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A simulation model of road user behaviour and traffic conflicts at unsignalized intersections Sayed, Tarek A. 1992

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A SIMULATION MODEL OF ROAD USER BEHAVIOURAND TRAFFIC CONFLICTS AT UNSIGNALIZED INTERSECTIONSbyTAREK A. SAYEDB.Sc. MN SHAMS UNIVERSITY, 1988A THESIS SUBMITTED IN PARTIAL FULFILMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF CIVIL ENGINEERINGWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAAPRIL, 1992© Tarek Sayed, 1992In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of ^C.,,iv kt. Etnetc. :v sThe University of British ColumbiaVancouver, CanadaDate^tAtx.c ON 31 ,DE-6 (2/88)ABSTRACTThis thesis describes a visual microscopic traffic conflicts simulation model for both Tand 4-leg unsignalized intersections. The objective of the model is to study trafficconflicts as critical traffic situations and understand the driver's behaviour at thesesituations. The Author rejected the use of pure gap acceptance criteria to describe driver'sbehaviour at unsignalized intersections. As an alternative, a combination of some aspectsof the gap acceptance criteria and the effect of several parameters including driver'scharacteristics such as age and sex and the waiting time are used to describe thatbehaviour. The model also investigates the effect of different traffic parameters such asvolume and speed on the number and severity of traffic conflicts. The model is uniquein so far as it stores the traffic conflicts that occur during the simulation for latter study.A graphical animation display is used to show how the conflict occurred and the valueof critical variables at this time. The model results were hypothetically validated againstprevious work in the literature and externally validated using field observations from twounsignalized intersections. In both cases the validation process proved successful.iiTABLE OF CONTENTS ABSTRACT ^  iiTABLE OF CONTENTS ^  iiiLIST OF FIGURES ^  viiLIST OF TABLES^  ixACKNOWLEDGMENT^1. INTRODUCTION ^  11.1 The Problem  11.2 Simulation of traffic conflicts at unsignalized intersections ^ 21.3 Visual Simulation Models ^  32. LITERATURE REVIEW ^  62.1 Traffic conflict techniques and road user behaviour ^62.1.2 Measures of traffic conflicts ^  72.1.3 The validity of traffic conflict techniques ^ 9iii2.1.4 Possible application of traffic conflict techniques.  ^102.2 Traffic simulation models  ^122.2.1 History and definitions  ^122.2.2 Rational of simulation models  ^142.2.3 Steps in developing Simulation models  ^162.3 Unsignalized intersections.  ^192.3.1 Terminology  ^192.3.2 The vehicles arrival ^  202.3.3 Gap acceptance criteria.  ^232.3.4 Factors affecting a driver's critical gap value  ^252.3.5 The effect of the stopped delay ^  313- THE SIMULATION MODEL^  323.1 Introduction ^  323.2 Overview of the simulation model ^  333.2.1 Assumptions ^  343.2.2 Input parameters  353.2.3 Vehicle generation ^  353.2.4 The approaching process  363.2.5 Entering the intersection  ^373.2.5.1 Factors affecting driver's critical gap value  ^383.2.5.2 The gap acceptance process ^ 41iv3.2.5.3 Conflict resolution  ^453.2.6 Model output ^  463.2.7 Some aspects of programming in GPSS/H ^ 463.3 Model Visualization ^  473.3.1 Generation of the animation files ^  484- MODEL VALIDATION^  524.1 Face validity  ^524.2 External validity ^  534.2.1 Site selection  ^534.2.2 Intersection geometry and traffic control ^ 574.2.3 Traffic conflicts observation  ^624.2.4 Observation methodology ^  624.2.5 Comparing results  645- FINDINGS ^  685.1 Relation between conflicts and traffic parameters ^ 685.1.1 Volume - Conflicts relation ^  685.1.2 Speed - Conflicts ^  735.1.3 Speed - severity of conflicts.  ^775.2 Conflicts and driver type ^  806- FURTHER RESEARCH^  817- CONCLUSION ^  83REFERENCES ^  86APPENDIX A SAMPLE MODEL OUTPUT ^  90APPENDIX B YIELD SIGN WARRANTS ^  92viLIST OF FIGURESFigure 2.1 Flowchart of the procedural elements of simulation models  ^18Figure 2.2 Step gap acceptance function ^  26Figure 2.3 Shifted exponential gap acceptance function ^ 27Figure 3.1 Delay modification function^  43Figure 3.2 Gap acceptance function  44Figure 3.3 A sample screen of the animation for a T-intersection ^ 50Figure 3.4 A sample screen of the animation for a 4leg-intersection ^ 51Figure 4.1 Site location of 156th Street and 20th Avenue intersection ^ 55Figure 4.2 Site location of Holdom Avenue and Broadway intersection ^ 56Figure 4.3 156th Street and 20th Avenue intersection geometry ^ 58Figure 4.4 Holdom Avenue and Broadway intersection geometry ^ 59Figure 4.5 Peak hour vehicle traffic volumes156th Street and 20th Avenue intersection ^  60Figure 4.6 Peak hour vehicle traffic volumesHoldom Avenue and Broadway intersection ^  61Figure 5.1 Relation between crossing conflicts and traffic volume for a T-intersection ^  70Figure 5.2 Relation between crossing conflicts and traffic volume for a T-intersection  ^71viiFigure 5.3 Relation between crossing conflicts and traffic volume for a 4-legintersection  ^72Figure 5.4 Relation between conflicts and approaching speedat Stop-controlled T-intersection  ^74Figure 5.5 Relation between conflicts and approaching speedat Yield-controlled T-intersection  ^75Figure 5.6 Relation between conflicts and approaching speedat Stop-controlled 4leg-intersection  ^76Figure 5.7 Effect of approach speed on conflicts severity for aStop-controlled T-intersection  ^78Figure 5.8 Effect of approach speed on conflicts severity for aYield-controlled T-intersection ^  79viiiLIST OF TABLESTable 2.1 Mean and standard deviation of crossing times for different drivers . . .^30Table 3.1 Mean and Standard deviation of the gap acceptance function ^ 39Table 4.1 Conflict observation schedule ^  63Table 4.2 Time to collision and risk to collision scores  ^63Table 4.3 Observed and predicted conflicts distribution 156th Street and 20thAvenue intersection ^  65Table 4.3 Observed and predicted conflicts distribution Holdom Avenue andBroadway intersection ^  66ixACKNOWLEDGMENT I would like to thank Dr. Francis P.D. Navin for his enthusiastic supervision and carefulguidance throughout the duration of this work. I would also like to thank Dr. G.R. Brownfor reviewing this thesis and for his constructive criticisms.Special thanks to Dr. W.F. Caselton who first introduced me to simulation modelling andalso to my graduate student colleagues; Abdulaziz Khayat, Chris Nutakor and Paul Deleurfor their advice and encouragement.The financial support of a research assistantship from the Natural Sciences andEngineering Research Council of Canada is gratefully acknowledged.Finally, I wish to render my most heartfelt and sincere thanks to my parents whose loveand support throughout my life has made me achieve this cherished goal.1. INTRODUCTION1.1 The ProblemTraffic engineering problems are becoming more computationally intensive due to boththe greater complexity of the problems and an improved understanding of the mechanismof the problems. This has led engineers to employ any promising advances in eithermathematical techniques or computer hardware. Three main areas seem to be emerged.The first is simulation and rule based systems which are gaining importance as computershardware capabilities increase. The second is studying extreme values (congestion orconflicts and accidents) and failure analysis as engineers gain better understanding of theengineering mechanism and the mathematical techniques required to solve such problems.The third is graphical visualization of events to improve ones understanding of theextreme values and to ease communicating results with others. A more completediscussion is given by Navin (1991).This thesis studies traffic conflicts (extreme events) at unsignalized intersections. Thethesis' objective is to gain a better understanding of the drivers' behaviour and the factorsaffecting the occurrence of conflicts. Simulation is employed to study the problem for tworeasons. The first is the uncertainty associated with human behaviour. The second is thegreat difficulty in considering all different aspects of that behaviour and the system1Chapter 1. Introductionoperation through using conventional methods.The model is unique in so far as it stores the traffic conflicts that occur during thesimulation for latter study. A graphical animation display is then used to show how theconflict occurred and the value of the critical variables at this time.1.2 Simulation of traffic conflicts at unsignalized intersections There is a considerable literature on simulation models for unsignalized intersections.However, most of these models only considered the capacity of the intersections and howtraffic volume affects the level of service and delay for the intersection. Only a fewauthors such as Cooper et al. (1976) and McDowell et al. (1983), considered simulatingtraffic conflicts at unsignalized intersections. This is surprising since it is known thatabout half of all reported injury accidents take place at or within a few meters ofintersections. The models that did consider traffic conflicts at intersections neglected todeal with driver's behaviour in depth; instead they adopted the gap acceptance criteria todescribe how drivers based their decision, and neglected some of the important aspectsof driver's behaviour such as the effect of the stopped delay on the driver's aggression.The Author's model rejected the use of a pure gap acceptance criteria to describe driver'sbehaviour. As an alternative, a combination of some aspects of the gap acceptance criteria2Chapter 1. Introductionand the effect of several other parameters are used to describe that behaviour.In practise, observing traffic conflicts requires skilled and trained people which isexpensive. An alternative to direct observation is to first utilize the results provided bya simulation modelling technique to understand the traffic situation. These models offera way of estimating traffic conflicts and also provides an in depth study of conflicts ascritical traffic events. The results of the simulation may eventually reduce the need fordirect observation of all except the most complex intersections.1.3 Visual Simulation ModelsAn old saying " A picture is worth a thousand words". A difficult problem associatedwith traffic simulation models is gaining confidence in the model output. If the model isto be used for decision making, the decision makers need to be confident that the modelis sufficiently accurate. Moreover, non-experts often experience difficulties understandingthe model results through the printed tabular output and the complicated statistics.The benefits of simulation models may be maximized if the users fully understand whatthe model represents and how it behaves. The best way of doing this is by a graphicalanimation. This graphical animation display is not only important for the model users butit is probably even more important to the programmer. There is no better way to find3Chapter I. Introductionprogramming and logic mistakes than to observe the model behaviour on the screen. Thisis particularly true for large and complex systems where finding mistakes is very difficult.Another important feature of visual simulation models is the ability to display the valueof different variables which affect the model behaviour while the simulation is running.This provides the user or the decision maker with knowledge of how these variablesaffect the model behaviour and further changes of the variables could lead to the modelbest possible performance.The benefits of visual simulation models were summarized by Bell et al. (1987) and theyinclude:1. " Situations may arise that... the decision maker may never have envisaged"(Brown 1978). A certain situation can be easily observed through visualization;whereas, the situation can be lost in the aggregate output from the ordinarysimulation.2. The pictures gives the user " The freedom to shift attention" (Rubens 1979)between different parts of the simulation.3. The picture has a " wide appeal" (Brown 1978). Users enjoy seeing a visualdisplay of the system.Ellson and Cox (1988) concluded that ' an animation is worth a million graphs'.4Chapter 1. IntroductionThese observations were in part the motivation behind developing a visual display of atraffic situation. The second motivation was to integrate more human factors into theactual interaction simulation.5Chapter 2. Literature Review2. LITERATURE REVIEW 2.1 Traffic conflict techniques and road user behaviour.2.1.1 History and Definition.The idea of near misses by vehicles or traffic conflict techniques has had a long historyin traffic safety research. Near accidents studies have been undertaken in the 1950-s byMcfarland and Moseley (1954) and Forbars (1957). The actual establishment of theTraffic Conflict Techniques (TCT) was proposed by the General Motors team of Perkinsand Harris (1967). Their objective was to define a technique to study events which; occurfrequently, can be clearly observed, and are related to accidents rather than depending onaccident data which, in many cases, is scarce, unavailable or unsatisfactory. They definedthe term traffic conflict as any potential accident situation, leading to the occurrence ofevasive actions such as braking and swerving.This definition has always been questionable and there has been a continuous debateabout it since the definition only associates conflicts with evasive actions. Researchersnoted that many accidents were not accompanied by an evasive action therefore theconflict definition should consider these kind of situations. This has led to another debateabout whether a conflict is an event or a situation. Although the early literature about6Chapter 2. Literature Reviewtraffic conflicts regarded conflicts as a potential accident situation, the definition equatesconflicts with evasive actions. Eventually, Older and Spicer (1976) suggested that a trafficconflict be defined as "a situation involving one or more vehicles where there is animminent danger of collision if vehicles movements remain unchanged". The mostinternationally accepted definition of traffic conflict is by Amundson and Hyden (1977)"a conflict is an observable situation in which two or more road users approach each otherin space and time to such an extent that there is a risk of collision if their movementsremain unchanged".2.1.2 Measures of traffic conflicts.There is a variety of observation methods developed to evaluate traffic conflicts. Ingeneral, these methods can be classified into two categories: subjective methods andobjective methods.1- Subjective methods:In the subjective methods one can find subjective terms such as "evasive action" or"sudden behaviour" as a part of the definition. These methods include considerableamount of judgement by the observer and were highly criticised by many researchers suchas Hauer (1978) and Allen et al. (1977) as the grading of severity of the evasive actionused a subjective element, which varies from one observer to another.7Chapter 2. Literature Review2- Objective methods:These methods adopted more objective measures to evaluate traffic conflicts. Hayward(1972) defined the time to collision (TTC) measure as " the time for two vehicles tocollide if they continue at their present speed and on the same path". The value of TTCis infinite if the vehicles are not on a collision course. On the other hand, if the vehiclesare on collision course the value of TTC is finite and is decreasing with time. Theminimum TTC as reached during the vehicles approach on the collision course is takenas an indicator for the conflict severity. According to this measure, a traffic conflict canbe redefined as a situation with a minimum TTC less than a certain threshold value.Hayward suggested a minimum TTC value of 1.0 second. This was criticised by Van derHorst (1983) who concluded that " the threshold value of 1.0 second is an arbitrary choiceand can depend on the type of interaction (car-car or car-cyclist) or on different speedclasses". Van der Horst (1984) used a threshold value of 1.5 sec as the minimum TTCvalue for defining a conflict between a car and a cyclist.The International Committee on Traffic Conflict Techniques (ICTCT) at a meeting inMalmo, Sweden (1983), had different teams from ten countries made observations at threelocal intersections. The TTC measure had a good performance as a conflict severitymeasure.8Chapter 2. Literature ReviewAnother objective measure, the Post-Encroachment-Time (PET), was defined by Allen etal. (1977) as " the time difference between the moment an offending vehicle passes outof the area of potential collision and the moment of arrival at the potential collision pointby the conflicting vehicle". In the first ICTCT calibration study, the PET measure had apoor performance. This poor performance of PET according to Oppe (1986) refers onlyto urban areas with mixed traffic. In a second ICTCT calibration study at a ruralsignalized intersection at Trautenfels, Austria, the PET measure had a better performance.2.1.3 The validity of traffic conflict techniquesThere has been a continuous debate about the validity of traffic conflict techniques intraffic safety. The main question is whether conflicts can predict accidents and whethercounting conflicts can be a substitution for accidents counts. Validation of conflicttechniques with regard to the number of accidents will probably always be difficult. Hauer(1975,1978) stated that conflicts can not predict the exact number of accidents becauseof the accidents random nature, but they can demonstrate the expected number ofaccidents through the product of the expected number of conflicts and the conditionalprobability of an accident given a conflict. Work by Garder (1985) and Glauz and Bauer(1985) showed that conflicts are generally as good as accidents in predicting the expectednumber of accidents. Hauer and Garder (1986) also stated that " a technique for theestimation of safety is valid if it produces unbiased estimates of the variance, which is9Chapter 2. Literature Reviewdeemed to be satisfactory".Hyden (1987) introduced the term "process validity" of traffic conflict techniques. Usingdetailed accidents reconstruction data, he compared the processes that leads to bothconflicts and accidents. He concluded that there are similarities between the events andbehaviours of these processes.The validity debate only considers the limited use of traffic conflicts as surrogates foraccidents. This narrow view, according to Grayson and Hakkert (1987), has been both anincentive to work at practical level (through attracting more researchers because of theshort term goal) and an obstacle to advance at theoretical level (because of the narrowview as accidents surrogates). If more attention is given to the validity issue of trafficconflict techniques regarding to their contribution to the study of unsafe traffic behaviour,the question of whether conflicts can be a substitution for accidents will be less important.2.1.4 Possible application of traffic conflict techniques.As mentioned earlier, accident data is often scarce, unsatisfactory, and in many casesunavailable. Traffic conflicts offer a rich source of data and a way of better understandingof how safety measures work. A summary of some of the important application of trafficconflicts are:10Chapter 2. Literature Review- a complement to accident data to help solving some safety problems, or to designnew countermeasures.- a research tool for studying road users' behaviour and as an educational tool toimprove driver's performance.- for before and after studies and short term evaluation studies where accident datais not appropriate.- to improve countermeasure design and get a better understanding of how thesecountermeasures work and how they influence road user's behaviour.It can be concluded that traffic conflicts techniques have a considerable potential in safetyresearch which will not be fully realized until the limited view of conflicts as asubstitution for accidents is changed.11Chapter 2. Literature Review2.2 Traffic simulation models2.2.1 History and definitionsThe word computer simulation means different things to different people according totheir use and objectives, but it can be generally defined as " a numerical technique forconducting experiments on a digital computer, which includes certain types ofmathematical and logical models to describe the behaviour of the system over extendedperiods of time" Shannon (1975).Digital Computer simulation modelling has a short history. The first work on digitalcomputers began in the 1930-s and was first used for simulation modelling in the 1940-s.The early simulation models dealt with problems which were expensive and dangerousto be experimentally solved such as ballistic trajectories and nuclear shielding. In 1954the first commercial digital computer became available and researchers in different areascould build simulation models.Traffic simulation models were first developed in the mid 1950-s by researchers whofound that traffic simulation models can represent stochastic situations which are toocomplex to be represented by reasonable mathematical models . The earliest computer12Chapter 2. Literature Reviewsimulation work in highway transportation was by Hillier et al. (1951) for intersections.This was followed by other simulation models such as Gerlough (1954) for freewayoperations and Webster (1958) for traffic signals phasing. Webester's traffic signal modelis probably one of the most influential models in traffic engineering as it is the foundationfor most signalized traffic delay models. The development of traffic simulation modelsgrew rapidly during the 1960-s and 1970-s. During the 1980-s, more attention was givento model improvements. These improvements included conversion to personal computers,adding optimization submodels, additional measures of effectiveness, integration ofsimulation models, and using computer graphics for the model output.For the general use of traffic engineers, many macroscopic and microscopic simulationmodels are currently available for different traffic environments. Some of them include:TRARR and TWOPAZ for rural highways, TEXAS and SIGSI1V1 for signalizedintersections, TRANSYT and SSTOP for arterial networks, and FREQ and INTRAS forfreeway corridors. Apart from these available simulation models, there is a greatopportunity for the traffic engineer to develop specific models necessary to solve a uniqueset of problems which face in daily practice.Traffic simulation models can be categorized into two main groups; microscopic andmacroscopic. Microscopic models represent each vehicle by a set of variables such asvehicle type, speed, acceleration and position then update these variables at a fixed or13Chapter 2. Literature Reviewvariable time interval. Macroscopic models handle vehicles in groups and represent trafficin terms of overall factors such as traffic volume, density, and speed.Microscopic models are often more precise than their macroscopic correspondence, largelydue to the fact that they make fewer assumptions. However, microscopic models dorequire more computer resources, but with the current advances in computer hardware,these resources are easily obtainable.2.2.2 Rational of simulation modelsSimulation models can be very powerful analytical procedures for many complextransportation problems. A summary of the main advantages of using simulationmodelling in traffic research are:Mathematical alternatives are often unavailable or limited in scope as theyincorporate simplifying assumptions which compromise the realism of theresults.Simulation models are effective in describing complex and stochasticprocesses.Using simulation, a system can be studied in real time, compressed time,or expanded time.Unsafe experiments can be undertaken without risk to the system users.14Chapter 2. Literature ReviewWhen new components are introduced into a system, simulation can beused to help foresee bottlenecks and other problems that may arise in theoperation of the system.Traffic simulation can yield valuable insight by identifying criticalvariables in the system and illustrating how these variables interact.The main reservations about using traffic simulation models are:Traffic simulation models may require some input characteristics which aredifficult to obtain.Some users may apply simulation models as "black boxes" without fullyunderstanding what these models represent.To apply solutions offered by simulation models, a lot of time and effortshould be taken to ensure that these models have been fully calibrated andvalidated.However, the majority of the reservation on using traffic simulation models can beeliminated through better understanding of their rule and where they should be applied.In conclusion, traffic simulation is not a solution for all traffic problems but can be a veryuseful technique especially in stochastic, time varying, and complex cases wheresometimes it might be the only solution to a problem.15Chapter 2. Literature Review2.2.3 Steps in developing Simulation modelsA flow chart of the procedural elements in building simulation models is shown in Figure(1.1). The Ten elements identified by Shannon (1975) are briefly explained in thefollowing paragraphs.1. Problem Formulation^The definition of the problem to be studied including astatement of the problem-solving objective.2. Model Building^The abstraction of the system into mathematical-logicalrelationships in accordance with the problem formulation.3. Data Acquisition^The identification, specification and collection of data.4. Model Translation^The preparation of the model for computer processing.5. Verification^The process of establishing that the computer programexecutes as intended.6. Validation^The process of establishing that a desired accuracy ofcorrespondence exists between the simulation model and thereal system.7. Strategic and Tactical^The process of establishing the experimental conditionsPlanning for using the model.8. Experimentation^The execution of the simulation model to obtain results.9. Analysis of Results^The process of analyzing the simulation output to drawinferences and make recommendation for problem16Chapter 2. Literature Reviewresolution.10. Implementation and^The process of implementing decisions resulting from theDocumentation^simulation and documenting the model and its use.Shannon (1975) presents more details on each of the previous steps.17Chapter 2. Literature Review(1) Problem Formulation1(2) Model Building(3) Data Acquisition1(4) Model translationr(5) Verificationr(6) Validation(7) Strategic and Tactical Planningi(9) Analysis of Resultsr(10) Implementation and DocumentationFigure 2.1 Flowchart of the procedural elements of simulation models.Source: Shannon (1975).18Chapter 2. Literature Review2.3 Unsignalized intersections. The unsignalized intersection is the most common type in road networks. Vehiclesmovements at an unsignalized intersection are controlled either by regulatory signs (Yieldor Stop) or by rules of the roads (such as first come first served). Models used to describetraffic operation at these intersections usually have three main parts: the arrival ofvehicles, the gap acceptance criteria of the minor road vehicle, and the method ofcombining these two parts into the model. A review of the terminology is useful beforeelaborating on the parts of the unsignalized intersection simulation model.2.3.1 Terminology.The essential terms needed to understand the operation of an unsignalized intersection arethe following:A gap is the elapsed time between arrival of successive major road vehicles at a specificreference point in the intersection area.A lag is that portion of a current gap remaining when a minor road vehicle arrives or inother words the elapsed time between arrival of a minor road vehicle and the arrival ofthe next major road vehicle.A lag is accepted by the minor road vehicle if this vehicle enters or crosses the majorroad before the arrival of the first major road vehicle.19Chapter 2. Literature ReviewA gap is accepted by the minor road vehicle if this vehicle crosses or enters between twomajor road vehicles compromising a gap.Stopped delay is the time that a minor road vehicle spends waiting in the queue beforebeing able to cross or join the major road stream.A considerable amount of research has been undertaken to investigate the statisticaldifference between the acceptance distributions of gaps and lags such as Wagner et al.(1965) and Polus (1983). However, no definite conclusion for that has been obtained andin the majority of the models dealing with gap acceptance criteria this statisticaldifference is ignored.2.3.2 The vehicles arrival.The arrival process includes choosing the traffic headway distribution which may beeither deterministic or probabilistic in nature. The choice of the headway distribution fora certain road mainly depends on the flow condition of that road. Some of the applicabledistributions are; negative exponential, shifted negative exponential and Erlang. Gerloughand Harber (1978) has a more complete description of these distributions. The followingis a brief discussion of the basic elements of these distributions.1- Negative exponential distribution.This distribution, which follows the Poisson process, assumes a random arrival rate of20Chapter 2. Literature Reviewvehicles. If X is the arrival rate, the cumulative distribution function of the negativeexponential distribution may be written as:P (hst) = 1 - e -Ar = 1 - e -6with the probability density functionf (t) = A e -xtwith mean and variance equal to= 1/A02^1/A2The negative exponential distribution can only be applied to situations with low trafficflow and where the vehicles speeds are independent. This implies that there is thecapability of overtaking.2- Shifted negative exponential distribution.As small time headways are very unlikely to occur, a situation possible with the negativeexponential distribution. It might be more realistic to introduce some minimum allowableheadway to the negative exponential distribution. This can be achieved by shifting thenegative exponential distribution by a fixed time interval c. The cumulative distributionfunction of the shifted exponential distribution may be written as:^P(h0 = I - e-W-010-0^for tc21Chapter 2. Literature Reviewwith the probability density function{0fit) = 1 e -w-00-0]t-cand with mean and variance equal tot<ct2ct = 11A,Q2 = 6-023- Erlang distribution.In the shifted exponential distribution the probability of headways less than c is equal tozero. The Erlang distribution gives a low probability for small headways but not zero.Thecumulative distribution function of the Erlang distribution can be written as:k-1nP(list) - 1 -^E ^n-O n!The probability density function of the Erlang distribution can be written as/(t) = A C A' (At)k-1(k-1)!22Chapter 2. Literature ReviewIf k=1 yields the negative exponential distribution.Both the shifted exponential distribution and the Erlang distribution can be used forrepresenting medium flow conditions, but when there is a significant amount of vehiclesinteraction then the vehicles should be generated in bunches (almost constant headways).2.3.3 Gap acceptance criteria.The gap acceptance criteria is used to describe how minor road drivers decide to join orcross the major road traffic at unsignalized intersections. A number of gap acceptancemodels have been developed . These models assume that drivers at the minor road decidewhether or not to join or cross the major road according to the size of the gaps (lags).The size of the gap (lag) can be expressed in either distance or time measures. Variousstudies [such as Cooper et al. 1976] have indicated that drivers base their decision on timegaps rather than distance gaps. Three main gap acceptance models were used to describethat gap acceptance behavioral of drivers. These models are: fixed critical gap, consistentbehaviour and inconsistent behaviour. The following is a brief discussion of the models.1- Fixed critical gap:The fixed critical gap concept assumes that there is a minimum (critical) gap (lag)acceptable to all drivers at all times. Drivers accept gaps (lags) greater than or equal tothis critical gap and reject all others.23Chapter 2. Literature Review2- Consistent behaviour:The consistent behaviour model assumes that there is a minimum gap (lag) acceptable toa driver at all times. All gaps (lags) smaller than this critical gap (lag) will be rejectedand all gaps (lags) larger then this critical gap (lag) will be accepted. This critical gap(lag) is considered fixed for a given individual and has a distribution over the population.[Ashworth 1968,1970; Ramsey 1973].If C is the driver critical gap, the gap acceptance function, a(t) for this kind of behaviourcan be expressed as:tsCa(t) = {01^t>CWhere a(t) is the probability of accepting a gap of size t.The graphical representation of this function is shown in Figure 2.2.3- Inconsistent behaviour:The Inconsistent behaviour model assumes that each driver has a variable critical gap(lag). The driver might accept a certain gap (lag) on certain occasions and reject the samegap (lag) size on other occasions. This might lead to the driver accepting a gap (lag)shorter than one he had previously rejected. This variable critical gap (lag) can bedescribed by some distribution (usually normal or log-normal) such that the samedistribution can be applied to each driver. [Ashworth 1975,1977]24Chapter 2. Literature ReviewAn example of a gap acceptance function, a(t) describing this kind of behaviour is:«(t) = 1 01-exp[-P(1-T)]^tsT t>Twhere (3 and T are constants for a given driver and which vary over a population ofdrivers. According to this function the probability of accepting gaps (lags) less than thethreshold value T is zero and this probability is increasing as t increases beyond T. Thegraphical representation of this function is shown in Figure 2.3.It is apparent that the real drivers behaviour is somewhere between the last two models.The second model considered the variability between individuals, which is a well knownaspect of all human behaviour. The third model considered the variability withinindividuals which may refer to the degree of concentration and the driver mode at thedecision time. However, it is known that the variability between drivers is much higherthan the variability within a driver. Therefore, the second model seems to be moreadoptable. A more complete discussion is given by Ashworth and Bottom (1975,1977).2.3.4 Factors affecting a driver's critical gap value.Many factors have been found to affect the driver's critical gap value including the typeof traffic control (Yield or Stop), the approaching speed, and the driver characteristics.25Chapter 2. Literature ReviewFigure 2.2 Step gap acceptance function(Consistent driver behaviour)26Chapter 2. Literature Review0.80.8a)u 0.7GSo_U1) 0.8UCuii; MbAt:11Cu 0.4.020.0.30.20.1 I1^2^3^4^a^s^7^a^a^10Gap Size t (seconds)Figure 2.3 Shifted exponential gap acceptance function(Inconsistent driver behaviour)Source: Ashworth et al. (1975)27Chapter 2. Literature ReviewThe type of control is important in drivers' decision. At Stop controlled intersections,drivers usually start from a stop condition, while at Yield controlled intersections somevehicles start from a low speed. It will obviously take the drivers starting from stopcondition longer to complete their manoeuvre. This leads to drivers accepting shorter gaps(lags) at Yield controlled intersections than those accepted at Stop controlled intersections.The approaching speed has an important effect as well. Drivers accept a gap (lag)according to its size and their confidence that this gap (lag) will remain stable duringexecuting their manoeuvre. As the approaching speed increases, the drivers confidenceabout the stability of the gap (lag) decreases and consequently they become moreconservative in their accepting decision. Cooper (1976) indicated that the gap size whichwould be accepted by a driver is related to the approach speed. He also suggested thatthere are errors of judgment associated with vehicles travelling with speeds different fromthe mean speed.The driver's characteristics such as age and sex have a significant effect on the gapacceptance behaviour. The data reviewed by Cooper (1976) indicated that younger driversgenerally accepted shorter gaps and are more consistent in their driving behaviour thanolder drivers. Cooper also indicated that female drivers are often more cautious than maledrivers in most traffic situations.28Chapter 2. Literature ReviewDarzentas et al. (1980) analyzed an unpublished data by Traffic Engineering and Controlon crossing times of different drivers. The mean and standard deviation of this data aregiven in Table 2.1.The values in Table 2.1 indicate that young male drivers have the shortest crossing times.Both young male and female drivers have much smaller standard deviation than olddrivers of the same sex. This means that young drivers are often more consistent in theirdriving behaviour than old drivers. Darzentas et al. (1980) also found that female driverswere involved in fewer conflict situations than male drivers.Wennel et al. (1981) studied the gap acceptance behaviour of men and women drivers atfour unsignalized intersections. They found that the median accepted gap for womendrivers are longer than that for male drivers in all situations. They also found that womendrivers were less involved in traffic conflict situations then male drivers.29Chapter 2. Literature ReviewClass Mean(seconds)Variance(seconds)Young males 2.48 0.035Old males 3.10 0.254Young females 3.42 0.065Old females 3.38 .121Table 2.1 Mean and standard deviation of crossing times for different drivers.(Source Darzentas et al. 1980)30Chapter 2. Literature Review2.3.5 The effect of the stopped delayThe value of the stopped delay significantly modifies the driver's gap acceptancebehaviour. Wagner (1965) introduced the term "pressure of traffic demand" which mayrefer to the pressure that the driver is exposed to after suffering delay. He found that thistraffic demand had a very significant effect on drivers behaviour. Ashworth (1977)divided the gaps presented to drivers into two categories: those gaps which werepresented to drivers who had been waiting at the head of the queue for less than 8seconds; and those presented to drivers who had been waiting at the head of the queuefor more than 8 seconds. He found that the proportion of gaps accepted increased withincreased waiting time. Another study by Adebisi et al. (1989), concluded that driversshowed significant changes in their gap acceptance behaviour when their stopped delaytime exceeded the range of 25-30 seconds, as they began to accept shorter than normalgaps.This can be explained by the fact that drivers are more relaxed and less sensitive to gapswhen they suffer minimal delay, while they are more alert and more sensitive to gapswhen they suffer higher delay. The result is that drivers tend to accept shorter gaps astheir waiting time increases.31Chapter 3. The Simulation Model3- THE SIMULATION MODEL.3.1 IntroductionA traffic conflict simulation models was built for both T and 4-leg unsignalizedintersections. A personal computer version of the discrete event simulation languageGPSS/H was used. GPSS/H is an enhanced version of the IBM mainframe computersimulation language GPSS (General Purpose Simulation System).GPSS/H was preferred to procedural languages (such as PASCAL and FORTRAN) inbuilding the model. Most of the simulation models built in procedural languages use theso-called fixed-time-step method (update all the variables in the system after each timeunit) rather than the discrete event method (updating the simulation clock to the nextevent time). Hogeweg (1978) has shown that discrete-event models are clearer and easierto develop than fixed time step models, particularly when using a capable simulationlanguage. For example the automatic maintenance of the built-in floating point simulatedclock enables the programmer to deal with very close events which might differ in timeby only a small fraction of a second without needing a very small time step.The basic elements of GPSS/H models are blocks and transactions. Transactions aredynamic entities which move from one block to another. Blocks can be considered asactions or events that affect the transactions and other system entities. In addition to32Chapter 3. The Simulation Modeltransactions, there are other classes of entities such as statistical, computational andresource entities. A full description of these elements is found in Schriber (1974).For example, a transaction can represent a vehicle which arrives to the model through the"GENERATE" block, joins a queue of cars through the "QUEUE" block, and departs themodel through the "TERMINATE" block. While transactions are moving through themodel, statistical entities (e.g. queues and tables) may be used to collect statisticalinformation, computational entities (e.g. variables and functions) can be used to performcertain computations, and resource entities can be used to represent limited capacityresources.3.2 Overview of the simulation model The simulation model developed for this work differs from the other simulation modelsof unsignalized intersections. Most of these models only considered the capacity of theintersection and how traffic volume affects the level of service and delay for theintersection. The main objective of the current model is to study traffic conflicts ascritical traffic situations and understand the driver's behaviour at these situations. Themodel also investigates the effect of different traffic parameters on the number andseverity of traffic conflicts.The model is microscopic (vehicle by vehicle simulation model) since it deals with the33Chapter 3. The Simulation Modelindividual vehicles as they approach, go through and depart the intersection. Events forvehicles in the model include:1. Vehicles generation2. Approaching the intersection3. Entering the intersection4. Conflict resolution and departureBefore proceeding to the discussion of each event, the model's main assumptions andinput parameters are introduced.3.2.1 AssumptionsThe basic assumptions of the model are listed below:No overtaking or lane changing is allowed at the intersection.An isolated intersection (the effect of nearby intersections is notconsidered).All drivers have an unobstructed view of the intersection.There is no pedestrian interference.All drivers must maintain at least a minimum headway between theirvehicle and the vehicle in front.All drivers looking for an acceptable gap have perfect knowledge aboutthe movement of vehicles having higher priority, and fully understand the34Chapter 3. The Simulation Modelrules of the road.3.2.2 Input parametersThe important input parameters to the model include:- Traffic volumes of all traffic streams.- Percentage of heavy vehicle traffic in relation to the total traffic volume.- Type of the intersection control (Yield or Stop).- Speed limit on the major road.- Percentage of each driver type in the drivers population.- Number of lanes in both major and minor roads.- Total simulation time.Several other input parameters such as: move-up time, minimum allowable headway,turning speed of vehicles, and maximum queue lengths are held constants in the model.It is possible to change the values of these parameters between simulation runs.3.2.3 Vehicle generationThis sections explains how vehicles are introduced to the simulation model. A negativeexponential distribution is used to generate vehicle headway about the average headwaycalculated from the traffic volume. A value of 2.0 seconds is used as a minimum35Chapter 3. The Simulation Modelallowable headway between vehicles in the same lane. If the generated headway is lessthan the minimum allowable headway, it is set to the minimum. In this case, the vehicleis considered a member of a platoon. The model uses a random number generator anda shifted exponential function to produce the required headway. Due the variability of therandom number generator, the actual flow rate generated by the model may differ fromthe required one. This is solved by calculating the flow rate generated by the model eachfour minutes. The difference between this flow rate and the required one is calculated andthen used to adjust the average headway used in the GENERATE block of the model.Each vehicle transaction has a number of parameters used to hold the necessaryinformation associated with the vehicle such as the vehicle type, the vehicle direction andthe driver type. This is achieved by using a random number generator to test a discretefunction containing the different function values and their corresponding cumulativefrequencies. Some parameters are also used for programming purposes; such as keepingthe instantaneous speed of the vehicle, the driver's critical gap, and the stopped delayvalue.3.2.4 The approaching processAfter the vehicles are generated, a lane selection process is used to ensure that vehicleswill reach their desired destination. After a lane is selected, vehicles try to proceed andenter the intersection. The minor road consists of two sections; the approaching section36Chapter 3. The Simulation Modeland the queuing (decelerating) section. At the approaching section vehicles have smallerspeed than the desired speed, as they are preparing to what is called "negotiating theintersection". The queuing section is the location in which vehicles decelerate and in somecases have to stop according to the number of vehicles in the queue and the type ofintersection control. Vehicles on the major road are either free movers or a platoonmember. Free mover vehicles can have their desired speed (controlled by the speed limit).The speed of all platoon members is the same as the speed of the platoon leader.3.2.5 Entering the intersectionMajor road vehicles are assumed to be unaffected by minor road vehicles, so they canproceed and enter the intersection directly without any speed change. In some situationsvehicles on the major road have to decelerate or stop as other major road vehicles in thesame lane are attempting to turn into the minor road.Minor road vehicles have to find a suitable gap (lag) to join or cross the major road. Ifthe intersection is Stop-controlled, vehicles have to come to a complete stop beforelooking for a suitable gap (lag). In the case of a Yield-controlled intersection, minor roadvehicles may proceed and directly enter the intersection if they can find a suitable gap(lag). The minor road driver decision wether the gap (lag) is suitable or not depends onits size compared with his critical gap.37Chapter 3. The Simulation Model3.2.5.1 Factors affecting driver's critical gap value1. The driver typeAs discussed before, drivers' characteristics such as age and sex have a remarkable effecton driver behaviour. Female drivers tend to accept longer gaps than male drivers. Theyare also less involved in traffic conflicts situations than male drivers. Young drivers areoften more consistent in their driving behaviour than old drivers.The model considers four types of drivers: young males, young females, old males, andold females. The model uses a truncated normal distribution gap acceptance function.Based on the work by Darzentas et al. (1980) and Polus (1983), the values in Table (3.1)were chosen for the mean and standard deviation of the gap acceptance function for eachgroup. The model allows these values to be changed with any other input values.The higher the mean of the gap acceptance function the more cautious the drivergroup is. The higher the standard deviation of the gap acceptance function the lessconsistent the driver group is. The value of mean and standard deviation of the gapacceptance function is considered to be equal for both merging and single lanecrossing manoeuvres.38Chapter 3. The Simulation ModelGroupYield Control Stop ControlMean(seconds)Std. Dev.(seconds)Mean(seconds)Std. Dev.(seconds)Young males 4.0 0.75 5.0 0.75Old males 4.5 0.85 5.5 0.85Young females 5.5 1.00 6.5 1.00Old females 6.0 1.25 7.0 1.25Table 3.1 Mean and Standard deviation of the gap acceptance function39Chapter 3. The Simulation Model2. Number of lanes being crossedNumber of lanes or traffic streams being crossed in the manoeuvre affects the criticalvalue of drivers. Based on the gap acceptance values provided by the Highway CapacityManual, a correction factor of 0.25 second is added to the critical gap value for each extralane being crossed.3. The vehicle typeHeavy vehicles requires about 30% larger critical gaps than cars because they accelerateand decelerate at slower rates than passenger cars.4. The Stopped delaySeveral researchers, Wagner (1965), Ashworth et al. (1977) and Adebisi et al. (1989),have indicated that drivers accept shorter gaps as their stopped delay time increases.Based on information from those authors the following stopped delay modification factoris used to alter the driver critical gap value:DL eD - QD+DL + C40Chapter 3. The Simulation ModelWhereOD = stopped delay modification factorDL = the delay value after which driver behaviour begin to change.QD = the stopped delay value (seconds)C = constant value.The value of DL and C were chosen 27, 0.5 respectively. These values were obtainedafter examining the data presented by Adebisi et al. (1989). Tudge et al. (1988) suggesteda similar function. They used a value of 8 seconds for the delay value after which driversbegin to accept shorter gaps based on the observations reported by Ashworth (1977).However, Ashworth only considered the time drivers wait as the head of the queue andnot the total delay. Adebisi(1989) suggested a total delay value of 25-30 seconds afterwhich drivers begin accepting shorter than normal gaps , this idea was used in thesimulation model. The Function is shown in Figure 3.1.3.2.5.2 The gap acceptance processThis process takes places when a vehicle has to cross or merge with other trafficstreams. Different traffic streams have different priority levels according to the rules ofthe roads. Generally, major road vehicles have a higher priority than minor road vehicles.Straight ahead major road vehicles also have a higher priority than turning left or rightmajor road vehicles. Each vehicle is assigned a primary critical gap value by testing the41Chapter 3. The Simulation Modelgap acceptance function according to the driver type and the intersection type of control.The primary critical gap value is modified according to the vehicle type and the numberof lanes to be crossed. Vehicles trying to cross or merge wait for a gap in the conflictingtraffic stream (streams) greater than or equal to their critical gap. The critical gap valueis obtained by multiplying the primary critical gap with the delay modification factor OD.The delay modification factor has an initial value of 1.5 when the vehicle faces no delayand this value decreases as the vehicle's stopped delay increases with a minimumtheoretical value of 0.5 when the vehicle faces infinite delay (Figure 3.2). The modelassumes that no driver will accept a gap that he/she thinks will certainly lead to acollision. Therefore, a minimum acceptable gap (G C i) is used. If the critical gap valueis less than the minimum acceptable gap, it is set to the minimum. A value of 2.5 secondsis used as a minimum allowable critical gap value based on the data provided by Wennelet al. (1981).Vehicle drivers who decide to enter the intersection are assigned a single lane manoeuvretime. This time is sampled from a truncated normal distribution function. The mean andstandard deviation of the function depend on the driver type (Darzentas et al. 1980). Thesampled manoeuvre time is then corrected according to the number of lanes to be crossedand the vehicle type.420.8Chapter 3. The Simulation Model1.61.40.6drivers begin accepting shorter gapsIv^I 0^20^40^60^80^100^120^140Stopped delay (seconds)Figure 3.1 Delay modification function43!I^,^i^I^1 digGc (seconds)Chapter 3. The Simulation ModelFigure 3.2 Gap acceptance functionChapter 3. The Simulation Model3.2.5.3 Conflict resolutionA conflict occurs when a driver decides to execute a manoeuvre which put him/her inrisk of collision with another vehicle. Conflicts in this model are classified into twogroups:Within the intersection conflicts, which result from conflicting vehiclesentering the intersection at close times and can mainly be divided intocrossing and merging conflicts.Rear-end conflicts which result from conflicting vehicles leaving theintersection through the same lane at close times intervals.The model uses the time to collision (TTC) as a measure of traffic conflicts. The TTC isdefined as "the time for two vehicles to collide if they continue at their present speedsand on the same path". The model first estimates whether the vehicles are on collisioncourse or not. If the vehicles are on collision course, the TTC value is calculated andcompared with the threshold value of 1.5 seconds. If TTC is less than or equal to thethreshold value the model records the conflict, its type, location, and the TTC value.There are basically three conflict types: crossing; merging and rear-end conflicts. Thelocation defines the two conflicting traffic streams from where the vehicles originated.The TTC value represents the conflict severity. The smaller the TTC value the more45Chapter 3. The Simulation Modelsevere the conflict. Conflicts with 'FTC value less than 1 second are usually consideredto be severe conflicts.3.2.6 Model outputThe main output statistics of the model is included in the file "OUTPUT.LIS" which isproduced with each simulation run. These statistics include:1- The input and generated traffic volumes for each direction.2- The average vehicle delay for each queue along with the average and maximumqueue contents.3- The total number of conflicts, their locations and the TTC values.A sample of the file "OUTPUT.LIS" is given in appendix A.3.2.7 Some aspects of programming in GPSS/HAlthough using GPSS/H has several advantages because of the many well tested built-incapabilities, it does not provide a very important feature which is the interprocesscommunication (parameters of one transaction is not readily available to othertransactions). This feature is very important for traffic simulation models to allow forvehicles interaction. Two methods can be used to overcome this problem. The first isusing global variables to hold data belonging to a certain transaction. This method is notefficient from a programming point of view, especially in large models where many46Chapter 3. The Simulation Modelglobal variables would be needed. The second is using the technique provided by Atkins(1980) which he referred to as "Atkins chain". In this technique, vehicles transactions aresplit (a copy of the transaction is obtained with the same parameters values) to be insertedinto a user chain. Other vehicle transactions can check the parameters values of the splittransaction through the Boolean-variable operand in the "UNLINK" block. The lastmethod is used in the model.Many other programming ideas in GPSS/H were developed in the model such ascalculating the gap (lag), adjusting the generated flow rate, handling acceleration anddeceleration and identifying conflict situations.3.3 Model VisualizationThe visualization process is a very important part of this model. Its objective is to showhow the model is behaving at extreme values, that is during traffic conflicts. This viewgives a better understanding of these critical situations and the parameters affecting theiroccurrence without having to view many average events.A general purpose system animation software for the IBM PC called "PROOF" is usedto provide this graphical representation of the simulation events. PROOF is generalpurpose for two reasons. First, it is independent of any simulation or programminglanguage. Second, the flexibility of its animation command set allows animation of a wide47Chapter 3. The Simulation Modelvariety of systems in many different ways.Two files are needed to run a PROOF animation. The first is the animation trace filewhich contains the sequence of timing information and other commands that make theanimation happen. The second is the layout file which contains all the background textand graphics for an animation. The animation trace file is generally written directly byan executing model or program designed to generate syntactically correct PROOFcommands. The layout file is created either by the graphical tool provided by PROOF (asthe case of the current model) or other programs such as CAD programs.3.3.1 Generation of the animation filesIn addition to the "OUTPUT.LIS" file, two other files are produced during the simulationrun. The first is the animation trace file (*.ATF) which contains the animation commandsfor the whole simulation time. The second is the presentation file (*.PSF) which containscommands for the animation of the times at which traffic conflicts occur.The animation trace file is generated during the simulation run and its commands areconnected with the model simulation blocks. For example, when a transaction whichrepresents a vehicle is generated through the "GENERATE" block, the model writes ananimation "CREATE" command to create the object representing the vehicle and thegeneration time to the animation trace file. The model also writes the values of important48Chapter 3. The Simulation Modelvariables affecting drivers' decision such as; the delay value, the presented gap (lag) size,and the driver critical gap to the animation trace file to be continuously displayed duringthe animation process.The presentation file is generated after the simulation run ends. The model stores thetimes at which traffic conflicts occur and uses these times to write the presentation file.Conflicts are viewed one at a time. The animation lasts one minute for each conflict 30seconds before the conflict and 30 seconds after. The user is able to jump or go backthrough these conflicts using the "+" and "-" keys. The following information is shownwith each conflict:- The driver type- The vehicle type- The primary critical gap- The stopped delay value- The driver critical gap- The conflict type- The TTC valueTwo sample screens of the animation of both T and 4-leg intersections are shown inFigures 3.3 and 3.4.49Chapter 3. The Simulation ModelSTOP CONTROLLED T-IU•ICTION1 SIMULATIONCONFLICT STUDYCMC11:1=0cimp r^Mane ouver inq^vehiclecritical ^g rip^4.68MA LEYOUNGC ONF LICTV ehicle^ CAPQueue dela ,/ 2 1.E.3 P rimaryc r Weal 90PCritical yap 4.81 Clposite^gap(lag)Queue delay 31.80Critical^gap 8.17Major road going laq 3.13 Conflict^# 1Conflict^t)ipt,-..• CROSSINIMajor road coming lag 0.00^ TTC^value 1.47Figure 3.3 A sample screen of the animation for a T-intersection50 Majc.r road going I a a • al ajor road corning lag 10.6 e1 Se ST.0ru•' u t/C FR4.63L-1FEH AL01111C1^ (ZENOConflictDri , .. , er typeVehicle t:::)pe-Primaryic alQueue d.-laCritical c.14-apConflict *Conflict typeTTC value2HEROIN/01.3690 PMoneouvering^hiCiPrimary critical gapQueue delayCritical gap3. E'1.00• 7 CIChapter 3. The Simulation Model1-1 - Le9 Uni9naIiz edI Fite' rs.^C i^S I in LI la -l- ianFigure 3.4 A sample screen of the animation for a 4leg-intersection51Chapter 4. Model Validation4- MODEL VALIDATION.Validation is an essential part in building any simulation model. Before a model can beapplied, it has to be shown that the model is both logically correct and adequatelyrepresenting the modeled system. An accepted definition of validation is " the process ofassessing the extent to which a test or instrument measures what it purports to measure"Grayson and Hakkart (1987).There are several philosophical views on simulation model validation. After examiningmany of these views, three approaches were used for the validation process of the currentmodel. The first is called the face validity. This is concerned with whether the modelseems to behave correctly. The second is the hypotheses validity, which determineswether the model results agree with other work in the literature. The third is the externalvalidity which looks at the relation between the model results and field observations ofthe system. Both face and external validity are discussed in this chapter while hypothesesvalidity is left to the next chapter on findings.4.1 Face validity. This type of validation was achieved by observing the model animation. Animation allowsobservation of the behaviour of individual vehicles at the intersection to decide if thevehicles behaviour is reasonable. Also, different model variables are viewed during52Chapter 4. Model Validationthe animation and these show the internal interaction between different model entities.Researchers such as McCormick et al. (1987) and Thomasma et al. (1991) indicated thatthe visualization process is a very important part in the model validation. Face validityprovides more trust in the model and ensures that the model is logically correct.4.2 External validity. This type of validation is achieved through comparing traffic conflicts observed at certainunsignalized intersections with traffic conflicts predicted by the model for theseintersections for the same period of time.A study of traffic conflicts at several intersections in the greater Vancouver area wascarried out by G.D. Hamilton & Associates Consulting LTD. The data of traffic conflictsfor two intersections were supplied from this study and used with the permission of theCity of Vancouver, The City of Burnaby, Road Safety Research of the InsuranceCorporation of British Columbia and G.D. Hamilton & Associates Consulting LTD. Thesedata were used to validate the simulation model.4.2.1 Site selection.The majority of the unsignalized intersections covered by the local conflict studies53Chapter 4. Model Validationincluded complex layouts which do not meet two basic intersection types used in thisanalysis. Only two intersections found to be suitable for the validation process, both are4-leg intersections. The model limitations were negligible grades, good visibility andsimple layout. The site locations intersections are shown in Figures 4.1 and 4.2 .54Chapter 4. Model ValidationFigure 4.1 Site location of 156th Street and 20th Avenue intersection.Source: G.D. Hamilton & Associates Consulting LTD. conflict study report.55Chapter 4. Model ValidationFigure 4.2 Site location of Holdom Avenue and Broadway intersection.Source: GD. Hamilton & Associates Consulting LTD. conflict study report.56Chapter 4. Model Validation4.2.2 Intersection geometry and traffic control.The first intersection, 156TH street and 20TH Avenue have four , one lane approacheswhich intersect at approximately 90 degrees. All four approaches permits left turn,through and right turn movements. Gradients on all approaches are negligible. Theeastbound and westbound approaches on 20th Avenue are controlled by STOP signs.Crossing sight distances and stopping sight distances for all traffic movements areadequate. The overall intersection geometry is illustrated in Figure 4.3.The second intersection, Holdom Avenue and Broadway consists of four approaches withthe two roadway intersecting at approximately 75 degrees. The grades are considerednegligible on all directions. Sight distances are adequate for all traffic movements. Theintersection configuration is shown in Figure 4.4. The northbound approach leg consistsof two lanes for left-turn, through and right turn movements. The northbound exit legconsists of a single lane. The southbound approach leg consists of a single lane for left-turn, through and right-turn movements, while the exit leg consists of two lanes. Theeastbound and westbound approach traffic movements on broadway are controlled bySTOP signs. In addition to the STOP signs on broadway, southbound left-turn movementson Holdom avenue are restricted between 0700 hours and 0900 hours, Monday throughFriday. The peak hour traffic volumes of the two intersections are shown in Figures 4.5and 4.6.57^i100mSTOP AHEADSIGNSTOP AHEADSIGN100mChapter 4. Model ValidationFigure 4.3 156th Street and 20th Avenue intersection geometry.58Chapter 4. Model ValidationFigure 4.4 Holdom Avenue and Broadway intersection geometry.59Chapter 4. Model ValidationFigure 4.5 Peak hour vehicle traffic volumes156th Street and 20th Avenue intersectionChapter 4. Model ValidationFigure 4.6 Peak hour vehicle traffic volumesHoldom Avenue and Broadway intersectionChapter 4. Model Validation4.2.3 Traffic conflicts observation.Traffic conflicts were recorded at both intersections by observers trained in the trafficconflict observation technique. A total of 32 man-hours of conflicts survey data wascollected for each intersection. The traffic conflict survey schedule is summarised in Table4.1.4.2.4 Observation methodology.Conflicts were observed and recorded for both intersections using the TTC (Time ToCollision) measure. TTC is the time for two vehicles to collide if they continue at theirpresent speed and on the same path. The severity of traffic conflicts is determined by thesum of two scores: the TTC score and the "Risk of Collision" or ROC score. The ROCscore is a subjective measure of the risk of collision and is dependent on the perceivedcontrol that the driver has over the conflict situation.The scale used to determine the TTC and ROC scores is shown in Table 4.2. Thesummation of the TTC and ROC scores gives the overall severity score which rangebetween two and six. Results of studies performed by Brown (1986) at the University ofBritish Columbia indicate that conflicts which have been assigned an overall severityscore of 4.0 or higher exhibit a correlation to accidents and are therefore indicative of asatisfactory significant accident risk.62Chapter 4. Model ValidationDAY Time of day (Hours) Number ofObserversNumber ofMan-HoursFirst day 0700 - 1000 2 61100 - 1300 2 41500 - 1800 2 6Second day 0700 - 1000 2 61100 - 1300 2 41500 - 1800 2 6Total 32Table 4.1 Conflict observation scheduleSource: G.D. Hamilton & Associates Consulting LTD. conflict study reportTTC and ROCScoresTime To Collision(TTC)Risk Of Collision(ROC)1 1.6 - 2.0 seconds Low Risk2 1.0 - 1.5 seconds Moderate Risk3 0.0 - 0.9 seconds High RiskTable 41 Time to collision and risk to collision scores.Source: G.D. Hamilton & Associates Consulting LTD. conflict study report63Chapter 4. Model Validation4.2.5 Comparing resultsA comparison between the observed conflicts and the predicted conflicts was carried out.The model was modified to allow for the traffic volume changes through the morning,noon and afternoon periods. There was another modification to allow the inclusion of therestricted southbound left-turn movement between 0700 and 0900 hours at HoldomAvenue and Broadway intersection.Since the simulation model only consider conflicts with TTC values less than or equal to1.5 seconds, observed conflicts with TTC greater than 1.5 seconds were excluded fromthe validation data. The speed limit was taken 50 km/hr which is the legal speed limit atboth intersections. The comparison are given in Tables 4.3 and 4.4.In the case of 156th Street and 20th Avenue intersection (Table 4.3), the model predicted5 conflicts out of 8 observed conflicts with a close distribution of conflicts over thedifferent locations within the intersection. The field study observed that typical vehiclesspeeds exceed the legal 50 km/hr limit along 156th Street. This may be a factorcontributing to the difference in number of conflicts. Increasing the speed limit in themodel to 70 km/hr caused the model to predicted 10 conflicts with a very closedistribution to the observed conflicts.64Chapter 4. Model ValidationConflict name and description ObservedconflictsPredictedconflicts50 km/hrPredictedconflicts70 km/hr156th street northbound, rear-endconflicts4 2 4156th street southbound, crossingconflicts1 1 1156th street northbound, left turncrossing conflicts2 1 2156th street southbound, rear-endconflicts1 0 1156th street northbound, crossingconflicts0 1 2Total 8 5 10Table 4.3 Observed and predicted conflicts distribution 156th Street and 20th Avenueintersection65Chapter 4. Model ValidationConflict name and description ObservedconflictsPredictedconflicts50 km/hrPredictedconflicts60 km/hrLeft turn crossing conflicts involvingwestbound left turning motorists andsouthbound through motorists.10 7 9Left-turn opposing conflicts involvingeastbound through motorists andwestbound left turning motorists.1 2 2Crossing conflicts involving eastboundthrough motorists and northbound orsouthbound through motorists.2 3 3Crossing conflicts involving eastboundthrough motorists and northbound orsouthbound through motorists.2 3 4Right turn (merging) conflicts involvingwestbound right turning motorists andnorthbound through motorists.2 1 1Rear-end conflicts involving southboundthrough motorists.0 0 1left turn opposing conflicts involvingsouthbound through motorists andnorthbound left turning motorists.2 1 1Total 19 17 21Table 43 Observed and predicted conflicts distribution Holdom Avenue and Broadwayintersection66Chapter 4. Model ValidationThe predicted results may be identical to the observed results if an appropriate approachspeed between 50 km/hr and 70 km/hr is selected.The Holdom Avenue and Broadway intersection model predicted 17 conflicts out of 19observed conflicts. Increasing the speed to 60 km/hr produced 21 conflicts. In both casesthe predicted conflicts distribution was very close to the observed conflicts distribution.The results of the comparison which is limited to two intersections shows that the modelresults do correlate very well with the observed field data. The comparison implies asuccessful external validation process. However, due to the limited number ofintersections used in the validation process and the variability of the conflict technique;more work on the validation is recommended.67Chapter 5. Findings5- FINDINGS This chapter presents some additional simulation results. A comparison of these resultsand previous work in the literature is also introduced for the purpose of the hypothesesvalidity of the model.5.1 Relation between conflicts and traffic parameters.5.1.1 Volume - Conflicts relation.Several researchers indicated that traffic volume has a significant effect on conflicts.Cooper et. al. (1976) suggested that number of conflicts occurring at a certain locationis proportional to the product of the two conflicting volumes. The same result wererecorded by Hodge et. al. (1978). Spicer et al. (1979) indicated that at relatively lowtraffic volumes, the total number of observed conflicts is proportional to the square rootof the product of the conflicting volumes. Darzentas et. al. (1980) proposed that conflictslinearly increased as a function of the traffic volume. None of the above researchersconsidered high traffic volumes.Figures 5.1, 5.2 and 5.3 are examples of the relation between traffic volume and conflictsrate obtained from the simulation model. These figures indicate that over a wide rangeof traffic volumes including congested conditions, an exponential relation seems to give68Chapter 5. Findingsa good fit. However, if only low traffic volumes are considered, conflicts seems to beproportional to the square root of the conflicting volumes as suggested by Spicer et. al.(1979). The product of the conflicting volumes is also found to be statistically related toconflicts for a limited range of traffic volumes.The curves representing conflicts for Yield and Stop controlled intersections, Figures 5.2and 5.3 were very close at low traffic volumes and the difference begin to increaserapidly as traffic volume increases. This agrees with the volume warrant for the use ofYield sign which specify a volume limit after which Yield signs should not be used tocontrol unsignalized intersections. An example of Yield sign warrants is shown inappendix B.69Chapter 5. Findingsgi = kg k = 0.3Approach speed = 60 km/hr2 lanes for both major and minor roadsFigure 5.1 Relation between crossing conflicts and traffic volume for a T-intersection70•Conflict locationq1 •0Stop controledYield ControledChapter 5. Findings1601401204%O• 100mC0%we 80•-.c 60O040200100^200^300^400^500^600^700^800Volume (VEH/HR)ql = kq^k = const.Approach speed = 60 km/hr2 lanes for both major and minor roadsFigure 5.2 Relation between crossing conflicts and traffic volume for a T-intersection71200•100 150 200 250 300 350 400 450Volume (VEH/HR)Stop controledYield Controled•Chapter 5. Findingsg1 = kg k = 0.3Approach speed =60 km/hr1 lane for both major and minor roadsFigure 5.3 Relation between crossing conflicts and traffic volume for a 4-legintersection72Chapter 5. Findings5.1.2 Speed - Conflicts.Early research by Cooper et. al. (1977) indicated that accidents risk increases as theapproach speed of major road vehicles increases. Darzentas et al. (1980) suggested a rapidincrease of conflicts rate at a fixed flow as the mean speed on the major road increases.The relation between the mean approach speed and number of conflicts from the currentmodel is shown in Figures 5.4, 5.5 and 5.6. The figures indicate an increase in thenumber of conflicts as the mean approach speed increases for a fixed volume. The valueof the increase is proportional to the traffic volume. A slight increase was obtained at lowtraffic volume and a significant increase at high traffic volumes. There was no significanteffect of the intersection type of traffic control (Yield - Stop) on the value of thisincrease.The number of conflicts estimated by the model increased as the dispersion of speeds onthe main road increased. This agrees with the published research which indicate that thereis a driver's error of judgement associated with vehicles having speeds different than themean speed (Brian 1962; Cooper et al. 1976). These results suggest that a decrease inmajor road vehicles speeds and the dispersion of these speeds can result in decreasingnumber of conflicts. This may be achieved by police activity at the intersection asreported by Cooper et al. (1977).73• Conflict locations650 VPH 550 VPH 450 VPHA------ -------------------------- -o -- --------------------^o------------------ O. a^............................ +.. ........^........^..^ t I^I^I --------...........................................^..Chapter 5. Findings706050U)r4040304E.02010040^45^50^55^60Speed (Km/hr)65^70ql = kq k=0.32 lanes approach for both major and minor roadsk ^Stop controlled intersectionFigure 5.4 Relation between conflicts and approaching speedat Stop-controlled T-intersection74• Conflict locations.-.-.1,....--■A........-0 -------0^----------------------...........0^........... b- --- - -.^0650 VPH 550 VPH 450 VPH,^ 4 ,^I t I^t^t^I^,120100800r0'I= 60u)(..)a.C00 402045^50^55^60Speed (Km/hr)040 65 70ql = kq k=0.32 lanes approach for both major and minor roadsYield controlled intersection-■^Chapter 5. FindingsFigure 5.5 Relation between conflicts and approaching speedat Yield-controlled T-intersection75Conflict locations000650 VPH 550 VPH 450 VPH0 ..............................o .......................---------^---------0 ^A1^4Chapter 5. Findings706050-c 400viU)g 30002010U)0040^45^50^55^60Speed (Km/hr)65^70q1 = kq k=0.3 No turning vehicles1 lane approach for both major and minor roadsStop controlled intersectionFigure 5.6 Relation between conflicts and approaching speedat Stop-controlled 4leg-intersection76Chapter 5. Findings5.1.3 Speed - severity of conflicts.The overall severity of traffic conflicts represented by the average time to collision(TTC) value (the TTC value is inversely proportional to the severity of trafficconflicts) increased as the mean approach speed of the major road vehicles increased,see Figures 5.7 and 5.8. The same results were reported by Copper et al. (1976, 1977)and Darzentas et al. (1980). This indicates that the percentage of injury accidents atunsignalized intersections may increase as the mean major road speed increases.The overall severity of conflicts was higher in the case of Yield-controlledintersections than Stop-controlled intersections. This may result because of the driverstendacy to accept shorter gaps at Yield-controlled intersections. This increased conflictseverity may put a constrain on using Yield sign to control intersections with relativelyhigh major road speeds even though other warranties for using Yield sign such astraffic volume and sight distance are satisfied.77Chapter 5. Findings1.51.451.2540^45^50^55^60^65Speed (KM/HR)ql = kq k=0.32 lanes approach for both major and minor roadsStop controlled intersectionFigure 5.7 effect of approach speed on conflicts severity for aStop-controlled T-intersection70 75781.51.456-2 1.40U0co0 1.35Tts->01.300Es1.25<1.21.1540^45^50^55^60^65Speed (KM/HR)70 75Chapter 5. Findingsql = kq k=0.32 lanes approach for both major and minor roadsYield controlled intersectionFigure 5.8 effect of approach speed on conflicts severity for aYield-controlled T-intersection79Chapter 5. Findings5.2 Conflicts and driver type.The model is based on the consideration of the effect of drivers' characteristics such assex and age on the drivers' behaviour. The model output reflected this consideration. Themodel output indicate that female drivers were generally less involved in conflictsituations than male drivers. It was also noted that older drivers were involved in moreconflict situations than younger drivers which indicates that older drivers are lessconsistent in their driving behaviour.The number of conflicts can be reduced by increasing the median acceptance gap (i.e.make drivers more cautious). This agrees with Storr et al. 1979 who indicated that policeactivity near an intersection makes turning drivers from minor road more cautious andconsequently decrease number of conflicts.All these results agree with our expectations and previous research and consequentlycontribute to both face and hypotheses validity of the model.80Chapter 6. Further Research6- FURTHER RESEARCHThere are several directions where further development to the model can be undertaken.The first direction is expanding the simulation model to include the effect of someparameters which are not considered in the model. These parameters might include theeffect of the surrounding environment such as buildings that obstruct the driver's viewand the weather conditions which are important in determining the driver's field of vision.The perceptual and decision making processes can be made more sophisticated in termsof current knowledge about human driving behaviour. For example the decision makingprocess might take into account the driver's degree of concentration and whether he isfamiliar with the intersection. Also, the process of estimating gaps which is currentlybased upon the driver's estimates of the relative times at which vehicles will arrive at theintersection can be expanded to take into account distance estimates and change insubtended visual angle.The model at the current stage is only capable of dealing with simple layout intersections.It might be of interest to add the ability of dealing with other layouts such as those withseparate turning lanes and corner islands. Another development is to include other typesof intersection controls. These controls would include the 4-way Stop, flashing red andtraffic lights.81Chapter 6. Further ResearchAnother important direction in which the model can be expanded is to include userinteraction with the model. Through this interaction, the user should be able to alter thevalues of different parameters and observe the change in the model behaviour. Userinteraction with the model allow for the integration of more human factors in the model.82Chapter 7. Conclusion7- CONCLUSIONA visual microscopic traffic conflicts simulation model for both T and 4-leg intersectionshave been developed using GPSS/H. The model considers different aspects of driversbehaviour and the effect of several parameters on drivers' decision at unsignalizedintersections. The visualization process is very important part of the model as it showshow the model behaves at extreme values, that is during traffic conflicts. This view givesa better understanding of these critical situations and the parameters affecting theiroccurrence. An external validation process was conducted to test whether the modelresults is indicative of the actual performance. The external validation process showed thatthe model results correlate well with the field observations.The significant findings of the model can be summarized in the following:1. Over a wide range of traffic volumes, including congested conditions, anexponential relation between traffic volumes and conflicts seems to give a goodfit.2. Conflicts rate increases as the mean approach speed increases. The value of theincrease is proportional to the traffic volume. This implies that imposing a speedlimit especially on intersections with high traffic volumes, can help reduce thenumber of conflicts.83Chapter 7. Conclusion3. The overall severity of conflicts represented by the average TTC value increasesas the mean approach speed increases. This indicates that the percentage of injuryaccidents may increase with higher approach speeds.4. The overall severity of conflicts in speed-conflicts relation was higher in caseof Yield-controlled intersections than Stop-controlled intersections. This may puta constrain on using Yield sign to control intersections with relatively high majorroad speeds.5. Police activities near or at intersections can help in reducing the number ofconflicts through increasing the median accepted gap of drivers and decreasing thedispersion of the mean approach speed.These results agrees with our expectations and previous work in the literature. Thisindicate that the model has both face and hypotheses validity.The model can be mainly used for two purposes. The first is assessing the safety andperformance of unsignalized intersections. The safety measure can be expressed by thenumber of conflicts predicted by the model, while the performance can be expressed bythe intersection level of service which is a function of the average delay to minor roadvehicles. The second is as a tool for investigating how to reduce accidents risk. As severalresearches emphasized on the value of behavioral studies and drivers education inreducing accidents risk, the model can be a useful tool in identifying the areas at which84Chapter 7. Conclusionthese kind of studies should be directed.85ReferencesREFERENCES Adebisi, 0. and Sama, G.N. (1989). "Influence of stopped delay on driver gap acceptancebehaviour." Journal of transportation Engineering, Vol. 115, No. 3, 305-315.Allen, B.L., Shin, B.T. and Cooper, P.J. (1977). "Analysis of traffic conflicts andcollisions." Dept. of Civil Engineering, McMaster University, Hamilton.Amundsen, F. and Hyden, C. (1977). Proceedings of first workshop on traffic conflicts.Oslo: Institute of Transport Economics.Ashworth, R. (1968). "A note on the selection of gap acceptance criteria for trafficsimulation studies." Transportation Research, 2, 171-175.Ashworth, R. (1970). " The analysis and interpretation of gap acceptance data."Transportation Science, 4(3), 270-280.Ashworth, R. and Bottom, C.G. (1975). "Driver gap acceptance behaviour at priority-typeintersections." Final Report. Research report No. R63, Department of Civil and StructuralEngineering, University of Sheffield.Ashworth, R. and Bottom, C.G. (1977). "Some observations of driver gap acceptancebehaviour at a priority intersection." Traffic Engineering and Control, Vol. 18, No. 12,569-571.Atkins, M.S. (1980). "A comparison of SIMULA and GPSS for simulating sparce traffic."Simulation Vol. 34, 93-100.Bell, P. and O'keefe, R. "Visual interactive simulation- History, recent development, andmajor issues." Simulation VolBrian, R. (1962). "Vehicle speed estimation at right-angled at-grade junction" Surveyorand Municipal and county Engineer, 789-791Brown, G.R. (1986). "Application of traffic conflicts for intersection hazards andimprovements." Proceedings of workshop on traffic Conflicts and other intermediatemeasures in safety evaluation, Budapest September 1986.Cooper, D.F., Smith, W., and Broadie, V. (1976). "The effect of the approach speed onmerging gap acceptance." Traffic Engineering and Control Vol. 17, No. 6, 256-257.Cooper, D.F., Ferguson, N. (1976). "A conflict simulation model." Traffic Engineeringand Control Vol. 17, No. 7, 306-309.86ReferencesCooper, D.F., Storr., P.A., and Wennell, J. (1977). "The effect of speed on gap acceptanceand conflict rate." Traffic Engineering and Control Vol. 18, No.3, 110-112.Cooper, D.F. and McDowell, M.R.C. (1977). "Police effects on accidents risk at T-junctions" Traffic Engineering and Control Vol. 18, No. 10, 486-487.Darzentas, J.,McDowell, M.R.C., and Cooper, D.F. (1980). "Minimum acceptance gapsand conflict involvement in a single crossing manoeuvre." Traffic Engineering andControl Vol. 21, No. 2, 58-61.Ellson, E. and Cox, D. (1988). " Visualization of injection molding." Simulation Vol. 51,184-188Garder, P. (1985)."Theory for strong validation; application to Swedish results."Evaluation 85, Proceedings of an international meeting on evaluation of local traffic safetymeasures. Paris: ONSER.Gerlough, D.L. (1954). "Analogs and simulation for the study of traffic problems."Proceedings, Sixth California Street and Highway Conference.Gerlough, D.G. and Huber, M.J." Traffic flow theory" Transportation Research Board,Special report 165, TRB, Washington, D.C., 1975, 21-31.Glauz, W.D. and Bauer, K.M. (1985). "Validation of the traffic conflict technique in theUSA." Evaluation 85, Proceedings of an international meeting on evaluation of localtraffic safety measures. Paris: ONSER.Grayson, G.B., and Hakkert, A.S. (1987). "Accident analysis and conflict behaviour."Road users and traffic safety, Traffic Research Centre, University of Groningen.Hauer, E. (1975). "The traffic conflicts technique: Fundamental issues." Publication 75-01,University of Toronto, Department of Civil Engineering, Toronto.Hauer, E. (1978). "traffic conflict surveys: some study design considerations." TRRLSupplementary Report 352, Transport and Road Research Laboratory, Crowthorne,Berkshire.Hauer, E., and Garder, P. (1986). " research into the validity of the traffic conflictstechnique." Accident Analysis and prevention (18), 471-481.Hayward, J.CH. (1972). "Near miss determination through use of a scale of danger."Report No. TTSC 7115, The Pennsylvania State University, Pennsylvania.87ReferencesHillier, J., Whiting, P., Wardrop, j (1951). "The automatic delay computer." RoadResearch Laboratory Research Note, RN/2291, Harmondsworth (unpublished).Hodge, G.A., and Richardson, B.E. (1978). "A study of intersection accident exposure."Australian Road Research Board Vol. 9, part 5.Hogeweg, P. (1978). "??ing the growth of cellular forms." Simulation September 1978,90-96.Horst, A.R.A. van der, (1983). " Registration analysis of traffic conflicts based on Video."Proceedings of the NATO advanced research workshop on international calibration studyof traffic conflict techniques. Copenhagen, May 1983.Hyden, C. (1975). "Relation between conflicts and traffic accidents." Lund:Lund Instituteof Technology.Hyden, C. (1987). "The development of a method for traffic safety evaluation."Lund:Lund Institute of Technology.McCormick, B., Defanti, A. and Brown, D. (1987). "Visualization in ScientificComputing." Computer Graphics, 21:6.McDowell, M.R.C., Wennell, J., Storr, P.A., and Darzentas, J. (1983). " gap acceptanceand traffic conflict simulation as a measure of risk." TRRL Report No. SR 776, Transportand Road Research Laboratory, Crowthorne.May, A.D. (1990). "Traffic flow fundamentals" Prentice Hall, Englewood Cliffs, NewJersey.National Cooperative Highway Research Program Report 320 (1989). "Guidlines forconverting Stop to Yield Control at intersections" Transportation Research Board,Washington, D.C.National Research Council. (1985). "Highway Capacity Manual." Transportation researchBoard, Special Report 209, Washington, D.C., Chapter 10.Navin, F.P.D. (1991). 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(1973) "A new approach to the analysis of gapacceptance times." Traffic Engineering and Control 15(7), 353-357.Schriber, T.J. (1974) " Simulation using GPSS" John Wiley & SonsShannon, R.E. (1975) "System simulation: the art and science." Prentice Hall.Storr, P.A., Cooper, D.F., and McDowell, M.R.C. (1979). "Analysis of gap acceptance ina complete traffic manoeuvre." European Journal of Operation Research.Thomasma, T. and xiang, Y. (1991). "Object oriented simulation for manufacturinginformation handling system design." Object Oriented Simulation: Simulation series Vol.23, No. 3.Tudge, R.T. (1988). " INSECT- the calibration and validation of an intersectionsimulation model." Proceedings of international workshop on intersections without trafficsignals, Bochum, West Germany.Wagner, F.A. (1965). " An evaluation of fundamental driver decisions and reactions atan intersection." HRB, Highway Research Record 118, 68-84.Wennell, J. and Cooper, D.F. (1981). "Vehicles and driver effect on junction gapacceptance." Traffic Engineering and Control 628-635.Wepster, F.V. (1958). "Traffic signal settings." Road Research Technical Paper, No. 39,H.M. Stationary Office, London.89Appendix A. Sample Model OutputAPPENDIX A SAMPLE MODEL OUTPUT SIMULATION OUTPUT FILETOTAL SIMULATED TIME 10.00 HOURSINTERSECTION CONTROL TYPE STOPSPEED LIMIT ON MAJOR ROAD 50.0 KM/HR1. TRAFFIC CONFLICTSNUMBER LOCATION TYPE TTC (SECONDS)1 MINOR TURNING RIGHT,MAJOR GOINGMERGING 1.432 MINOR TURNING LEFT,MAJOR GOINGCROSSING 1.413 MINOR TURNING LEFT,MAJOR GOINGCROSSING 1.464 MAJOR TURNING LEFT,MAJOR COMINGCROSSING 1.445 MINOR TURNING LEFT,MAJOR GOINGCROSSING 1.436 MINOR TURNING LEFT,MAJOR GOINGCROSSING 1.431- TOTAL VOLUMESDIRECTION INPUT VOLUME(VPH) GENERATED VOLUME(VPH)STRAIGHT AHEAD^400^403MAJOR GOING90TURNING RIGHTMAJOR GOINGSTRAIGHT AHEADMAJOR COMMINGTURNING LEFTMAJOR COMMINGTURNNING LEFTMINORTURNNING RIGHTMINORAppendix A. Sample Model Output100^ 100400^ 398100^ 98120^ 120120^ 1192- AVERAGE DELAY/VEHICLEQUEUE LOCATION^DELAY (SECONDS) AVERAGE CONTENTMINOR ROAD 23.47^1.0TURNING LEFTMINOR ROAD^10.86^0.5TURNING RIGHTMAJOR ROAD^6.69^0.2TURNING LEFT91Appendix B. Yield Sign WarrantsAPPENDIX B YIELD SIGN WARRANTS WARRANTS TO BE CONSIDERED FOR INSTALLATION OF YIELD SIGN1. The sum of the ADT's on the intersecting streets is at least1,500 vpd but not more than 5000 vpdAC^D^(A + B) + (C + D) = 1500 to2^2^5000 vpdB2. The occurrence of at least two accidents unpreventable byless restrictive means in the two latest 12-month periods. Theaccidents should be of the type correctable by Yield signs.3. The safe stopping sight distance speed must be greater than12 mph (triangle distance of about 45 feet).Source: National Cooperative Highway Research Report 32092

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