with those presented for the basic version. However, the answer to why there is such an inconsistency and why it is of no significance wil l be discussed later. The A D T of the incidents detected within the 10-minute window is presented in the bottom part of Figure 8.1. In sharp contrast to the diagrams for detection rate, when considering the A D T , the U B C ADD has significantly outperformed the other methods. The A D T found for other California#8 and McMaster are 40-100% higher than those o f U B C method depending on the F A R and method. A visual check similar to what was done for the first series of data sets shows that the congestion caused by the incidents takes about 3 minutes to reach the upstream station. This shows again that effective use of information carried by expansion waves enables the U B C system to surpass what is a limiting bound for other methods. The operating characteristic curves are informative but do not provide a full picture for a comparison. I f A I D was the sole means of detection, then these curves were more useful but given that there are other means of detection as well, the D R curves could be misleading. The 152 value of the D R does not represent the contribution of the A I D component in the whole detection system. This is clearer considering that the values of D R and A D T are defined for a specified period of time after the occurrence of the incident, but their dependence is not observed in the operating characteristic curves. During most of the daytime, any lane-blocking incident is expected to cause a disruption strong enough to trigger the alarm of A I D methods at some point. What is important then is i f a high number of such cases are detected first by that A I D system to justify its use. To include the time element and compare the results in a more meaningful way, use of different diagrams is suggested here to provide insight into the history of detection. First, Figure 8.2 shows the number of cases detected for each time period after the occurrence of the incident is drawn for each of the three methods. In this chart and the next two charts 5 3, a fixed F A R , about 0.1% in this case, are used to make the curves comparable. Since finding exactly the same number of false alarms, when considering the 54000 decisions involved, is very time consuming, close enough F A R have been used here 5 4. It is very clear that most of the incidents detected by the U B C A I D method are detected in the second and third time-period (i.e., 1-1.5 minutes after the onset of incident). In the other methods, the detection starts from third and fourth time period and continues for next 6-10 time periods as the presence of the shock waves are sensed. The decision tree in California#8 is such that one time period is essentially used as a persistence check, while in McMaster, an observation of 5 3 Figure 8.3 and Figure 8.4. 5 4 The actual vales are 0.106%, 0.115%, 0.102% for California#8, McMaster, and UBC methods respectively. Although none of the systems is sensitive to such a small difference in this range of FAR, the FAR for UBC was intentionally selected to be lower than the others to remove any doubt. 153 congestion is ignored unless the condition remains congested for the next two periods. This causes a time lag of one time period between the curves of McMaster 5 5 compared to that of California#8 that can be easily observed. :s Detected o o o , ,—, j - - - Caifornia#8 c 60 4 •a o £ 40 o i 20 0 1 ] f « l • i # I — i — ~ ^ r '. i S V * | ^^ — ivicivtas ler 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Time Period (After Incident) Figure 8.2. Comparison of the number of Incidents Detected as a Funct ion of Time Elapsed After the Onset of Incident ( X X X A X X e ) Figure 8.3 presents the history of the A D T for the three methods and shows the dependence of the A D T values to how long the process has been considered. As seen in this figure, eventually the curves wil l asymptotically reach some value, but before then, the A D T depends on where the detection has stopped. This also explains some apparent differences between the Experiments with first series of data sets suggested that McMaster method would benefit from using at least one less persistence check. Removing the persistence check would increase the FAR, but this could be compensated by changing the calibration parameters and ending up with same FAR and better ADT (and sometimes DR). 154 comparison results presented in section 7.2.5 and those presented in this section as the former were calculated for the first five minutes after the onset of incidents. 4 T -Time After Onset of Incident (min) Figure 8.3. Comparison of the ADT as a Function of Time Elapsed after the Onset of Incident (XXXAXXe) The detection rate history for a given FAR as shown in Figure 8.4 is suggested by the author to make the most meaningful comparison between the AID methods. If drawn for various FAR it could be used as the single most informative picture of the AID system performance. As discussed in section 3.3 since many of the incidents will be detected through other means before they are detected by the AID system, the detection rate is only important when calculated for the first few minutes. 155 The Figure 8.4 clearly shows that about three-quarters o f the incident have been detected by U B C A I D within a minute and a half after their occurrence (much before the congestion is sensed at upstream station). This is while on average it has taken about three more minutes for the other methods to reach the same level of detection. It is also easy to consider an example in which, as suggested by the traffic management authorities in Seattle, the cellular calls would be made within the first 2-3 minutes. While the majority of incidents are detected by this time through U B C method, other methods have detected 30-60% less cases by this time. Time After Onset of Incident (min) Figure 8.4. Comparison of the DR as a Function of Time Elapsed after the Onset of Incident (XXXAXXe) 156 The Figure 8.4 also clarifies the apparent difference between the performances presented in section 7.2.5 and those presented earlier in this section. It is easy to see that for the first 7-8 minutes the U B C method leads the other methods while after that it marginally lags the others. From the appearance of the curves, it is reasonable to assume that using any data beyond ten minutes would not significantly change the detection rates. Given the above discussions about the role of other means of detection, it is reasonable to assume that the final D R do not represent the degree of contribution of the A I D systems to the whole detection system. Therefore, on the contrary to the D R values for the first few minutes, the final values are of no significance. 8.2 Detailed Performances In this section, more detailed results wil l be presented. They would provide a better picture of the three performance measures of U B C - A I D system as a function of time and location. In all o f the charts presented in this section the distribution o f performance measures were calculated with the set of thresholds that caused a F A R of about 5 6 0.1% when calculated for all o f the data series. The reason for this selection was to be able to include as many false alarms while remaining within the desired range of false alarm rates. Higher numbers of false alarms are needed to make the values presented for each hour or zone in F A R charts more meaningful. To maintain a consistency, the same set of thresholds was used for all the rest of charts. 157 In Top chart of Figure 8.5 the Detection Rate as a function of incident zone and lane is presented along with the average values. Each column represents 27 incident cases per lane. It shows that D R does not change much with incident zone. The detection rate in the zone#l and Zone#2 are only slightly less than the average. This is reasonable considering that as shown in Figure 5.2, 10 out of 12 incident locations in these zones carry the least volume, which at 11 a.m. is lower than 1000 vehicle/hour/lane. The middle chart of Figure 8.5 similarly shows the variations of D R as a function of incident location within the zones. The labels " U " , " D " , and " M " as shown in Figure 5.2 represents incident locations closer to the upstream station, downstream station, and the middle of two stations respectively. Each column represents 45 incident cases per lane. As expected, no significant difference can be observed among the values calculated for each column. The actual value is 0.102%. Please see footnote 54 and Figure 8.1. 158 100 -p -=• 80 4-• TO 60 DC J 40 o S 20 I Lane#1 ^Lane#2 - A v e r a g e 100 £ 80 60 = 40 20 100 ^ 80 -1 I 60 DC o 40 4 ** o o o 20 r !~ Incident Zone l i Lane#1 l | L a n e # 2 H ^ M A V& ra g 6 U M D Locat ion of Incident W ithin a Zone ^Lane#1 ]Lane#2 Average 10 11 12 13 Time of day (Hour) 14 15 16 Figure 8.5. Detection Rates as a Function of Incident Zone, Incident Location, and Time of Day The variation of the D R with time of day is shown in the lower chart o f Figure 8.5 where each column represents 15 incident cases per lane. In this chart, the columns corresponding to 11 a.m. show about 15% lower detection rates than the average, while the rest o f the columns have performed either about or above average. This is reasonable considering that at that time, the volume in many segments of the freeway is very low and therefore no significant effect would be caused by an incident. The increase in the volume, up to a certain point, increases the likelihood o f the incidents being detected virtually by all indirect methods. Consequently, a similarity between this chart and the curve showing the weighted average volumes 5 7 in Figure 8.6 can easily be seen. The chart in this Figure also shows the volumes for the freeway segments with highest and lowest values. The lowest values in this chart correspond to zone #1 and part of Zone#2 that falls between Boundary off-ramp and Grandview on-ramp. As stated above, the incidents that were simulated for 11 a.m. in this segment of freeway occur in a volume less than 1000 Veh/Hour/lane and have little or no impact on the traffic. These incidents remain virtually undetectable for all o f the indirect methods. Therefore, this value for the lane volume can be considered as the lower bound for the effective operational range as suggested by the results of the simulation. As shown in the charts of the Figure 8.5, there is no significant difference between the detection rates for various lanes. The actual detection rates for lane#l and #2 are 92.6 and 94.8% respectively. The fact that the D R of Lane#2 is slightly higher, or as wil l be shown its 5 7 To calculate a representative value for each hour, considering that volumes vary with both time and location, a weighted average value has been calculated. To calculate this value the length of each segment of the freeway with a fixed volume has been used as the weight for its volume. Obviously, the summation of all such values for all segments can be divided by the site length to find the weighted average. 160 ADT is slightly lower could be attributed to the higher degree of uniformity that can be observed in the traffic flow of lane#2. 2 5 0 0 S 2 0 0 0 - J — J I | 1 5 0 0 J 01 Average Weighted > 1 0 0 0 i E | 5 0 0 -> 0 -i 8 9 10 11 12 13 Tim e of Day (Hour) 14 15 16 17 Figure 8.6. Distribution of Highest, Lowest, and Weighted Average Volumes of the Study Site as a Function of Time of Day Figure 8.7 shows the distribution of false alarm rates experienced in various zones 5 8 and times of day. In the top chart, where each column represents 5,400 decisions, there are some minor deviations from the average level of False alarm rates. While the more perturbed flow of traffic in the first two zones may have been a contributing factor, the deviations could also be assumed as natural random variations. Furthermore, considering the small number of false alarms represented in each column compared to the number o f decisions involved, the reliability of the decisions made can be assumed acceptable. The zones refer to where the alarm is triggered and not the zone where an incident has been simulated as in other charts. 161 As opposed to the top chart in Figure 8.7, the bottom chart shows a considerable variation of false alarm rate with time of day. Particularly, the F A R at 8 a.m. is about thee times the average level. It should be noted that at this time of day, a volume of about 2100 Veh/Hour/Lane is experienced in a segment of the freeway. At such a volume, the congestion is often enough to cause frequent compression waves, which can be verified by visual check of the detectors readings5 9. Adopting the enhancements discussed in section 7.3.1 and 7.3.3 has allowed a considerable drop in the number of false alarms for this volume while maintaining a very low A D T for the entire range of volumes and locations. The level of F A R for 8 a.m., although representing only one false alarm for every 300 decisions, may be too high for operational purposes. Therefore, this volume can be considered as the upper bound for the operational range of the proposed system at this stage, though some suggestions that wi l l be discussed in section 9.2, may increase this limit. There are a number of points that should be considered on the implications from an operational point of view: • If the data sets representing 8 a.m. (that constitutes one-ninth of the data sets) is excluded, the average level of F A R would be about 30% less while the A D T and D R would remain about the same. Therefore, i f the entire range of times of day (e.g., 6 a.m. to 10 p.m.) is considered, the average level of F A R is expected to be lower while the D R and A D T is expected to remain about the same. It should also be noticed that for the range of FAR level tested (i.e., 0.03%~0.1%), the FAR figures corresponding to 8 a.m. for the other two methods were higher than UBC method. A visual check of the individual signals for the cases that had caused false alarms showed that the flow condition is very unstable, which given the chosen speed (50 miles/hour) is not surprising. Therefore a high number of incident-like patterns can be observed which depending on the method and the selected thresholds may or may not trigger an alarm. 162 During the morning and afternoon rush hours the probability o f having an incident as well as the seriousness o f its effects are higher and therefore a larger number of operators are expected to work. This in turn may increase the level of tolerance for false alarms at these times. Although there has been an emphasis on using one set of thresholds for the entire site and all times o f day, i f the latter point proves to be insufficient, then it is better to use a different set of thresholds only for the fraction of time where the volume reaches a certain limit. 0.4 0.35 0.3 025 0.2 0.15 0.1 -| 0.05 0 F A R in e a c h Z o n e A v e r a g e F A R j 1 Zone#1 Zone#2 Zone#3 Zone#4 Zone#5 Alarm Zone 0.4 0.35 -S« — 0.3 -o « 0.25 0.2 -0.15 0.1 --0.05 0 j H o u r l y F A R - A v e r a g e F A R • 10 11 12 13 14 Time of Day (Hour) 15 16 Figure 8.7. Distribution of False Alarm Rates Experienced in Various Zones and Times of Day 163 It should be noted that as opposed to D R and A D T that are functions, even though weakly, of the incident zone, location within each zone and lane, the F A R has no relationship to these factors and any variation of it should be assumed as a random occurrence. Therefore, the F A R has not been drawn as a function of these factors. Figure 8.8 presents the average detection time as a function of incident zone and location as well as time of day. A general look shows that the charts in this figure have a higher variation than charts in Figure 8.5. This is reasonable because the D R depends only on the number of detected incidents at the end of 10-minutes period irrespective of how much the detection time was, and therefore the D R should show less variation than A D T . The top chart in Figure 8.8 shows the variations by zone where each column represents 27 incident cases per lane. The first two zones that have the highest degree of change in traffic volume as well as the segment in which the lowest volume occurs show an A D T that is higher than average. On the other hand, zone #5, which has no on-ramp or off-ramp, shows the lowest A D T . In this and the other two charts, variations with incident lanes, although higher than those of D R because of the reason mentioned above, are generally o f reasonable degree. On average, the A D T for incidents in Lane#2 is about 14% lower than A D T for incidents in Lane #1. This is consistent with the D R and the fact that Lane#2 has a more uniform and less disrupted flow of traffic. 164 01 £ c o o Q 01 a re 01 > < 3 2 . 5 2 1.5 1 0 .5 0 • Lane#1 l i L a n e # 2 + A v e r a g e Zone#1 Z o n e # 2 Z o n e # 3 Z o n e # 4 Inc iden t Z o n e Z o n e # 5 o o o Q 0) O ) ra > < 3 2.5 2 •ELS 0 . 5 jLane#1 • L a n e # 2 - A v e r a g e U M D L o c a t i o n o f I n c i d e n t W h i t h i n a Z o n e Ol E u Ol Ol Q Ol UI re > < 3 2 .5 2 1.5 1 0 .5 I | L a n e # 1 I | L a n e # 2 A v e r a g e 10 11 12 13 T i m e of D a y (Hour ) 14 15 16 Figure 8.8. Average Detection Time as a Function of Location and Time of day 165 The A D T for various locations within each zone are presented in the middle chart of Figure 8.8. Each column represents 45 incident cases per lane. A s expected the " M " location where on average the incident effects have to travel the longest distance has the highest A D T . The incidents which occurred closer to the downstream station have the lowest level of A D T . The bottom chart in Figure 8.8 shows variations of A D T with time of day where each bar represents 15 incident cases per lane. When compared to the bottom chart in Figure 8.5, it shows a consistency in the fact that performance at 11 a.m. is at its lowest and it generally improves when volume increases. This is an additional evidence that while the volumes as low as 1000 Veh./hour/lane can be handled by the proposed system, lower volumes may cause a considerable increase in A D T and/or decrease in D R . Another perspective can be attained by analyzing the results based on the contributions o f the two classifiers6 0. To do this, the two charts of Figure 8.9 are presented in which each pair of bars represent 90 incidents to be detected. The top chart of this figure shows the number of incidents detected by each of the two classifiers. Whenever the detection o f an incident has been triggered by both classifiers at the same time, that incident has been counted as half for each classifier. It shows that while on general, a higher number o f incidents have been detected by E W D , the number of detected incidents by both E W D and S W D increases as the location moves closer to the respective detector station (i.e., the upstream station for S W D and vice versa). This is obviously as expected as it is to observe that a much larger share of incidents detected at location " M " are detect by the E W D . 166 o l 0) Q E 3 O E c o 33 S £ o E Q m Ol 90 80 70 60 50 40 30 20 10 0 > < 4 3.5 3 2.5 2 1.5 1 0.5 0 e g s s a B v SWD I | By EWD • A v e r a g e U M D Location of Incident Within a Zone | By SWD I | By EWD » A v e r a g e U M D Location of Incident Within a Zone Figure 8.9. Number of Incidents Detected and Their ADT for Each Classifier and Location within a Zone Similarly, the bottom chart of Figure 8.9 shows the ADT as a function of location and classifier61 by which they were detected. When averaging for each classifier, the detection time of incidents whose alarms were triggered by both classifiers at the same time has been weighted down by half for each classifier. Again, this chart shows that the EWD has been 6 0 The Shock Wave Detector (SWD) and Expansion Wave Detector (EWD) 167 more successful in achieving a lower A D T . It is also clear that the A D T for various zones when detected by E W D increase slightly with distance from downstream station. This is while in case of S W D , there is a major difference between the values representing locations " M " and " U " . The reason for both of these statements are the higher speed of the expansion waves compared to often much lower speed of the shock waves. The A D T s achieved by E W D 6 2 is more than 25% lower than those obtained by S W D . These charts provide further evidence that an independent exploitation of the information carried by the expansion wave has a significant effect on the performance of the A I D system. It is clearly shown that usage of E W D wil l increase the likelihood of detecting the incident even before the smallest effects have been sensed by the upstream station. This is in addition to the fact that the proposed architecture is such that one wave detector complements the other. It should be noted that in charts o f Figure 8.9, the values do not represent potential detection or misses by each classifier, but rather, show which one has successfully detected an incident first. One can roughly assume that using S W D and E W D in conjunction with each other is as i f using 3-4 times smaller spacing between stations without the drawbacks associated with it (i.e., higher cost and larger number of false alarms due to increased number of decisions made). If one divides the spacing between the neighboring stations by three or four, the 6 1 the value for the SWD at location "D" is not shown because it only represents one case and ceratinly is of no statistical value. 168 closest third or quarter of the spacing can be roughly assumed the detection domain of SWD and the rest that of EWD (as observed in Figure 8.9). This assumption leads to an expectation that the contribution of EWD be as much as 2~3 times of the SWD as is presented in Figure 8.10. This chart simply shows the percentage contributions of each classifier to the detection of incidents and summarizes much of the above discussions. A similar chart in Figure 8.11 shows the contribution of each classifier to the false alarms experienced for the 54000 decisions made. The false alarms are almost shared equally by each classifier. This to a high degree is arbitrarily set by the user who selects the calibration thresholds. Since the two sets of thresholds are mainly independent of each other, it is possible to determine an approximate ratio for the number of false alarms caused by each classifier. 6 2 The actual values (averaged in a sense described for charts of Figure 8.9) are 2.07 and 1.58 minutes for SWD and EWD respectively. Same numbers if averaged independently for the incidents detected by both would be: 2.10, 1.53, and 1.98 for SWD, EWD, and both respectively. By Shock Wave Detector i 30% By Expansion Wave Detector 62% Detectors 8% Figure 8.10. Percentage Contribution of the Two Classifiers to Incident Detection 169 Although the two numbers were selected about the same, the expected optimal ratio would depend on the sensitivity of the ADT (or DT for first few minutes) to changes in FAR of each classifier (around the desired operational values). A few experiments showed that for the values at hand the ratios close to unity were appropriate. By Both Detectors 4% Figure 8.11. Percentage of False Alarms caused by each Classifier 170 CHAPTER 9 CONCLUSIONS AND FURTHER RESEARCH This chapter presents the conclusions of the research, a number o f research suggestions to follow-up on this study and further enhancements of the U B C A I D system 9.1 Conclusions Through a comprehensive survey of the existing A I D methods, it was shown that despite the diversity of the approaches taken by researchers in this area, there is a certain limit for the performance of the developed systems. It was shown that through an effective use of the information carried by the expansion waves, which has been overlooked by other researchers, a significant improvement in the performance of an A I D system can be achieved. A new approach for an effective use of this information was proposed and its feasibility was demonstrated. To do this, two of the existing and "in use" algorithms were also assessed in a similar way. Using the conventional methods of presenting performance measures, the superiority of the proposed system was shown. It was also argued that the conventional methods of presenting the performances of A I D systems are not necessarily the best way to assess them and may lead to overestimation of their practical effectiveness. Therefore, rather than simple tabulations of three traditionally used performance measures, or drawings of operating characteristic curves, new historical 171 diagrams were suggested. The suggested diagrams provide information that is more relevant to the assessment o f various A I D methods. M o s t importantly, they better demonstrate the effectiveness and operational significance o f using A I D along with the other detection means available. T h e results o f the detailed analysis showed that although there are natural variations in the performance o f the U B C A I D system with operating and geometric conditions, the performance is mainly consistent. It was also shown that a wide range o f traffic volumes can be accommodated by the system while maintaining an acceptable performance. F o r volumes lower than 1000 Veh/hour/lane, the A D T and D R may start to deteriorate simply because the effects are often very insignificant. O n the other hand, volumes above 2100 Veh/hour/lane may cause too many false alarms for the system at present stage. Therefore, these two values can be considered as approximate operational limits for the proposed system at present. This covers 70-90% o f the daily traffic and represents virtually all o f the commuting traffic. 9.2 Further Research In this section, some specific areas are suggested for further research on enhancements, optimization o f the proposed A I D system and further verification o f its performance. T h e following ideas either have emerged during the course o f this study or are steps that could be taken in the continuation o f the research. 172 While the number of lanes in the proposed site was fixed, the applicability of using the U B C A I D system for a more general case requires further experiments. This is because in the proposed system, the number of inputs for each o f the two classifiers is proportional to the number of lanes. The original idea to tackle this issue is that since the inputs represent the discrepancy from a normal condition, the inputs corresponding to the non-existing lanes could simply be assumed as unity. This however, may or may not be appropriate for the transitional segments o f the highway where much of the merging takes place. I f the latter proves to be not effective enough, then more than one set o f networks could be used. Obviously, the analysis and assessment of these alternatives require proper site selection and design of the simulation models. In this study, equal spacing between the detector stations was used which may not necessarily lead to the optimum use o f the facilities. It appears that at least segments of the freeway where there are no ramps, the spacing could be larger than in the other segments. This and other scenarios can be examined with a more detailed simulated data sets specifically designed for this purpose. The traffic parameters in this study were divided by their expected normal values to obtain non-dimensional values. This procedure contributed significantly to the robustness of the system and the ability to use only one set o f thresholds for the entire site and all times of the day. To further improve this idea, it seems reasonable to take into account the expected level of noise at any given time and location as well. For example, a 30% discrepancy between the normal and 173 measured value of a traffic parameter might be considered normal at some point or certain time, while 10% could be considered abnormal at another point or time. To do this, one may use an estimate o f the expected noise level by calculating the standard deviation of the readings for the last 15 minutes. The 15-minute period stated here is only a suggestion (to be consistent with the period used for estimating the normal values) and obviously, i f the idea proves to be beneficial, the proper duration for both periods can be further examined. 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