Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Morshedzadeh, Yeganeh
Master of Applied Science - MASc
University of British Columbia
Work zones are lane closures essential to protect workers during highway maintenance and construction activities; however, they lead to congested traffic movement. To mitigate delay effectively, it is essential to understand factors that impact delay and develop the ability to predict delays accurately. Given the rapid availability of big data, machine learning (ML) models are becoming increasingly popular in traffic flow prediction. Their ability to capture complex non-linear patterns can enhance predictions obtained using traditional tools. This thesis aims to employ ML models to predict delays observed at work zones. This is achieved through developing data-driven predictive models that leverage the growing usage of large-scale data in transportation. The vast dataset was assembled by integrating 15 million travel times observations from probe vehicles over a 700-km corridor with various factors such as weather conditions, work zone design, traffic conditions, and temporal elements gathered from a wide range of sources. The data was used to achieve two primary objectives: (i) identify relationships between various factors and work zone delay and (ii) compare usage of ML algorithms in accurately predicting work zone delays. To achieve the first objective, unsupervised clustering as well as ordinal logistic and mixed-effects regression were used. The findings highlight the proportional impact of the length of transition areas and work zones and the significant effects of environmental factors on work zone delays. To assess the use of ML models in predicting delays, a comparative evaluation of multiple techniques was conducted, highlighting the strengths and weaknesses of each approach. This included artificial neural networks (ANN), decision trees, gradient boosting regression, support vector regression, and ridge regression. Among the models evaluated, the decision tree and ANN achieved the best overall performance with the lowest RMSE of 0.05 and 0.150 minutes and the highest R-squared value of 0.99 and 0.95, respectively. By leveraging accurate delay predictions, transportation agencies can devise effective traffic management plans, such as implementing detours or adjusting signal timings before delays occur. Furthermore, understanding delay-influencing factors enables agencies to better mitigate delays after they occur through targeted measures tailored to the specific influencing variables.
Using Big Data and MachineLearning for Microscopic DelayModelling at Construction WorkZonesbyYeganeh MorshedzadehB.Sc., Iran University of Science and Technology, 2021A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinThe College of Graduate Studies(Civil Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)April 2024© Yeganeh Morshedzadeh 2024The following individuals certify that they have read, and recommend to theCollege of Graduate Studies for acceptance, the thesis entitled:Using Big Data and Machine Learning for Microscopic Delay Mod-elling at Construction Work Zonessubmitted by Yeganeh Morshedzadeh in partial fulfillment of the requirementsfor the degree of Master of Applied Science.Dr. Suliman Gargoum, School of EngineeringSupervisorDr. Mahmudur Fatmi, School of EngineeringSupervisory Committee MemberDr. Qian Chen, School of EngineeringSupervisory Committee MemberDr. Wouter Bam, School of EngineeringUniversity ExamineriiAbstractWork zones are lane closures essential to protect workers during highwaymaintenance and construction activities; however, they lead to congested trafficmovement. To mitigate delay effectively, it is essential to understand factors thatimpact delay and develop the ability to predict delays accurately. Given the rapidavailability of big data, machine learning (ML) models are becoming increasinglypopular in traffic flow prediction. Their ability to capture complex non-linearpatterns can enhance predictions obtained using traditional tools.This thesis aims to employ ML models to predict delays observed at workzones. This is achieved through developing data-driven predictive models thatleverage the growing usage of large-scale data in transportation. The vast datasetwas assembled by integrating 15 million travel times observations from probevehicles over a 700-km corridor with various factors such as weather conditions,work zone design, traffic conditions, and temporal elements gathered from a widerange of sources. The data was used to achieve two primary objectives: (i) identifyrelationships between various factors and work zone delay and (ii) compare usageof ML algorithms in accurately predicting work zone delays.To achieve the first objective, unsupervised clustering as well as ordinal logisticand mixed-effects regression were used. The findings highlight the proportionalimpact of the length of transition areas and work zones and the significant effectsof environmental factors on work zone delays.To assess the use of ML models in predicting delays, a comparative evaluationof multiple techniques was conducted, highlighting the strengths and weaknessesof each approach. This included artificial neural networks (ANN), decision trees,gradient boosting regression, support vector regression, and ridge regression.iiiAbstractAmong the models evaluated, the decision tree and ANN achieved the best overallperformance with the lowest RMSE of 0.05 and 0.150 minutes and the highestR-squared value of 0.99 and 0.95, respectively.By leveraging accurate delay predictions, transportation agencies can deviseeffective traffic management plans, such as implementing detours or adjustingsignal timings before delays occur. Furthermore, understanding delay-influencingfactors enables agencies to better mitigate delays after they occur through targetedmeasures tailored to the specific influencing variables.ivLay SummaryConstruction activity along roads results in substantial delays for drivers. Ac-curate prediction of the anticipated delay is vital for effective mitigation. Thisresearch has two objectives: (i) identify the various factors that contribute toincreased delays at work zones, and (ii) assess the use of machine learning mod-els to accurately predict delays. Data from more than 700 km of constructionsites, weather conditions, and traffic conditions were integrated with 15 millionobservations to achieve this goal. Statistical modelling was used to quantify therelationships between different variables and delay levels. An evaluation of ma-chine learning models like artificial neural networks was then conducted. Thesemodels demonstrated highly effective predictive capabilities by capturing complexpatterns in the data. The results of this thesis are expected to assist transportationagencies in better planning and management of highway work zones to reduceinconvenience for drivers while ensuring efficient construction operations andworker safety.vPrefaceThis thesis is based on research work conducted under the supervision of Dr.Suliman Gargoum and the contents of this work have been reviewed by him.Work presented in this thesis is published in below journal and conferenceproceeding:• Morshedzadeh et al. (2024) “Using Deep Neural Networks and Big Datato Predict Microscopic Travel Time at Work Zones” Transportation ResearchRecord: Journal of the Transportation Research Board. Accepted January 2024.• Morshedzadeh et al. (2023) “Microscopic Analysis of Work Zone Delayusing Big Data and Logistic Regression” proceedings of the TransportationAssociation of Canada. Accepted June 2023.viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . 11.2 Knowledge Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Research Objective . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.5 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Review of Related Work . . . . . . . . . . . . . . . . . . . . . . . . 82.1 Analytical and Simulation Models in Work Zone Impact Assess-ment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8viiTable of Contents2.2 Studies on Work Zone Delay Prediction . . . . . . . . . . . . . . 92.3 Analysis of Other Work Zone Attributes . . . . . . . . . . . . . . 122.4 Research Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Data Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.1 Data Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2 Data Description . . . . . . . . . . . . . . . . . . . . . . . . . . 183.2.1 Travel Time-Related Variables . . . . . . . . . . . . . . . 183.2.2 Weather Variables . . . . . . . . . . . . . . . . . . . . . 193.2.3 Temporal Variables . . . . . . . . . . . . . . . . . . . . 203.2.4 Segment-Related Variables . . . . . . . . . . . . . . . . 213.2.5 Work Zone Characteristic Variables . . . . . . . . . . . . 223.3 Summary of Data Preprocessing Workflow . . . . . . . . . . . . 253.3.1 Correlation Analysis . . . . . . . . . . . . . . . . . . . . 264 Exploring Variable Relationships and Delay Factors . . . . . . . . . 304.1 Work Zone Clustering . . . . . . . . . . . . . . . . . . . . . . . 304.1.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . 314.1.2 Results and Discussion . . . . . . . . . . . . . . . . . . 344.2 Logistic Regression Modelling . . . . . . . . . . . . . . . . . . . 374.2.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . 374.2.2 Results and Discussion . . . . . . . . . . . . . . . . . . 394.3 Mixed-Effects Linear Regression . . . . . . . . . . . . . . . . . 424.3.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . 434.3.2 Results and Discussion . . . . . . . . . . . . . . . . . . 474.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505 Using Machine Learning Models for Delay Prediction . . . . . . . . 525.1 Dataset Preparation . . . . . . . . . . . . . . . . . . . . . . . . . 545.1.1 Feature Encoding . . . . . . . . . . . . . . . . . . . . . 545.1.2 Train and Test Split . . . . . . . . . . . . . . . . . . . . 55viiiTable of Contents5.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.2.1 Artificial Neural Network . . . . . . . . . . . . . . . . . 565.2.2 Ridge Regression . . . . . . . . . . . . . . . . . . . . . 595.2.3 Support Vector Regression (SVR) . . . . . . . . . . . . . 595.2.4 Decision Tree Regression . . . . . . . . . . . . . . . . . 605.2.5 Gradient Boosting Regression . . . . . . . . . . . . . . . 615.3 Evaluation Metrics . . . . . . . . . . . . . . . . . . . . . . . . . 615.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . 635.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716 Discussion, Conclusion, and Limitations . . . . . . . . . . . . . . . 736.1 Conclusion and Takeaways . . . . . . . . . . . . . . . . . . . . . 736.2 Limitations and Future Work . . . . . . . . . . . . . . . . . . . . 77Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79ixList of Tables2.1 Summary of Existing Work Zone Delay Prediction Models . . . . 113.1 Work Zone Characteristic Variables Definition . . . . . . . . . . . 243.2 Descriptive Statistics of Quantitative (Numerical) Variables . . . . 273.3 Summary of Qualitative (Categorical) Variables . . . . . . . . . . 284.1 OLR Model Results Summary . . . . . . . . . . . . . . . . . . . 404.2 Statistical Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . 464.3 Results of MELR Fit by Restricted Maximum Likelihood (REML) 484.4 Comparison of the Each Model’s Results . . . . . . . . . . . . . . 515.1 Comparison of Evaluation Metrics Across Regression Models . . 645.2 Summary of Advantages and Disadvantages of Models . . . . . . 67xList of Figures1.1 Proposed Framework . . . . . . . . . . . . . . . . . . . . . . . . 53.1 Map of Operation Zones and Work Zones for the TMEP MapSource: Earthstar Geographics, RDCO, Earthstar Geographics, Esri Canada,Esri, HERE, Garmin, SafeGraph, FAO, METI/NASA, USGS, EPA, NRCan,Parks Canada, Esri Canada, Esri, HERE, Garmin, SafeGraph, GeoTechnologies,Inc, METI/NASA, USGS, EPA, US Census Bureau, USDA, NRCan, Parks Canada 233.2 Features in a Work Zone Traffic Control Plan . . . . . . . . . . . 254.1 Pie Chart for Delay Cluster Distribution . . . . . . . . . . . . . . 344.2 Polar Plot Showing Averaged Feature Values for Delay Time Clusters 354.3 Features in a Work Zone Plan for Clustering . . . . . . . . . . . . 365.1 An Illustration of a Fully Connected Feed-Forward Neural Network 575.2 Architecture of ANN and Input Variables . . . . . . . . . . . . . 585.3 Evaluation Metrics Across Models . . . . . . . . . . . . . . . . . 635.4 True vs. Predicted Across Regression Models . . . . . . . . . . . 655.5 Scatter Plot Comparing Actual and ANN Predicted Values . . . . 695.6 Scatter Plot Comparing Actual and ANN + K-Fold Predicted Values 71xiAcknowledgementsI give my deepest gratitude to my teammates. I feel blessed to have shared thisjourney with you all.To my amazing friends, near and far, having you in my corner made this journeyso much more bearable and manageable.To the beautiful souls at UBC, thank you for all the hallway and office chatsand the moments we shared together; I shall hold them dear to my heart.To my beloved family, the patient hearts, thank you for being my understandingsupporters, compassionate listeners, and wise advisors. A special gratitude to mydear Maman, your belief in me has been a great source of encouragement anddriving force.To those who are far from here but close to my heart, thank you for beingintegral part of my journey.But most of all, to the One and Only, in whose remembrance hearts find comfortand rest, who suffices as guardian and witness.xiiDedicationDedicated to the experiences we never expected but needed, and the paths thatwere redirected. To the cherished bonds formed along the way that have made itall worthwhile.xiiiChapter 1Introduction1.1 Background and MotivationRoad networks serve as critical transportation infrastructure enabling the move-ment of people and goods in a safe and efficient manner. An interconnected andsafe road network reduces travel time and cost, which is vital for economic growth.Effective monitoring and management of delays also help reduce greenhouse gasemissions [1].Traffic congestion can be classified as recurrent congestion, which occurs dur-ing peak hours, and non-recurrent congestion, which occurs due to accidents,spills, and debris on roadways, inclement weather, or the existence of a work zone(WZ) [2–4]. Construction and maintenance activities at highway work zones cansignificantly disrupt traffic operations and safety. A work zone or construction areais established at locations where maintenance or construction activities are per-formed, such as paving, marking, patching, surfacing, or utility work. Accordingto the United States Department of Transportation Federal Highway Administra-tion (FHWA) 1, over 24% of US freeway non-recurrent congestion results fromwork zones, accounting for a loss of 60 million vehicle-hours annually [5]. Inanother report, non-recurrent delays in 9 major Canadian cities cost between $2.0billion and $6.3 billion per year [6]. Such capacity loss is because work zonesintroduce lane closures, narrowed lanes, reduced speed limits, merging traffic, andother alterations to roadway capacity and conditions that interrupt normal trafficflow. This creates complex, interrupted, stop-and-go congestion patterns that make1Federal Highway Administration is a division of the United States Department of Transporta-tion that specializes in highway transportation.11.1. Background and Motivationaccurately predicting travel times and delays challenging.To appropriately manage traffic flow, especially during peak hours, simplyincreasing speed through work zone areas is not an appropriate solution, as itexposes construction workers to high safety risks. For this, an accurate estimateof anticipated delays, while considering all different variables that impact delay,helps wisely manage traffic situations and devise proactive strategies to alleviatedelays. Accurate prediction of delays is also important for situations when it isnot possible to accurately measure travel times, such as when construction activitytakes place at remote locations with limited cell coverage, which are particularlycommon in countries with a large geographic footprint such as Canada.While transportation agencies implement various strategies such as restrictionsand alternate routes to mitigate work zone impacts, planning and evaluation relyheavily on simulation tools and assumptions rather than data-driven predictivemodels. Although simulations are often calibrated using real-world data, theyhave inherent limitations. For example, they may fail to capture the complexand non-linear interactions between a multitude of factors influencing work zonedelays.More recent studies have started using real observations and applying statis-tical and machine learning (ML) techniques to address these limitations. Theuse of statistical and ML methods offers several advantages, such as the abilityto make accurate predictions without relying on assumptions about the statisticaldistribution of the data. Those models also have the capacity to capture complex,non-linear relationships between various factors and work zone delays. Addi-tionally, these methods can integrate diverse factors, including detailed weatherimpacts and work zone-specific conditions, leading to more comprehensive andaccurate predictive models.Recent advancements in employing big data and using the computational powerof ML models have motivated the development of advanced predictive models [7].These models are tailored specifically to quantify and estimate delays at workzones using extensive real-world observations. Accurately forecasting anticipated21.2. Knowledge Gapconstruction delays and travel times is crucial for transportation agencies to deviseeffective proactive traffic management plans while ensuring construction produc-tivity, cost efficiency, and worker safety. Moreover, an enhanced understandingof the factors influencing work zone delays also enables better proposals of miti-gation strategies. Therefore, the intricacies of real-world work zones necessitateobtaining sufficient data that captures traffic conditions across diverse scenarios.While parametric and simulation studies have dominated the industry on pre-dicting and modelling delays at work zones, there has been growing researchinterest in leveraging ML-based models in the field of transportation [8] (furtherdiscussed in Chapter 2: Review of Related Work). In fact, ML techniques morerecently have been increasingly utilized for travel time prediction and work zoneimpact assessment. However, transportation agencies in North America still relyon simulation tools designed for freeway travel times due to the lack of widespreadadoption of ML-based approaches in practice [9].1.2 Knowledge GapWhile existing studies have made valuable contributions, there are still sig-nificant gaps that limit our understanding and ability to accurately model workzone delays. A major limitation has been the reliance on small datasets collectedover brief periods or limited road segments [10–14], preventing the learning ofcomplex delay patterns across diverse scenarios. Additionally, most prior workexcludes key external factors like weather, seasons, and temporal variables, despitetheir significant impact on delays [10–15]. Failing to account for such factors risksomitted variable bias and limits predictive accuracy.Furthermore, there is an evident lack of focus on explaining the intricaterelationships and interactions between variables influencing work zone delays.Current models also do not adequately capture unobserved heterogeneity – theunmeasured characteristics and differences between work zones that may impactdelays, such as variability in driver behavior or specific site conditions.31.3. Research ObjectiveLastly, there exists a significant gap in leveraging advanced ML techniquestailored for the complex task of work zone delay prediction. Traditional statisti-cal methods and classical ML algorithms may struggle to effectively model thehigh-dimensional data and non-linear interactions across the numerous variablesinfluencing delays in diverse work zone scenarios. Moreover, the literature lackscomprehensive comparative studies evaluating different ML architectures for thisprediction task. A thorough evaluation of various ML models is needed to identifythe most effective approaches capable of handling the complex nature of workzone delay data and providing accurate forecasts.1.3 Research ObjectiveThe goal of this research is to provide insights into factors impacting delay anddevelop predictive tools to help better manage anticipated and ongoing delays.Figure 1.1 represents the framework that was followed in this thesis to (i)identify variables impacting work zone delays and (ii) develop the ML-baseddelay prediction models. The framework was split into 3 phases:I. Phase 1 involved collecting and preparing the data. This thesis assembles anextensive dataset of real-world travel time observations across highway workzones over 700 km of roadways. It integrates traffic and travel time data,work zone layout details, and other relevant data such as weather conditions.Subsequently, data cleaning and preprocessing are required to ensure dataquality. Then, data engineering process, including feature encoding, scalingand normalization, and feature aggregation is used to create new, moreinformative variables for analysis and modelling.II. Phase 2 employed fixed-effects and random-effects analyses to understandthe statistical significance and impact of both observed and unobservedvariables (related to unmeasured work zone characteristics) on work zonedelays. Methods such as clustering, ordinal logistic regression, and mixed-41.4. Contributioneffects linear regression enabled analyzing delay causes while exploring howthe set of explanatory variables is related to different congestion levels.III. Phase 3 conducted a comprehensive comparative assessment to evaluate theuse of different ML models for predicting work zone delays. The exploredML regression models included feed-forward artificial neural networks,ridge regression, support vector regression, decision trees, and gradient-boosted trees. These models were trained on the preprocessed data tocompare their performance in accurately estimating construction delays.The framework is adaptable and can serve as a model when using ML tools tosolve other complex problems within the transportation field.Traffic andTravel TimeDataWork ZoneLayoutDetailsOther Data(e.g.Weather)DataCleaningand Pre-processingData Engi-neeringPredictiveMachineLearningDevelopmentFixed-EffectsAnalysisRandom-EffectsAnalysisFigure 1.1: Proposed Framework1.4 ContributionThe contributions of this work lie in several different areas. The followingparagraphs summarize the research contributions:51.4. ContributionI. The thesis utilizes a large-scale dataset for analyzing work zone delays. Byintegrating information from multiple sources including segment data (traf-fic volume, length), weather conditions (temperature, precipitation, windspeed), temporal factors (hour of day, day of week), and extracting detailedwork zone characteristics (length, transition configuration, closure details)from layout plans, a comprehensive raw dataset of approximately 15 mil-lion travel time observations was constructed across 674 work zones on thehighway network. Such a large-scale dataset, capturing delay measurementsevery 2-3 minutes between 2021-2022, along with a multitude of relevantfactors at a number of work zones, has not been previously assembled forstudying work zone congestion impacts. This extensive dataset data-drivenmodelling allows us to uncover insights that can guide strategies to mitigatedelays and optimize work zone planning and operations.II. Unlike previous work, this thesis works on identifying and quantifying therelationships between various factors and work zone delays, while explicitlyaccounting for both fixed and random effects of attributes. This allows theconsideration of unexplained variability which is related to some unmea-sured characteristics of the work zones. Previous studies have analyzed theimpacts of certain variables like traffic volume or work zone configuration ondelays, but this thesis goes further by simultaneously considering the effectsof detailed segment characteristics, weather conditions, temporal factors,and work zone geometry features extracted from layout plans of work zonesspread along a 700 km corridor. The ability to quantify both fixed effectsfrom the observed variables as well as random effects has not been exploredbefore for work zone delay analysis at this scale.III. The thesis also conducts a comprehensive comparative assessment of ad-vanced ML techniques, including artificial neural networks, and ensemblemethods (e.g. gradient boosting, decision trees), for accurate work zonedelay prediction modelling. The performance, strengths, and weaknesses of61.5. Outlinethese ML models specifically within the context of predicting delays at workzones were explored.1.5 OutlineThe remainder of this thesis is organized as follows:• Chapter 2 provides a review of related literature and research on delaysthrough work zones, highlighting key research gaps addressed in this thesis.• Chapter 3 details the comprehensive dataset that was compiled and usedacross analyses and modelling. The section provides details on the data col-lection approach and location, data cleaning method, and the data assemblyprocess.• Chapter 4 applies data analysis techniques to uncover insights into the at-tributes that contribute to excessive delays at work zones. This includesclustering to identify variables that impact a work zone belonging to certaindelay level categories. Additionally, ordinal logistic and mixed-effects re-gression to statistically assess the relationships between delay and multipleindependent variables.• Chapter 5 conducts a comprehensive comparative analysis of the perfor-mance of different ML regression models (ridge regression, support vector,decision trees, gradient boosting, and artificial neural networks) when usedto predict delay at work zones.• Chapter 6 summarizes key conclusions, limitations, and directions for futurework toward enhanced data-driven modelling of delays at work zones onhighways.7Chapter 2Review of Related Work2.1 Analytical and Simulation Models in WorkZone Impact AssessmentTraditional analytical and simulation models have been widely used for workzone impact assessments. The HCM2 proposed methods to estimate the work zonecapacity based on lane closures and speed reductions [16]. However, HCM meth-ods rely on generalized parameters that may not capture site-specific conditions.Microscopic traffic simulation tools, such as VISSIM [17] and CORSIM [18–20], model the movement of individual vehicles through work zones under differentscenarios. However, simulations require detailed coding of network geometry, traf-fic control, driver behavior models, and calibration to local conditions. Criticallane volume techniques, such as Highway Capacity Software, analyze the inter-section level of service and delays at signalized intersections affected by workzones.Analytical queuing methods, such as the Queue and User Cost Evaluation ofWork Zones (QUEWZ) [21], can estimate expected queue lengths and delays basedon work zone capacity reduction. However, queuing methods require accurateinputs for arrival rates and capacity. These traditional analytical and simulationmodelling approaches have been valuable for work zone assessment. However,they rely on approximations of traffic flow and driver behavior, which may not fullyreflect real-world intricacies. By contrast, data-driven ML offers new opportunitiesto model delays based directly on field observations of travel times through work2Highway Capacity Manual82.2. Studies on Work Zone Delay Predictionzones under various conditions.2.2 Studies on Work Zone Delay PredictionBecause collecting and aggregating comprehensive data from multiple sourcesis challenging, previous studies have been limited to the variables considered. Forexample, Du et al. [13] used a multilayer feed-forward neural network calledmulti-layer perceptron (MLP) to estimate the work zone delay using probe-vehicledata. They used data from 430 work zones across different freeways in New Jerseyin 2014, which considered segment speed, work zone length, ratio of open lanes,and basic work zone hours in their models. However, they did not account fordetailed work zone characteristics such as transition lengths, lane closure details,traffic control elements, or environmental factors like weather conditions. Theresults showed that the ANN model estimated travel delays more accurately thanthe traditional deterministic queuing model. In a later study, that involved 181work zones, Du et al. [14] integrated the previous ANN model with a SupportVector Machine (SVM) to account for capacity in their predictions. In the hybridmodel, the SVM layer predicts the work zone capacity, and this output is fed intothe ANN that regressed the 15-minute speed data to predict spatiotemporal delays.The proposed hybrid model outperformed an ANN model that did not utilizetraffic volume as a feature, thereby indicating the importance of traffic volume asa crucial factor. The model’s performance was evaluated along three work zonesthat only included short segments, while observations were also collected over ashort timeframe.Abdelmohsen and El-Rayes [22] adopted an unconventional approach to max-imize safety and mobility in work zones (i.e., minimize crash probabilities anddelay) by identifying the optimal values for work zone characteristics. The modelaimed to find optimal values for work zone speed limit, starting time, shoulder use,lateral clearance, length, access and egress method, and temporary traffic controlmeasures. To get the shortest traffic delay, the multi-objective optimization model92.2. Studies on Work Zone Delay Predictionsets the maximum value for the work zone speed limit, starting time, shoulderuse, and minimum segment length. In the case of minimizing crash indexes, theopposite is true. In the same vein, they introduced an optimization model forreducing work zone delays and minimizing construction costs. Traffic delays wereminimized by using the maximum speed limit, starting work zone activities atnight, and minimizing segment length [15].Using a connected vehicle environment, Wen [10] attempted to simulate workzone travel time. A simulation model was developed using data from a singlework zone in New York. Travel time analyses were conducted using four typesof models: linear regression, multivariate adaptive regression splines (MARS),stepwise regression, and elastic nets.Bae et al. [23] proposed a multi-contextual approach for modelling the trafficimpact of urban highway construction work zones. They also benefited fromML techniques to predict long-term traffic flow rates and the respective truckpercentages. A third-order polynomial curve-fitting model was used to estimatework zone travel time delays in large urban cores.To determine the impact of work zones on non-recurrent delay separately,Chung et al. [11, 12] used one year (2009) of archive data from Korea’s freeways.The model used a dataset of 20,078 records gathered for 14 major freeways inKorea. The results showed that the number of closed lanes, average daily delay,work zone length, and work zone duration directly affected the delay caused bythe work zones.While some previous studies have focused specifically on predicting delayscaused by work zones, this remains an emerging area of research with limitedexisting literature, as summarized in Table 2.1. This table summarizes key de-tails and limitations of five models for estimating work zone delays. To provideadditional context, the literature review was expanded to encompass studies thatmodelled and predicted other related work zone attributes besides just delay time.102.2. Studies on Work Zone Delay PredictionTable 2.1: Summary of Existing Work Zone Delay Prediction ModelsStudy (Ref-erence) MethodologyData and Sam-ple Size Key Details and LimitationsDu et al. [13]Multilayer Feed-Forward NeuralNetwork (ANN)Number of obser-vations not men-tioned in the studyConsidered segment speed,work zone length, open lane ra-tio, work hours; Did not ac-count for detailed work zone orweather factors. Limited vari-ables.Du et al. [14]Hybrid ANN andsupport vectormachine (SVM)181 work zonesand 50,000 15-minute speedrecords collectedover one year(2014)Added work zone capacity pre-diction from SVM; Limitedwork zone segments and time-frame. Small sample size withlimited variables.Wen [10]Simulation Model:Linear regres-sion, MARS,stepwise regres-sion, elastic nets34,560 observa-tions from a sin-gle 2-mile NewYork State workzoneSimulated work zone traveltime; Compared multiple mod-els. Single work zone limitsgeneralizability. Not account-ing for non-work zone-relatedimpacting factors.Bae et al.[23]ANN for long-term predictions;3rd order polyno-mial curve fittingfor delays17,518 traffic sen-sor readings; Datafor urban highwaywork zones in LosAngeles, CAPredicted long-term traffic andtruck percentages; Estimateddelays. Did not focus on de-tailed, microscopic delay pre-diction.Chung et al.[11, 12] Statistical Model31,128 workzones over 1year (2009) from14 South KoreafreewaysAnalyzed impact of workzone characteristics on non-recurrent delays. Older, limiteddataset from single country.112.3. Analysis of Other Work Zone Attributes2.3 Analysis of Other Work Zone AttributesIn a limited number of studies that took into consideration both work zonecharacteristics and variables external to work zones, Kamyab et al. [24] focusedon capturing patterns in non-recurrent traffic congestion, particularly when hourlytraffic volume data were unavailable. For this purpose, the research initially fo-cused on cases where hourly traffic volume was unavailable, using the distributionof historical traffic speed as an alternative baseline for mobility. The authorsutilized historical lane closure information on 1160 work zones located on Michi-gan interstates between 2014 and 2017 to forecast the spatiotemporal mobility forfuture lane closures. A mobility profile for historical observations was createdusing the probe vehicle data. This profile was used to train the random forest,XGBoost, and ANN models, among which the ANN outperformed the rest inaccuracy. One drawback of this study is that it placed speed data into wide 20 mphbins which makes a significant difference when the focus is on predicting delay ona microscopic level. The three models’ inputs included work zone configurationand features such as the number of open lanes, closed lanes, segment length, dis-tance to lane closure location, roadway geometry, Annual Average Daily Traffic(AADT), and spatial and temporal aspects like month, day of the week, and hourof the day. The most effective model achieved an accuracy of 85%.Hou et al. [25] also developed four models, including random forest, regressiontree, MLP, and nearest neighbor nonparametric regression, to investigate both long-and short-term traffic flow forecasting. Using work zone data on two different typesof roads, a freeway (i.e., I-270) and a signalized arterial (MO-141) at St. Louis,Missouri, USA. The results showed that the random forest model achieved the mostaccurate traffic flow forecast. Additionally, the most influential factors affectingtraffic flow varied based on the type of road, with the latest interval’s look-backtraffic flows at upstream, downstream, and current sites or traffic flows from thethree preceding intervals at the current site being the most significant factors.Bian and Ozbay [26] also attempted the prediction of work zone capacityusing the data for work zones on freeways in seven states of the USA to develop122.3. Analysis of Other Work Zone Attributestwo models; the Black-Box Variational Inference (BBVI) in the Bayesian neuralnetwork (BNN) and Monte Carlo (MC) dropout in regular ANN. In addition,the BBVI and MC dropout methods were compared with traditional methodssuch as ridge linear models and deterministic ANN. They used data from 225work zones on freeways in Maryland, Oregon, Texas, Indiana, South Carolina,Kansas, and Missouri. The results showed that while BBVI outperformed ridgelinear regression and deterministic ANN, MC dropout yielded less accurate butacceptable results compared to BBVI. In a similar study, Weng et al. [27] developeda model for estimating the work zone capacity that incorporates uncertainty. Themodel is based on a mixed linear regression function, where capacity is considereda random variable following a lognormal distribution. The parameters of thisdistribution were determined using the Bayesian approach. It should be noted thatdue to limitations in the available data, the study did not investigate the impact ofadditional factors such as the existence of ramps and traffic control devices.Additionally, Mashhadi et al. [28] reviewed 40 studies from 1981-2019 onestimating work zone capacity rather than travel time and delay. The most com-mon predictors of work zone capacity in previous studies consist of the reportedpercentage of heavy vehicles, the grade of the work zone, the intensity of the workzone, the type of road (rural or urban), the number of open and closed lanes, theduration of the work zone (short or long), the time of day (day or night) duringwhich the work is conducted, the width of the lanes, the location of lane closures(left or right), the length of the work zone, the weather conditions (clear or rainy),the composition and population of drivers, the presence of ramps, the speed limit inthe work zone, the normal speed, the weekday, and the lateral clearance. Anotherreview conducted by [29] provides an overview of the elements that influence thecapacity of work zones.Lu et al. [30] investigated the effects of work zones on traffic speed-volume-density curves and the roadway capacity using traffic data collected on freewaysin Iowa, USA. Four work zones in Iowa were investigated in this study during the2015 and 2016 construction seasons. A modified five-parameter logistic model132.3. Analysis of Other Work Zone Attributeswas developed to describe the speed-density relationship, based on which anoperational capacity prediction method was proposed considering the relationshipbetween free-flow speed and work zone characteristics.Using a logistic model-based approach, the speed-density relationship predicted by the model is closeto the estimated one from the field data. In addition, the predicted operationalcapacities were closer to the estimated values than those predicted by the decision-tree-based approach developed by Weng and Meng [31].Prior to these studies, classical ML methods were also developed. Weng andMeng [31] developed a decision tree–based model to estimate free-way work zonecapacity accurately. F-test splitting was used as a criterion to split the nodes andfurther grow the tree. Pruning was applied to minimize the mean square error(MSE) of the predictions. Subsequently, another study [32] used an ensemble treeapproach to estimate the work zone capacity. The ensemble tree model predictionwas more accurate than that of the model based on a single decision tree.The Smart Work Zone Deployment Initiative, in collaboration with the Centerfor Transportation Research in Austin, Texas, published a report summarizingefforts to develop ML models for the prediction of work-zone traffic impacts,including local speed and traffic volume changes and corridor-level travel timeincreases [33]. The researchers implemented ANNs to forecast speed and volumechanges for planned closures. The researchers also analyzed the performanceof three short-term travel-time predictions (STTTP) techniques. This includeda time-series analysis model and two types of ANNs. The study found that, onaverage, the new models outperformed traditional approaches by up to 50 percentduring the peak period travel time prediction; however, the study noted that theperformance was not as reliable when predicting travel times when work zoneswere present. The study concluded that the results were promising, with MLmodels consistently outperforming traditional approaches.Other studies have attempted to model and predict other work zone features.This includes the work zone speed [34], queue length [35–37], and safety [38–40].Meng and Weng’s [41] heterogeneous cellular automata model of traffic delay at142.4. Research Gapwork zones demonstrated that, particularly in light traffic conditions, the length ofthe transition area has far more significant effects on traffic delay than the lengthof the activity area in a work zone.2.4 Research GapAs evident in this section, the review of prior work zone delay studies revealsseveral limitations that restrict the model generalizability, predictive accuracy, andunderstanding of variable relationships.Firstly, many papers studying delays in the presence of work zones rely onrelatively small dataset observations collected over brief time periods or limitedroad segments [10–15, 22, 23]. Such limited samples prevent learning of complexdelay patterns and variable interactions.Secondly, most existing studies also exclude external variables including weather,seasons, and temporal factors from the analysis even though they have a signifi-cant impact on construction delays. Failing to account for these external factorslimits model accuracy and creates a risk of unobserved heterogeneity and omittedvariable bias.Thirdly, there is a lack of focus on explaining the underlying relationships andinteractions between variables that drive work zone delays. Enhanced explanatorycapabilities can provide crucial insights to guide mitigation strategies and designpractices.Fourthly, current models do not account for unobserved heterogeneity in therandom effects of work zones. Unobserved heterogeneity refers to unmeasured orunquantified characteristics and differences between entities (i.e. work zones) thatimpact the delays. These factors, although potentially impactful, are not measuredby predictor variables. Examples of these can include factors like variability indriver behavior or specific site conditions.Lastly, most prior work relied on traditional statistical approaches rely onassumptions about the underlying data distributions for analyzing work zone de-152.4. Research Gaplays. However, such assumptions may not fully represent patterns for work zonecongestion. More recent studies leveraged classical statistical and standard MLtechniques like linear regression and support vector machines. These models maystruggle to perform well on high-dimensional data and interactions between themultitude of variables influencing delays across diverse work zones. Additionally,the literature lacks comparative benchmarking of ML architectures for this delayprediction task.16Chapter 3Data Description3.1 Data OverviewThe data used in this thesis were collected by ATS Traffic’s IntelliTrafik Divi-sion, a traffic technology company with headquarters in Edmonton, AB. The rawdata included approximately 15 million travel time observations, captured every2-3 minutes, and collected between 2021 and 2022. The data was collected along a700 km corridor between the western borders of Alberta and the City of Vancouverin British Columbia (BC), Canada, and includes 710 planned work zones as partof the Trans-Mountain Expansion Project (TMEP).Of the 710 work zones, 674 had already been activated at the time of datacollection. We focused on the year 2022 due to COVID-19’s3 impact on trafficpatterns and work zone activities in 2021. Along with travel time data, the designspecifications and details of 123 work zones on Highway 5, where the postedspeed limit is 100 km/h, were extracted directly from work zone traffic controlplans (TCPs).Travel time data was captured based on probe vehicle data collected by Google.Such data has been used in many projects to monitor travel times and delays [42–46]. This includes the TMEP, which extends along the highway between westernAlberta and Vancouver. To ensure that delays due to construction activities do notexceed the thresholds set by the BCMoTI4, the project team utilized probe vehicledata for real-time estimation of under-construction travel times.3Coronavirus Disease of 20194BC Ministry of Transportation and Infrastructure173.2. Data Description3.2 Data DescriptionIn order to assess the impacts of different attributes on travel time throughwork zones, it was necessary to compile a comprehensive dataset. This sectionprovides a description of all different variables, including their respective sourcesand how they were integrated with the travel time data. It is important to note thatwhile all are described in this chapter, not all of them are necessarily utilized inevery model for a variety of reasons.3.2.1 Travel Time-Related VariablesGoogle probe vehicle data provides real-time and historical traffic information.The travel time data considered in this thesis included real-time estimates of traveltime through work zones of interest that are obtained every 2-3 minutes for eachactive work zone.Travel time estimation involves predicting how long it will take to travel be-tween two points considered as the endpoints of the work zone (refer to Figure 3.2for an illustration of a work zone). Google’s estimate of the travel time is influencedby various factors:• Speed Limits: The maximum legal speed allowed on a particular roadsegment.• Historical Data: Past travel times for the same route, which can indicatetypical patterns and variations.• Actual Driving Conditions: Real-time information obtained from driversusing Android-based apps to navigate their journey. This estimate integratesthe impacts of variables including traffic congestion, accidents, weatherconditions, and road closures.Google collects probe vehicle data from users who have enabled locationservices on their mobile devices. This data is anonymized and aggregated to183.2. Data Descriptioninclude information about the location, speed, and direction of travel for eachdevice. This data is used to generate real-time traffic information, including traveltimes, traffic congestion severity, and suggested alternate routes.This Google data is provided through a service provider to Intellitrafik ina readily usable format (i.e. each travel time observation is time-stamped andcontains information about the work zone asset it belongs to).Under-Construction and Baseline Travel TimeTwo estimates of travel time were considered in this thesis. (i) Under-construction travel time and (ii) Baseline travel time. The “Under-constructionTravel Time” refers to the estimated travel time through a work zone during activeconstruction activities. In contrast, “Baseline Travel Time” represents the typi-cal travel time through the same road segment under normal conditions (i.e. ata time before the construction zone existed). It serves as a reference point forunderstanding the impact of the work zone on travel time.Delay TimeDelay was computed as the difference between the under-construction (current)and baseline estimates of travel time using Equation. 3.1.𝐷𝑒𝑙𝑎𝑦 𝑇𝑖𝑚𝑒 = 𝑇𝑟𝑎𝑣𝑒𝑙 𝑇𝑖𝑚𝑒 𝑈𝑛𝑑𝑒𝑟−𝐶𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡𝑖𝑜𝑛 − 𝑇𝑟𝑎𝑣𝑒𝑙 𝑇𝑖𝑚𝑒 𝐵𝑎𝑠𝑒𝑙𝑖𝑛𝑒 (3.1)3.2.2 Weather VariablesOne-hour weather data records were gathered from 40 Environment Canadaweather stations in BC and appended to travel time information. This data ismaintained by the Government of Canada’s environment resources [47]. Weatherdata includes hourly temperature, precipitation, and wind speed information. Thisinformation was linked to the travel time observations based on temporal and193.2. Data Descriptionlocation data. A script was written to automatically perform the execution anddata collection procedure.3.2.3 Temporal VariablesSeasonTraffic volume and congestion typically differ among different seasons. There-fore, the season during which data was collected is also included in dataset. Sinceconstruction activity is often limited to summer and spring, only two seasonsexisted in the dataset.Day TypeThe day type variable categorizes each observation into either weekday orweekend. Weekdays (Monday to Friday) typically experience higher traffic vol-umes due to commuting and work-related travel, while weekends (Saturday andSunday) often see reduced traffic congestion as fewer people commute to work.Time of DaySimilar to season and day type, traffic congestion also varies during differenthours of the day. Time of day is a categorical variable that is used to capture thedifferences between daytime and nighttime hours in a day. 6 a.m. to 6 p.m. areconsidered daytime hours, and nighttime hours are the remainder of the day.Other extracted variables were minute in day, hour, weekday 5, day in month,day of year, and month. The selection of temporal variables varied across differentmodels based on expert opinion and the modelling goals. Not all of these variableswere used in every model, as their inclusion depended on the specific requirementsof the analysis.50 for Monday to 6 for Sunday203.2. Data Description3.2.4 Segment-Related VariablesRoad Type and Travel DirectionWork zones considered in the thesis are located along different sections ofthe highway corridor and include four road types: Multi-Lane Divided Road-ways, Multi-Lane Undivided Roadways, Two-Lane Roadways, and Low VolumeRoadways with no center line. Each road segment could be leading traffic in twodirections. In case the traffic was moving in the direction of moving away fromVancouver to the borders of Alberta, the road segment is Northbound (NB) and ifit was leading the traffic entering Vancouver it would be Southbound (SB).Traffic VolumeConsidering traffic volume information is also crucial when modelling delays.This information was obtained through BCMoTI’s Traffic Data Program. As partof this program, BCMoTI installs multiple permanent and temporary traffic countersites at various locations throughout British Columbia [48]. A script was writtento automatically locate traffic count sites that were within close proximity of eachof the work zones.It is worth noting here that some of the traffic counter sites were permanentwhile others were temporary. For temporary traffic count stations, traffic volumesduring the times when travel time data was collected were not always available.To account for this, the hourly traffic volume (HTV) information for those recordswas estimated using the following projection equation recommended in the AlbertaHighway Design Guide [49] for annual average daily traffic (AADT) projections(Equation 3.2).𝐻𝑇𝑉 ′ = 𝐻𝑇𝑉 × (1 + (𝑇𝐺𝑅 × (𝐶𝑌 − 𝑅𝑌 ))) (3.2)Where• 𝐻𝑇𝑉 ′ = estimated 𝐻𝑇𝑉 during the current year (𝐶𝑌 )213.2. Data Description• 𝐻𝑇𝑉 = observed 𝐻𝑇𝑉 during the most recent year where data is available(𝑅𝑌 )• 𝑇𝐺𝑅 = Traffic growth rate• 𝐶𝑌 = Current year• 𝑅𝑌 = Recent year –– the most recent and latest year that data is available.Segment LengthBesides traffic volume, segment length was also considered in the models. Thisis defined as the distance between two points representing the start and end pointsof the traffic control area for a construction site as outlined in the approved TCP(further detailed under Section 3.2.5: Work Zone Characteristic Variables).SpreadsConstruction activity for the TMEP project was split among four differentcontractors. These contractors operated within seven distinct operation zones,also referred to as “Spreads,” each covering a specific length of the corridorranging from 84 to 184 km. Within each operation zone, multiple work zoneswere established to carry out construction activities.Figure 3.1 illustrates the distribution of work zones across the seven operationzones, highlighting the diverse nature of construction activity along the corridor.3.2.5 Work Zone Characteristic VariablesWhile the exact impacts of work zone characteristics on delays are unknown,these variables are hypothesized to play a key role in enhancing predictions forunder-construction travel times and potential delays. The hypothesis is that workzone features significantly affect the delays observed at work zones. Assumingthis, characteristics, such as the existence of multiple signs, their placement and223.2. Data Description(a) Work zones in proximity to Abbotsford andMerritt(b) Work zones in proximity to Kamloops andValemountFigure 3.1: Map of Operation Zones and Work Zones for the TMEPMap Source: Earthstar Geographics, RDCO, Earthstar Geographics, Esri Canada, Esri, HERE,Garmin, SafeGraph, FAO, METI/NASA, USGS, EPA, NRCan, Parks Canada, Esri Canada, Esri,HERE, Garmin, SafeGraph, GeoTechnologies, Inc, METI/NASA, USGS, EPA, US Census Bureau,USDA, NRCan, Parks Canadadistances between signs, speed limits, lane configurations, and other features thatmay influence traffic flow and delays are captured in the data. Further analysisis done in Chapter 4: Exploring Variable Relationships and Delay Factors todetermine their relationships with work zone delays.For example, the presence of an intersection or side road within the work zonecan introduce additional merging and yield maneuvers. Some variables capturethe length and location of speed reductions when approaching the work zonesince gradual reductions in speed allow drivers to adjust their behavior, potentiallyimpacting travel times compared to sudden speed changes. Similarly, the lengthand location of speed increase zones after exiting the work zone could affect travel233.2. Data DescriptionTable 3.1: Work Zone Characteristic Variables DefinitionVariable DescriptionConstruction Sign Speed LimitDistanceDistance between the “Construction Ahead” sign andthe first speed limit sign1st Transition Length Start Distance between the first speed limit sign before thework zone and the work zone speed limit signCombined Transition LengthStartConstruction Sign Speed Limit Distance + 1st Transi-tion Length Start2nd Transition Length Start Distance between the work zone speed limit sign andthe “Traffic Control Person” signTransition Speed Limit Speed limit before entering the work zonePrepare to Stop? Presence of a “Prepare to Stop” sign just before thework zone areaWork Zone Length Total length of the work zone (distance between “Traf-fic Control Person” signs at both ends)Work Zone Speed Limit Designated speed limit within the work zoneBarrel Spacing Spacing between traffic control barrels within the workzone areaMinor Approach? Presence of an intersection or side road within thework zone areaTransition Length End Distance between the end of the work zone and the“Thank You” sign or the first speed limit sign afterexiting the work zoneThank You Sign Speed Limit Distance between the “Thank You” sign and the speedlimit sign after exiting the work zoneBidirectional Work Zone? Indicates if the work zone allows traffic flow in bothdirections (0 for separate lanes, 1 for shared lane)Originally Divided? Indicates if the original lane configuration had a di-vider between the two boundsOriginal Lane Count Number of lanes available to traffic before the workzone (1 or 2)New Lane Count Number of new lanes available within the work zone(usually 1)Closed Lane Count Number of lanes closed due to the work zone (0 or 1)243.3. Summary of Data Preprocessing WorkflowFigure 3.2: Features in a Work Zone Traffic Control Plantimes. Lane configuration within and around the work zone can significantlyimpact traffic capacity and flow, thereby travel times.The variables considered in this thesis are listed in Table 3.1. The variableswere obtained from the information provided by ATS Traffic based on the workzone design drawings and the field layout. These designs are based on the approvedTCPs that were submitted on a regular basis by their respective contractors. Anillustration of work zone layouts is drawn in Figure 3.2. Regarding the trafficcontrol setup, indicating the type of traffic control that is proposed for any worksite,these work zones were using Single Lane Alternating Traffic (SLAT).3.3 Summary of Data Preprocessing WorkflowThe raw highway work zone dataset underwent multiple iterations of prepro-cessing to ensure high-quality and consistent data for analysis. Initially, raw recordswere gathered from diverse sources including probe vehicle and sensor data, workzone layout designs, and traffic counts, resulting in a total of 14,994,469 traveltime records.253.3. Summary of Data Preprocessing WorkflowSubsequently, errors, duplicate records, and invalid data such as negative valuesfor delay in work zones were identified and cleaned, resulting in 5,365,472 validtravel time records. These records were then checked for consistency and filteredto retain only valid observations matching work zones during active construction,resulting in 2,914,140 valid travel time records matched to work zones.External data sources, including matched speed data, weather information, andtraffic volumes, were integrated to augment the records. Additionally, relevantwork zone characteristics were extracted from project TCPs to create an integrateddataset with all variables. It is important to note that in some cases, external datawas missing or invalid, resulting in the exclusion of those observations from thedataset.The resulted dataset was further filtered to focus solely on the records neededfor each analysis, as specified in each chapter. The final preprocessed datasetcontained 485,783 records enriched with all necessary variables for modelingwork zone delays.The descriptive statistics of quantitative (numerical) variables are summarizedrespectively in Table 3.2. The transition speed limit through these work zones is70 km/h. Table 3.3 shows the frequency and respective proportions of qualitative(categorical) variables.3.3.1 Correlation AnalysisCorrelation analysis was used to identify issues of multicollinearity betweenthe variables considered in this research. The correlation matrix detects highlycorrelated variables, indicating potential redundancy. While some correlationis expected in real-world data, multicollinearity can lead to inflated errors andinstability in regression models. In the identified sets of correlated variables,one variable can potentially be removed without significant loss of information.Eliminating redundant but non-identical variables can simplify models withoutsacrificing predictive power. However, it is imperative not to remove variablesthat provide complementary information, even if they are somewhat correlated as263.3. Summary of Data Preprocessing WorkflowTable 3.2: Descriptive Statistics of Quantitative (Numerical) VariablesVariable Mean Std. Dev. Min MaxUnder-Construction Time (minute) 2.17246 0.65666 1.4 8.93Delay Time (minute) 0.16 0.303 0 5.92Weekday 2.2372 1.62964 0 5Day of Year 120.2022 20.83762 84 159Month 4.49565 0.81174 3 6Day 15.3634 10.56314 1 31Hour 11.91606 3.22515 0 23Minute in Day 744.7889 193.1409 2 1438Temperature (centigrade) 9.80764 4.90612 -6.1 23.1Precipitation (mm) 0.07866 0.29483 0 2.8Wind Speed (km per hour) 6.738 4.71748 0 25Segment Length (km) 3.23367 0.7 5538 2.567 6.25Traffic Volume (vehicle per day) 3916.956 830.5267 2958.16 4976.96WZ Transition Length Start (m) 287.2736 149.4593 150 450WZ 2nd Transition Length Start (m) 500.1309 83.52551 450 855WZ Length (m) 146.8693 173.9146 50 625WZ Transition Length End (m) 636.6251 204.6725 300 1050WZ Construction Sign Speed Limit (m) 172.8244 53.87682 150 300WZ Thank You Sign Speed Limit (m) 75.00339 0.13008 75 80WZ Barrel Spacing (m) 104.7710 234.6021 0 1050WZ Speed Limit (km per hour) 60.84842 9.96395 50 70273.3. Summary of Data Preprocessing WorkflowTable 3.3: Summary of Qualitative (Categorical) VariablesVariable Categories FrequencyTravel DirectionNorthbound 245,425 (50.5%)Southbound 240,358 (49.5%)Road TypeMulti-Lane Undivided Road 219,151 (45.1%)Two-Lane, Two-Way Roadway 266,632 (54.9%)SeasonSpring 443,589 (91.3%)Summer 42,194 (8.7%)Bidirectional Work Zone?No, Not Shared 358,334 (73.8%)Yes, Shared 127,449 (26.2%)Were Lanes Originally Divided?No, No Divider 385,100 (79.3%)Yes, Divider Exists 100,683 (20.7%)Number of Lanes Before WZ1 478,501 (98.5%)2 7,282 (1.5%)Number of Closed Lanes0 367,022 (75.6%)1 118,761 (24.4%)∗ Operation zones are not shown in the table.dropping variables based solely on correlation can introduce bias [50]. For that,domain expertise guides which variables get kept or dropped.For this work, the Pearson correlation coefficient between independent vari-ables was calculated and a low correlation existed for most variables. However,the correlation matrix also revealed that certain work zone parameters like minorapproach, bidirectional, originally divided, and closed lane count have high cor-relations, leading to their exclusion from the dataset. Some correlated featureslike 1st transition length and construction sign speed limit distance were replacedwith their summation creating a new feature named “Combined Transition LengthStart”. Furthermore, among multiple temporal variables, only the informative set283.3. Summary of Data Preprocessing Workflowwas used in each model.29Chapter 4Exploring Variable Relationshipsand Delay FactorsUnderstanding the relationships between work zone features and delays is cru-cial for the management of excessive delays and accurate delay prediction. How-ever, existing work suffers from several limitations that restrict a comprehensiveunderstanding of variable relationships. Many previous studies relied on relativelysmall datasets over brief periods or limited road segments, preventing the learningof complex delay patterns and variable interactions. Additionally, most studiesexcluded key external factors like weather, seasons, and temporal elements, de-spite their significant impact - risking omitted variable bias. Furthermore, currentapproaches do not account for unobserved heterogeneity and random effects acrosswork zones. This chapter aims to uncover insights into the relationships betweenwork zone characteristics, road features, traffic conditions, weather, seasons, etc.,and the resulting delays. The modelling conducted in this chapter was conductedwith two primary aims:I. understand whether certain attributes lead to a work zone being clusteredinto certain delay categories andII. identify variables with potential statistically significant impacts on delay.4.1 Work Zone ClusteringTo identify whether particular work zone characteristics result in that workzone exhibiting low, moderate, or high delay levels, clustering was employed304.1. Work Zone Clusteringas an exploratory technique. Unlike classical statistical approaches that makeassumptions about the underlying relationships between variables, clustering doesnot require such assumptions. Instead, it allows the data to group observationsinto distinct clusters based on their associated delay.According to Xu and Tian [51], there are four types of clustering, namelycentroid-based, density-based, distribution-based, and hierarchical clustering. Density-based algorithms suffer when the data has high dimensions and the density varies.Distribution-based algorithms make assumptions about the distribution of data(e.g. Gaussian distribution), making it unsuitable for cases where the type ofdistribution for data is unknown or not assumed. Hierarchical clustering creates ahierarchy of clusters and is efficient for small-sized datasets.Since (i) the number of delay groups (=3) is defined based on expert opinion torepresent “Low”, “Medium”, and “High” delay clusters, (ii) there is no assumptionmade about the underlying distribution of delay, and (iii) the dataset is large,centroid-based clustering algorithms were chosen. Among these algorithms, K-means was selected for its simplicity, computational efficiency, and ability to handlelarge datasets, also referred to as scalability. More specifically, the algorithm’scomplexity is of 𝑂 (𝑛)6 making it a suitable choice as the runtime is in proportionto the number of items. By partitioning the work zone data into clusters basedon similarity in delay times, K-means clustering enables the identification ofkey factors that differentiate low, medium, and high-delay scenarios, providingvaluable insights into the potential delay causes.4.1.1 MethodologyK-means clustering is an unsupervised machine learning algorithm that isused to identify groups of work zones with similar delay time patterns. K-meansclustering partitions data points into 𝑘 clusters by minimizing the within-clustervariation, also known as inertia, i.e. maximizing inter-cluster variation [52]. Thevariation can be described as the sum of squares or Euclidean distance.6Big-O Notation314.1. Work Zone ClusteringK-Means Clustering AlgorithmK-Means is an iterative clustering algorithm that minimizes the sum of squares,i.e. Euclidean distance, within each cluster. The algorithm steps are:I. Define the number of clusters 𝑘 .II. Initialize the centroids/cluster centers (𝜇1, 𝜇2...𝜇𝑘 ) randomly or using aheuristic like k-means++ initialization (refer to Section 4.1.1: CentroidInitialization and Convergence).III. Assign each data point 𝑥𝑖 to its closest cluster center 𝜇 𝑗 based on the Eu-clidean distance (| |𝑥𝑖 − 𝜇 𝑗 | |).IV. Recompute the cluster centers 𝜇 𝑗 as the mean of all data points assigned tothat cluster.V. Repeat steps 3 and 4 until the assignment of data points to clusters does notchange significantly; therefore, the algorithm converges.The objective function minimized by K-Means can be stated as below (Equa-tion 4.1):𝐽 =𝑘∑︁𝑗=1∑︁𝑖∈𝐶 𝑗| |𝑥𝑖 − 𝜇 𝑗 | |2 (4.1)Where:• 𝑘 is the number of clusters,• 𝐶 𝑗 is the set of points belonging to cluster 𝑗 ,• 𝜇 𝑗 is the mean of cluster 𝑗 , and• 𝑥𝑖 is a data point.324.1. Work Zone ClusteringCentroid Initialization and ConvergenceK-means generally converges over time but may get stuck in a local minimum,especially depending on how centroids are initially defined. Due to this issue, re-peating the algorithm steps and computation with different centroid initializationscould help mitigate it. The k-means++ initialization method is employed for thispurpose, in which initial cluster centers are selected that are distant from each otherand dispersed. This approach enhances convergence speed which avoids gettingcaught in local optima and potentially leads to better results compared to randominitialization.Data PreparationAfter augmenting, cleaning, and refining the dataset, the descriptive statisticsof the nearly a quarter of a million data records were estimated for 38 work zones.The dataset contains columns relevant to analyzing delay time. The construc-tion sign and speed limit distance is added to 1st transition length start to create anew column named combined transition length start to have a higher variability.The categorical columns are label-encoded into numeric values for visual-ization purposes. The numeric columns are standardized independently usingStandard Scaler (Equation 4.2) to make the visualizations comparable.𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑆𝑐𝑎𝑙𝑒(𝑥) = 𝑥 − 𝜇𝜎(4.2)where:• 𝑥 is the feature value,• 𝜇 is the mean of the feature values, and• 𝜎 is the standard deviation of the feature values.334.1. Work Zone Clustering4.1.2 Results and DiscussionTo group the work zones into “Low”, “Medium”, and “High” delay clusters,𝑘 = 3 clusters were defined. Since K-means is based on calculating means foreach cluster, clustering is performed on the scaled delay times. The centroids wereinitialized using k-means++.The three clusters “Low”, “Medium”, and “High” have resulted in averagedelay times of 0.098 mins, 0.573 mins, and 1.618 mins, respectively. The relativeproportions of each cluster are highlighted in Figure 4.1.Figure 4.1: Pie chart showing relative sizes of the “Low”, “Medium”, and “High”delay clusters in the dataset with their respective sample counts.344.1. Work Zone ClusteringWhen analyzing the cluster means, the polar (Figure 4.2) plot effectively vi-sualizes these patterns across the clusters. The results of the K-means clusteringanalysis provide valuable insights into the dataset.Figure 4.2: Polar plot depicting averaged feature values for the delay time clusters.The radial axis represents scaled feature values. The axes of the plots are scaledto enable comparison across different features.These clusters can be used to understand the underlying structure of the dataand to identify patterns and trends. For instance, it can be derived that work zones354.1. Work Zone Clusteringbelonging to the cluster associated with higher delay tend to have longer segmentlength, transition length end, combined, and 2nd transition length start, which theiralignment with respect to each other is illustrated in Figure 4.3. This is reasonablesince work zones, by their very nature, disrupt the normal patterns of vehicularmovement, causing congestion and delays. Longer segment lengths mean a longerstretch of the road is affected by the work zone, leading to a greater potentialfor traffic flow disruption. Similarly, longer transition areas, both at the start andend of the work zone, involve more complicated merging and shifting of trafficpatterns. In addition, larger work zones often require more extensive traffic controlmeasures, such as lane closures and temporary barriers, which can create queuesof motorists.Figure 4.3: Features in a Work Zone Plan for ClusteringAdditionally, the “High” cluster shows a lower mean hour value (11.63) com-pared to the Medium (12.13) and “Low” (11.75) clusters. This suggests that the“High” cluster may represent events that tend to start earlier in the day. Therefore,traffic management strategies could be adjusted to minimize the impact duringpeak hours. Additionally, shortening the segment length, and work zone transitionlength start and end can potentially reduce delays.It is crucial to address the inherent limitations observed in the K-means clus-364.2. Logistic Regression Modellingtering approach. The K-means algorithm, while effective in identifying distinctclusters within the dataset, operates under the assumption that clusters are convexand isotropic. This assumption does not always hold true, especially in complexreal-world datasets. Furthermore, the measure of cluster coherence, known asinertia, is not a normalized metric leading it to become less meaningful and rep-resentative in high-dimensional spaces due to the curse of dimensionality, whereEuclidean distances tend to inflate. The clustering also provides no data on whethercertain variables have statistically significant effects on a work zone belonging to aspecific cluster or not. Given these constraints, the use of ordinal logistic regression(OLR) as an analytical method was necessary.4.2 Logistic Regression ModellingIn this section, Logistic Regression (LR) is used to assess the statistical sig-nificance of the probability a work zone of certain characteristics belonging to acertain delay level. LR offers a more flexible approach to performing analysis forreal-world data patterns. Unlike K-means, LR does not rely on distance measuresbut instead focuses on the statistical relationship between ordinal outcomes andpredictor variables. Moreover, LR provides interpretable results through coeffi-cients that indicate the direction and strength of associations between predictorsand ordered response categories.4.2.1 MethodologyThe specific form of logistic regression used in the analysis of the data wasOrdinal Logistic Regression (OLR), also known as Cumulative Logit Model. Lo-gistic regression makes no assumptions about the distributions of the independentvariables, which can be binary, continuous, or categorical variables.The dependent variable that was used in the models is the level of delay. Thedelay value was classified into one of three categories to give a sense of the level of374.2. Logistic Regression Modellingdelay. The thresholds for levels were inspired by the clustering results (Section 4.1:Work Zone Clustering). The first level, “Low” represents a delay between 0 to 0.5,“Moderate” represents a delay of 0.5 to 1, and “High” represents a delay over 1.The ordinal nature of the response, in our case, the level of delay, also makesit challenging to meet the assumptions of the ordinary linear regression.ModelLogistic regression is used to predict the odds of a certain event occurringbased on the values of several independent variables. For this, let 𝑌 be an ordinaloutcome variable that denotes the level of delay observed at a particular locationduring a specific time. In addition, consider 𝐾 as the number of levels in thecategorical response variable (delay levels), i.e. low, moderate, and high delay.Then the cumulative probability of 𝑌 less than or equal to a specific category𝑘 = 1, .., 𝐾 − 1 can be defined as Equation 4.3:𝑜𝑑𝑑𝑠(𝑌 ≤ 𝑘) = 𝑃(𝑌 ≤ 𝑘)𝑃(𝑌 > 𝑘) =𝑃(𝑌 ≤ 𝑘)1 − 𝑃(𝑌 ≤ 𝑘) (4.3)Note that the max value for 𝑘 is 𝐾 − 1 because (𝑃 ≤ 𝐾) = 1 => (𝑃 > 𝐾) = 0.This probability can be represented as log odds, using a logit model of thefollowing functional form (Equation 4.4):𝑙𝑜𝑔𝑖𝑡 (𝑌 ≤ 𝑘) = 𝑙𝑛( 𝑃(𝑌 ≤ 𝑘)1 − 𝑃(𝑌 ≤ 𝑘) ) (4.4)The cumulative logistic model for ordinal response data is given by (Equa-tion 4.5):𝑙𝑜𝑔𝑖𝑡 (𝑌 ≤ 𝑘) = 𝛼𝑘 + 𝛽𝑘1𝑋1 + ... + 𝛽𝑘𝑚𝑋𝑚 (4.5)Where 𝛽𝑘𝑚 are regression parameters of the model (i.e. intercepts and slopes), and𝑋𝑚 are the covariates representing 𝑚 factors that have alleged effects on the oddsratio of delay.The regression parameters are evaluated using an iterative maximum likelihood384.2. Logistic Regression Modelling(ML) procedure. All analysis was done using IBM SPSS Statistics version 29.Model FitUnlike linear regression, a well-accepted measure of goodness-of-fit (GOF),such as 𝑅2, does not exist in logistic regression. Alternatively, the Chi-square(𝜒2) method in the Omnibus test was used to assess model GOF. The Omnibustest assesses whether including explanatory variables in the model improves GOF.This is achieved by computing the difference between the deviance of the modelbefore and after the variables are added, as in the following notation:𝐺 = 𝜒2 = −2𝐿𝐿𝑁𝑢𝑙𝑙 − (−2𝐿𝐿𝑝) (4.6)Where G is the goodness-of-fit estimate, and −2𝐿𝐿 is the deviance estimate forthe null (intercept only) model and the model with 𝑝 variable, respectively.It is worth noting here that the Hosmer and Leshow (H-L) test cloud also beused to measure the difference between prediction with and without the modelvariables. However, the test has been found unreliable, especially when using alarge sample size, since the test becomes too sensitive [53]. This means that evena small difference between observed and model-predicted values gets flagged assignificant.4.2.2 Results and DiscussionTable 4.1 shows a summary of the OLR results. It displays the coefficientestimates, standard errors, Wald chi-square statistics, and odds ratios for eachconsidered predictor variable. The odds ratios quantify the impact of each variableon the likelihood of observing higher delay levels. According to the results, allvariables considered in the analysis except Time of Day had statistically significanteffects on the level of delay observed at the work zones at the 0.5% confidencelevel (i.e. p-value < 0.05).The model reveals that segment length increases are associated with an increase394.2. Logistic Regression ModellingTable 4.1: OLR Model Results SummaryVariable Level Estimate Std. Error Wald Odds Ratio p-valueDelayLow (level = 1) 28.215 4251.7681 0 1.794E+12 0.995Moderate (level = 2) 30.171 4251.7681 0 1.268E+13 0.994High (level = 3) 0 . . 1 .SeasonSpring 0.724 0.0397 331.835 2.062 <0.001Summer 0* . . 1 .Day TypeWeekday -0.286 00399 51.536 0.751 <0.001Weekend 0* . . 1 .Time of DayDaytime 20.876 4251.7681 0 1164495288.4 0.996Nighttime 0* . . 1 .Travel DirectionNorthbound -0.085 0.0177 23.422 0.918 <0.001Southbound 0* . . 1 .Temperature -0.027 0.0021 157.622 0.974 <0.001Precipitation 0.124 0.0237 27.295 1.132 <0.001Wind Speed 0.072 0.0018 1686.750 1.075 <0.001Segment Length 0.332 0.0197 282.942 1.393 <0.001Combined Transition Length Start 0.289 0.0626 21.403 1.336 <0.0012nd Transition Length Start 0* . . 1 .Work Zone Length 51.700 1.1331 2081.787 2.837E+22 <0.001Transition Length End 0* . . 1 .Barrel Spacing -59.014 1.2773 2134.775 <0.001 <0.001Traffic Volume 0.001 0.0002 8.029 1.001 0.005* Set to zero by the model because this parameter is redundant.404.2. Logistic Regression Modellingin the level of delay. The odd ratio shows that a unit increase in segment length(1 km) increases the likelihood of delay level increasing by 39.3%. Similarly, thework zone length has an outsized impact, with longer lengths increasing delayodds by over 50 times. Additionally, the combined transition length start also hasa direct effect, increasing odds by 33.6%.Higher traffic volumes unsurprisingly increase delay odds, as more vehiclesconstrain flow and worsen bottlenecks. Each 1 vehicle increase raises odds by0.1%. This quantification highlights the impacts that small traffic volume increasescan have on congestion through the work zone. The northbound travel directiondecreases the likelihood of delays by 8.2% compared to the southbound. Thisdirection-specific effect may result from particular bottlenecks or merge areas thatimpact southbound traffic.Environmental factors were also found to have statistically significant impactson the level of delay observed at a particular location during a certain time instance.Temperature increases are associated with the likelihood that delay decreases inlevel, potentially due to inclement weather suppressing travel demand. This couldalso be attributed to inefficient traffic management in work zones at times whenthe temperature is low. In contrast to temperature, each 1 km/hr increase in windspeed raises delay odds by 7.5%, potentially due to heightened driver caution inhigh winds. In addition, strong crosswinds may also deter overtaking maneuvers,impacting flow.The impacts of temporal factors on delay are also intuitive. Compared toweekends, weekdays are affiliated with a lower level of delay through work zones.The odds ratio shows that the likelihood of high delay drops by 24.9% for weekdays.These results indicate that delays through work zones increase due to intra-citytravel, which increases on weekends when compared to other days of the week.Overall, the statistical significance testing by OLR identified which featureshave a meaningful relationship with the observed effects. Additionally, severalfindings align with expectations. Weekday travel and higher traffic volumes all in-crease the odds of higher delays, likely due to busier traffic conditions. Conversely,414.3. Mixed-Effects Linear Regressionnorthbound travel direction and precipitation decrease delay odds.These observations are consistent with the clustering analysis presented earlier,which identified that longer segment lengths and combined transition length startare associated with increased delay levels.While OLR provides valuable insights into factors influencing categoricaldelay levels, it has its own limitations which led to further exploration of linearmixed-effects regression in the next section.4.3 Mixed-Effects Linear RegressionMixed-effects linear regression (MELR) is well-suited for analyzing work zonedelay data due to the hierarchical and longitudinal nature of the observations. Inthe dataset, there are repeated measurements of delay times at multiple work zonesover different time periods. This violates the assumption of independence requiredfor OLR. Furthermore, work zones are not homogeneous units and each one hasits own unique quirks and unobserved sources of variability that impact delays.Simply treating work zones as fixed effects in OLR is not optimal, as it assumesconstant variable effects across all observations.The decision to move from a categorical dependent variable (delay level) inthe OLR to a continuous dependent variable (delay time) in the MELR modelwas driven by several key considerations. The thresholds used to categorize thedelay into low, moderate, and high levels were based on the clustering resultsand may be subjective. The choice of these thresholds can vary across differentcontexts, work zones, and even contractors, introducing uncertainty and limitingthe generalizability of the categorical delay levels. Additionally, by categorizingthe continuous delay time variable, OLR only captures the odds of observing ahigher delay level. However, it does not provide a precise quantification of theactual delay time experienced.In contrast, the MELR allows for a more flexible and continuous representa-tion of the delay time outcome variable. This enables the application of different424.3. Mixed-Effects Linear Regressionthresholds and categorizations after obtaining the model predictions, rather thanbeing constrained by preset delay level definitions. Moreover, MELR provides away to model this hierarchical data structure explicitly. By treating work zones asrandom effects, it can account for unobserved heterogeneity across sites and modelwork zone-specific variability as a random quantity. Treating a work zone as arandom effect captures the inherent differences between locations that impact de-lays beyond the fixed predictors. The longitudinal aspect, where there are repeateddelay measurements at each work zone over time, also violates the independenceassumption of OLR. MELR models can incorporate temporal structure and cor-relations within work zones through the inclusion of random effects. In essence,the MELR model along with panel data7, allows controlling for unobserved het-erogeneity that differs from one work zone to the next and is not correlated withindependent variables but is constant over time. Additionally, this model is able tocontrol for variables that change through time but do not vary across work zones(time-fixed effects), therefore, eliminating omitted variables bias.This section presents MELR analysis to investigate the impact of various factorson work zone delays. The model incorporates fixed effects for variables like trafficvolume, weather, temporal factors, etc. along with random effects to account fordifferences between individual work zones.4.3.1 MethodologyThe mixed-effects regression model has different intercepts for each entity(work zone). These intercepts absorb the influences of all omitted variables thatdiffer from one entity to the next but are constant over time. The MELR isformulated in Equation 4.7 and was initially introduced by Laird and Ware [54].Let 𝑌𝑖 be a variable that denotes the delay time observed at a particular work zone𝑖,7Longitudinal data about 𝑁 different entities (work zones) observed at different time periods.434.3. Mixed-Effects Linear Regression𝑌𝑖 = 𝑋𝑖 𝛽 + 𝑍𝑖 𝑢𝑖 + 𝜖𝑖𝑖 = 1, . . . , 𝑚(4.7)Where• 𝑌𝑖 is a 𝑛𝑖 × 1 column vector representing the dependent variable (delay timeobserved at work zone 𝑖).• 𝑋𝑖 is a 𝑛𝑖 × 𝑝 covariate matrix of the 𝑝 fixed-effects predictor variables forwork zone 𝑖.• 𝛽 is a 𝑝 × 1 column vector of the fixed-effects coefficients.• 𝑍𝑖 is a 𝑛𝑖 × 𝑞 covariate matrix for the 𝑞 variables with random effects acrosswork zones.• 𝑢𝑖 is a 𝑞 × 1 row vector of 𝑞 random-effects coefficients assuming it followsa normal distribution.• 𝜖𝑖 is a 𝑛𝑖 × 1 column vector of the errors assuming it follows a normaldistribution.• 𝑛𝑖 is the total number of observations for work zone 𝑖.• 𝑚 = 38 is the number of work zones.• 𝑝 indicates fixed-effects predictors.• 𝑞 is the random intercept considered for each of the 𝑚 work zones.In this formulation, 𝑌𝑖 represents the delay time observed at a particular workzone 𝑖, which is modeled as a linear combination of the fixed-effects predictorvariables (𝑋𝑖 𝛽), the random effects component (𝑍𝑖 𝑢𝑖), and the random error term(𝜖𝑖).The random effects component, 𝑍𝑖 𝑢𝑖, allows the model to capture the unob-served heterogeneity or cluster-level differences among work zones, by introducing444.3. Mixed-Effects Linear Regressionrandom intercepts (𝑢𝑖) for each work zone. These random intercepts are assumed tofollow a normal distribution and are estimated from the data along with the fixed-effects coefficients (𝛽). The random error term, 𝜖𝑖, accounts for the remainingunexplained variability in the delay times that is not captured by the fixed-effectspredictors or the random effects component. By explicitly separating the randomeffects (𝑍𝑖 𝑢𝑖) from the random errors (𝜖𝑖), the MELR can effectively model thehierarchical structure of the data, where observations are nested within work zoneswhile accounting for both the observed predictor variables and the unobservedheterogeneity across work zones.The fixed-effects variables considered in the development of the model aresegment length, traffic volume, temperature, precipitation, wind speed, season, daytype, time of day, travel direction, and work zone-related features (i.e. combinedtransition length start, 2nd transition length start, work zone length, transitionlength end, and barrel space) on four different spreads. Therefore, 𝑝 = 15 and𝑞 = 1 since only intercept was considered to reflect the random effects of variouswork zones.Model FittingThe regression parameters are evaluated using an iterative maximum likelihood(ML) procedure. The data were fitted to a MELR with fixed effects for slopes andintercepts and random effects for intercepts using the lmer function from packagelme4 version 1.1-35. All analysis was done using R version 4.3.2.Table 4.2 presents the statistical metrics utilized to assess the model’s perfor-mance. The standard deviation of 0.315 for the work zone random effect showsvariability in the estimated intercepts for each work zone not explained by themodel’s fixed effects.The model reported an ICC of 0.6. A value of 𝐼𝐶𝐶 = 0 indicates that the totalvariance is due to individual differences within groups, while 𝐼𝐶𝐶 = 1 means thatall of the variation is due to differences between groups. This ICC of 0.6 for thework zone random effect indicates that 60% of the total variance in delay times454.3. Mixed-Effects Linear RegressionTable 4.2: Statistical MetricsMetric / Formula DescriptionR-squared Marginal (𝑅2marginal) [55]𝑅2marginal =Variance of Fixed EffectsTotal VarianceMeasures the proportion of variance ex-plained by fixed effects merely, ignoringrandom effects. Provides insight into thecontribution of these fixed effects to theoverall variability.R-squared Conditional (𝑅2conditional) [55]𝑅2conditional =Variance of Fixed + Random EffectsTotal VarianceQuantifies the proportion of variance ex-plained by both fixed and random effects.Used for assessment of the model’s ex-planatory power and how well the modelcan capture the variability of data.Intra-Class Correlation (ICC) [55]ICC = Between-Group VarianceTotal VarianceMeasures the proportion of variance inthe outcome (delay time in this case) thatcan be attributed to clustering by groups(work zones).Akaike Information Criterion (AIC)Measures the model’s goodness offit (GOF), balancing the trade-off be-tween model complexity and explanatorypower.Bayesian Information Criterion (BIC)Evaluates model fit while penalizing formodel complexity. Tends to penalizecomplex models more severely than AIC.is due to differences between work zones that are not explained by the model’sfixed effects. In other words, there are meaningful differences in average delaytimes across highway work zones that relate to some unmeasured characteristicsof those work zones. Some potential reasons for an ICC this high in this context:The relatively high ICC of 0.6 highlights that even after accounting for measuredvariables in the model like traffic volume and work zone characteristics, thereremains significant cluster-level variance in delays attributable to the individual464.3. Mixed-Effects Linear Regressionwork zones. This emphasizes the importance of modelling the work zones asrandom effects rather than simply adjusting for fixed effects, and the suitability ofthe mixed-effects model approach used here.To assess the fit of the selected model, the AIC and BIC for the developedmodels were compared to a base model with traffic volume as the only predictor,the AICs were 189,617.88 and 62,432.89, for the baseline and the selected model,respectively. Similarly, the BIC values were 189,649.18 and 62,641.59. Formodel comparison, the model with the lowest AIC and BIC scores is preferred(the absolute values of the AIC scores do not matter). Lower values suggest abetter balance in explaining the data while avoiding overfitting.The model also reported 𝑅2marginal = 0.294 and 𝑅2conditional = 0.697 whichshowcases the collective contribution of both fixed and random effects.It is worth mentioning that traditional linear regression models might overesti-mate the 𝑅2 if they fail to account for inherent differences between work zones. TheMELR model addresses this by including random intercepts for each work zone.These intercepts capture the unexplained variability associated with unmeasuredcharacteristics unique to each work zone.4.3.2 Results and DiscussionTable 4.3 shows a summary of the mixed-effects model results to examine therelationship between delay time and different variables controlling for individualdifferences in work zones. It displays coefficient estimates with standard errorsand p-values for predictor variables. The mixed-effects model accounts for asset-level variations via random intercepts. The variables, that were found to havestatistically significant effects on the delay time observed at the work zones on the1% significance level (i.e., p-value <0.001), were highlighted. This includes theoperation zone (not shown in the table). T-tests were calculated using Satterth-waite’s method. The coefficients of the categorical or binary variables indicatethe incremental impact of belonging to that category relative to the base case, theomitted category.474.3. Mixed-Effects Linear RegressionTable 4.3: Results of MELR Fit by Restricted Maximum Likelihood (REML)Variable Level Estimate Std. Error p-valueSeasonSpring 0 . .Summer -0.013* 0.002 <0.001Day TypeWeekday 0 . .Weekend -0.002 0.002 0.356Time of DayDaytime 0 . .Nighttime -0.342* 0.007 <0.001Travel DirectionNorthbound 0 . .Southbound 0.070 0.104 0.500Temperature -0.001* 0.000 <0.001Precipitation -0.004* 0.002 0.035Wind Speed 0.006* 0.000 <0.001Segment Length 0.136* 0.045 0.003Combined Transition Length Start 0.042 0.363 0.9092nd Transition Length Start 0.107 0.906 0.906Work Zone Length -0.022 0.115 0.849Transition Length End -0.063 0.544 0.908Barrel Spacing 0.025 0.130 0.848Traffic Volume 0.004* 0.001 <0.001* p <0.05484.3. Mixed-Effects Linear RegressionThe results reveal several key insights into factors impacting delay time throughwork zones. As expected, increases in traffic volume are associated with higherlevels of congestion and longer delay times. A 1-unit increase in volume isassociated with a 0.004-minute rise in delay. With traffic volume accounted forin the model, variables for travel direction became statistically insignificant. Tomitigate increased delays from higher traffic, conducting construction during off-peak periods could help relieve congestion.The model also reveals a strong link between segment length and delay time.For every 1 km increase in length, delays are estimated to increase by 0.136 minutes.As vehicles travel longer distances through construction segments, congestionaccumulates, and speed decreases.Characteristics of the work zone itself impacted delays too. A 1 km increase inwork zone combined and 2nd transition length start related to a 0.042-minute and0.107 increase in delay, respectively. This indicates longer work zone transitionlength allows slower flow throughout the transition part. Wider barrel spacingcorresponded to higher delays as well, potentially due to more complicated drivingconditions.Environmental factors like temperature, precipitation, and wind also signifi-cantly impact delay times. The coefficient associated with temperature is -0.001showing that if the temperature is increased by 1 centigrade, the delay time willdecrease by a small, yet statistically significant, value of 0.001 minutes. This couldbe a matter of less construction activity taking place during warmer temperatures.Wind speed increase of 1 unit correlates with 0.006-minute respective increasesin delay, likely from more cautious driving. Unfavourable weather possibly com-pounds existing work zone delays.Seasonality impacts delay as well, with Spring showing a 0.013-minute in-crease versus Summer, attributable to seasonal traffic in which Spring has highertraffic volumes. This higher travel volume might contribute to recurrent conges-tion (i.e., congestion in regions where there are no construction zones). Recurrentcongestion might have spillover effects on the non-recurrent congestion at work494.4. Conclusionzones.The impacts of temporal factors on delay are also intuitive. As expected,nighttime and weekends also see lower delays than daytime and weekdays, withnightime having a 0.342-minute reduction. This is likely from increased intra-cityand inter-city travel in daytime when compared to nighttime.4.4 ConclusionThis chapter performed an in-depth analysis on the extensive highway workzone dataset with two primary aims - to investigate if certain attributes lead to awork zone being clustered into a specific delay level, and to determine factors withstatistically significant effects on delays. This is achieved through three techniques:clustering, ordinal logistic regression, and mixed-effects linear modelling.The data-driven clustering approach grouped work zones into low, mediumand high delay categories while revealing longer segment and transition lengthsare associated with higher delays, aligning with expectations. Both the ordinal andmixed-effects linear models quantified significant relationships between delays andkey variables related to road geometry, work zone structures, weather, seasons andtimes of day.Table 4.4 summarizes the insights on the variables’ relationship with the workzone delay observed. For instance, the OLR reports higher traffic volumes, segmentlength, combined transition length, and work zone increase the odds of delays. TheMELR estimates the exact effects on delay time in minutes, showing relationshipslike increased delays with longer segment lengths and higher traffic. Both modelsindicate that the impact on the length of transition areas (i.e. 2nd transition lengthstart and transition length end) is insignificant. Environmental variables, such astemperature and wind speed showed significant effects on the delays experiencedat work zones.The quantified relationships offer valuable guidance for data-driven work zoneplanning and design aimed at minimizing congestion and project delays. Trans-504.4. Conclusionportation agencies could leverage these findings to optimize work zone configura-tions, refine traffic management plans, and implement proactive measures tailoredto the specific delay factors identified. The insights gained serve as a foundationfor developing robust predictive models explored in subsequent chapters.Table 4.4: Comparison of the Each Model’s ResultsVariable OLR MELRSeason - Spring to Summer ↓ ↓Day Type - Weekend to Weekday ↓ NSTime of Day - Daytime to Nighttime NS ↓Travel Direction - Northbound to Southbound ↑ NSTemperature ↑ ↓ ↓Precipitation ↑ ↑ ↓Wind Speed ↑ ↑ ↑Segment Length ↑ ↑ ↑Combined Transition Length Start ↑ ↑ NS2nd Transition Length Start ↑ NA NSWork Zone Length ↑ ↑ NSTransition Length End ↑ NA NSBarrel Spacing ↑ ↓ NSTraffic Volume ↑ ↑ ↑NS/NA: P-value not significant (p >0.05) or not applicable.51Chapter 5Using Machine Learning Models forDelay PredictionAccurate prediction of under-construction delays is critical for effective trafficmanagement and planning. Delays at work zones can significantly impact trafficflow, causing congestion, increased travel times, and delays. Precise forecastingallows transportation agencies to take proactive measures such as adjusting trafficsignal timings, implementing detours, or deploying additional personnel to mit-igate disruptions. Moreover, reliable delay estimates enable contractors to meetproject deadlines and avoid costly overruns by optimizing resource allocation andadherence to predetermined delay thresholds.However, predicting work zone delays can be a complicated task due to themany factors influencing traffic flow in work zones. The decision to rely onmachine learning (ML) models for delay predictions, rather than traditional statis-tical approaches, was driven by several key factors. ML techniques offer distinctadvantages in capturing the complex, non-linear relationships between the manyvariables influencing delays. The dataset available contains a large number offeatures and a vast number of records, making it well-suited for the data-driven,flexible nature of ML models. Additionally, previous studies have demonstratedthat ML approaches, such as ANN and hybrid models, outperform traditional sta-tistical methods in estimating travel delays. Unlike the limited, simplistic datasetsused in earlier research, the extensive real-world data on traffic, weather, andwork zone characteristics available for this study enables the development of morerobust, data-driven predictive models.To that end, this chapter has two key aims. First, to develop ML models52Chapter 5. Using Machine Learning Models for Delay Predictionto reliably predict delays, as accurate delay forecasts are critical for proactivetraffic management, contractor planning, and minimizing disruptions (outlined inthe earlier chapters of the thesis). ML techniques offer distinct advantages inmodelling intricate data patterns by learning relevant feature interactions and theircomplex non-linear relationships from large datasets. These models can effectivelyhandle datasets with a large number of input features and are designed to scale andtrain efficiently on very large datasets. Additionally, unlike parametric statisticalmodels with rigid assumptions, ML techniques are non-parametric and make fewerassumptions about the underlying data distribution.The second objective is to compare the performance of different ML algorithmsfor delay prediction. With the increasing adoption of ML approaches acrossvarious domains in recent years, a range of ML models and architectures havebecome available. This comparative assessment aims to provide insights to guidefuture model selection for researchers and practitioners interested in leveragingML for work zone delay analysis and forecasting.While the explanatory analysis provides valuable insights into factors influenc-ing delays, predictive modelling enables the estimation of expected delays in futurework zone scenarios. ML techniques like artificial neural networks and ensemblemodels are particularly well-suited for delay prediction task. They can modelcomplex non-linear relationships between many variables that impact delays andidentify complex data patterns for estimating under-construction travel times.This chapter conducts a comprehensive comparative study across multiplestate-of-the-art ML algorithms, including fully connected feed-forward neural net-works, decision trees, ridge regression, and support vector regression. By evaluat-ing these diverse models, an in-depth understanding of their relative strengths andweaknesses for predicting delays under various conditions is achieved. This anal-ysis guides the appropriate selection of models based on context and performancerequirements.535.1. Dataset Preparation5.1 Dataset PreparationFor the analysis of this chapter, 485,783 records for 81 activated work zoneswere considered. The larger dataset size compared to Chapter 4: Exploring Vari-able Relationships and Delay Factors is due to several factors. ML algorithms likeANN can handle more input features [56], even with some correlation, by learningcomplex relationships without assumptions about the functional form or distribu-tion of data [57, 58]. This allowed retaining more unique observations with theincreased feature space. Additionally, data imputation techniques enabled keepingobservations that would have been dropped for traditional statistical models [59–61]. The robust architecture of ML models like ANN also allows learning fromlarger, noisier, imbalanced datasets containing some redundancy, requiring lessrestrictive data preprocessing compared to statistical approaches more susceptibleto outliers and biases [62, 63].5.1.1 Feature EncodingAs discussed in Chapter 3: Data Description, the dataset contains a mix ofcategorical, cyclical, and numerical features. To prepare the data for ML models,it is necessary to encode these features into a numerical representation.For the categorical features (e.g. road type), one-hot encoding is applied.One-hot encoding is a way of representing categorical variables as binary vectors.The basic idea is to create a new binary column for each unique category in thefeature, where each row is assigned a value of 1 in the column corresponding toits category, and 0 in all other columns. This allows the ML models to treat thecategorical variables as numerical inputs without making any assumptions aboutthe ordering or relationship between the categories.The dataset also contains cyclical features, such as time and date that havean inherent periodicity. Therefore, sinusoidal/cosinusoidal encoding is used toconvert the cyclical features into their corresponding sine and cosine components,which allows the models to learn the underlying periodic patterns in the data.545.2. MethodologyLastly, the numerical features (e.g. segment length) are normalized usingmin-max scaling. Min-max scaling, also known as feature scaling, transforms thenumerical features to a common range, typically between 0 and 1.5.1.2 Train and Test SplitThe train-test split is a critical step in ML model development, aimed atevaluating the model’s performance on unseen data and assessing its generalizationability.To generate the split, the initial step was to randomly shuffle the entire dataset(485,783 records) to mix up the sample order. Once shuffled, the dataset was splitinto training and test sets based on specified proportions. We used a 90%/10% split,with 90% of samples (437,204 records) allocated for model training and validatingand the remaining 10% held out exclusively for testing (48,579 records).Using a larger portion for training and validating provides more examples forthe model to learn from, and shuffling ensures the test set is a random subset thatfairly represents the overall data distribution. In contrast to regression models,which frequently employ a conventional test/train split ratio, for ML models, suchas ANN, there is no optimal divide that can be applied to all cases [64–68].According to the literature, what might be considered a low percentage, such as10% of large datasets can evaluate model performance adequately [69, 70]. Thesizable test set obtained from a tiny portion of the huge dataset still resulted in48,579 test cases, which is significantly more than the samples usually used todevelop and assess regression models.5.2 MethodologyIn this chapter, several ML regression models were developed to predict thetravel time in the presence of work zones. As already noted, comparing multiplemodelling techniques provides insight into their relative strengths and weaknesses555.2. Methodologywhile providing a performance benchmark in this problem and dataset. This alsohelps professionals interested in utilizing ML models, to select the most appropriatemodel for the delay prediction problem at hand.The regressors considered in this thesis include Feed-Forward Neural Network,Ridge Regression, Support Vector Regression, Gradient Boosting Regression, andDecision Tree Regression. These regression algorithms were selected to cover arange of approaches, from linear models to non-linear, artificial neural networks,tree-based, and ensemble techniques. In the next subsection, we discuss the modelmathematical formulation and architecture of each of the methods.5.2.1 Artificial Neural NetworkANN is a computational model based on the idea of how neurons in the humanbrain are connected. In ANNs, a neuron is a function of inputs’ summation, withthe history from the past being a contributing factor to interconnection weights[71]. This idea was further developed by McCulloch and Pitts into a computationalmodel of neurons [72]. In 1949, the Hebbian learning algorithm was proposed toadapt weights for learning examples [73]. Rosenblatt then introduced perceptron,the first ANN, that was influenced by visual perception in humans [74].A feed-forward neural network is a common type of ANN. Deep Fully Con-nected Feed-Forward Neural Network (FFNN) intakes the preprocessed inputfeatures and passes them through multiple dense layers to learn non-linear, com-plex relationships between the input features like weather, traffic conditions, roadattributes, and output travel time. The multiple layers and non-linear activationfunctions provide the capacity to model real-world intricacies of work zone trafficflow.Model ArchitectureFFNNs are comprised of multiple layers of interconnected nodes or neurons.By using multiple computational units, called artificial neurons, the model trains to565.2. Methodologycapture the complex patterns and relationships within datasets. The learning andtransfer of knowledge happen through the weighted connections among neuronsin the hidden layers and output layer (Figure 5.1).More specifically, as shown in Figure 5.1, each neuron receives inputs fromthe previous layer, calculates a weighted sum (𝑤1, 𝑤2, ..., 𝑤𝑚) of its m inputs(𝑥1, 𝑥2, ..., 𝑥𝑚), added by a bias term 𝑏, applies an activation function 𝑓 to producethe output 𝑦, and passes it to neurons in the next layer:𝑦 = 𝑓 (𝑚∑︁𝑖=1𝑤𝑖 ∗ 𝑥𝑖 + 𝑏) (5.1)This allows each neuron to learn a non-linear combination of the inputs to approx-Figure 5.1: An Illustration of a Fully Connected Feed-Forward Neural Network575.2. Methodologyimate the target function, the output’s pattern.Model DevelopmentThe network consists of an input layer to receive the encoded 27-feature vector,followed by 4 hidden layers of 128, 512, 256, and 128 neurons respectively as il-lustrated in Figure 5.2. Each hidden layer applies the Rectified Linear Unit (ReLU)Figure 5.2: Architecture of ANN and Input Variablesactivation function [75] to learn non-linear combinations of the inputs. Dropoutregularization (discussed further in Section 5.4: Advantages and Disadvantages)with a rate of 0.5 is applied after hidden layers to prevent over-fitting.The parameters of the ANN including the weights and biases are learnedthrough back-propagation [76], calculating the Mean Squared Error (MSE) (referto Section 5.3: Evaluation Metrics) between predictions and true/observed outputs,also known as the loss (cost) function. Subsequently, the Adaptive Moment585.2. MethodologyEstimation (ADAM) method [77] is used to update parameters to minimize theloss function. The output layer contains a single neuron with a linear activationfunction to predict the continuous target variable of travel time.5.2.2 Ridge RegressionRidge regression is a linear regression technique that incorporates L2 regu-larization to penalize large coefficients [78, 79]. It aims to minimize the sum ofsquared residuals while constraining the magnitude of the coefficients, thus reduc-ing overfitting. The ridge model is fit by minimizing the following cost function,also known as linear least squares:𝐽 (𝑤) =𝑛∑︁𝑖=1| |𝑦𝑖 − 𝑤𝑇𝑥𝑖 | |2 + 𝛼 | |𝑤 | |2 (5.2)Where:• 𝑥𝑖 are the input features,• 𝑦𝑖 are the true target values,• 𝑤 are the model weights,• 𝑛 is the number of samples, and• 𝛼 is a scaling factor to control the strength of L2 regularization.In the training, 𝛼 is considered 1. When 𝛼 = 0, the objective is equivalent toordinary least squares.5.2.3 Support Vector Regression (SVR)Support Vector Regression (SVR) with the linear kernel is an extension ofSupport Vector Machines (SVM) for regression tasks [80, 81]. Similar to SVM,595.2. MethodologySVR seeks to find the hyperplane that best fits the training data while maximizingthe margin and minimizing prediction error.It uses kernels to map inputs to a high-dimensional feature space. Additionally,SVR uses a tunable parameter, acceptable error margin 𝜖 which defines the widthof the tube around the estimated function (hyperplane). Points falling inside thisregion are considered correct predictions and the points outside it are penalizedby the algorithm. The algorithm aims to minimize the error by identifying anestimated function that places more original points inside the tube while simul-taneously reducing the distance to points outside the region. This hyperplane isdefined by finding 𝑤 and 𝑏 that optimally fits the data:𝑦𝑖 = 𝑤𝑇𝜙(𝑥𝑖) + 𝑏 (5.3)Where 𝜙(𝑥𝑖) maps 𝑥𝑖 to the higher dimensional space. SVR uses epsilon-insensitive loss and regularizes model complexity by minimizing |𝑤 |.5.2.4 Decision Tree RegressionDecision trees recursively partition the feature space into subsets based on fea-ture values [82]. The feature space is split into rectangular regions and predictionsare made by averaging the target variable within each partition.The construction process for the tree is done by recursively splitting the trainingdata into subsets (rectangular regions). This split or cut is based on the valuesof the attribute that maximizes the purity of the split (i.e. minimizes impurity).The impurity metric quantifies how well a candidate feature separates the databy different output values, i.e. indicates the number of different values for thetarget variable in a subset of data. At each internal node, the algorithm selectsthe feature that produces the maximum reduction in impurity across the resultingsubsets. The explained recursive partitioning continues until a stopping criterionis met, such as maximum tree depth or minimum number of samples in a node.This results in a tree-like model, where the internal nodes represent feature tests,605.3. Evaluation Metricsthe branches are outcomes of those tests/conditions, and the leaf nodes contain thefinal predicted values.In the training process of this chapter, the minimum number of samples requiredto split an internal node is considered 2 and no cap has been set for the maximumdepth of the tree.5.2.5 Gradient Boosting RegressionGradient Boosting Regression is an ensemble learning technique that builds apredictive model by sequentially adding weak learners [83]. It is part of Boostingtechniques. The commonly used weak models are decision trees that are combinedtogether to minimize the loss function. In a greedy approach, each new modelfocuses on minimizing the loss (i.e. residual errors) of the previous ensemble.Mathematically, let 𝑦𝑚𝑖 be the prediction at iteration 𝑚 for sample 𝑖. Thegradient boosting model updates this prediction by adding a new weak learner(e.g. decision tree) ℎ𝑚 (𝑥𝑖) weighted by a learning rate 𝛾:𝑦𝑚𝑖 = 𝑦𝑚−1𝑖 + 𝛾ℎ𝑚 (𝑥𝑖) (5.4)At each iteration𝑚, the objective is to find a weak learner ℎ𝑚 (𝑥) that minimizesthe following loss function L over 𝑛 data samples:ℎ𝑚 = arg minℎ𝑛∑︁𝑖=1L(𝑦𝑖, 𝑦𝑚𝑖 ) (5.5)In the training, number of boosting stages (i.e., the number of trees in theensemble) is defined as 100 and the learning rate = 0.1.5.3 Evaluation MetricsThe performance of the ML models was evaluated using various regressionmetrics between the predicted and observed travel times:615.3. Evaluation Metrics• MSE: The model optimizes for MSE during training (loss function), whichmeasures the average squared difference between the n pairs of predicted( ?ˆ?) and true values (𝑦𝑖) (Equation 5.6).𝑀𝑆𝐸 =1𝑛(𝑛∑︁𝑖=1𝑦𝑖 − ?ˆ?)2 (5.6)• RMSE: The more interpretable measure of MSE is Root Mean SquaredError (RMSE) which takes the square root of MSE converting the unit oferrors to minutes. RMSE is the standard deviation of prediction errors.• MAE: Additional metrics include Mean Absolute Error (MAE), which cal-culates the average magnitude of errors or absolute errors (Equation 5.7):𝑀𝐴𝐸 =1𝑛𝑛∑︁𝑖=1|𝑦𝑖 − ?ˆ? | (5.7)• MAPE: Mean Absolute Percentage Error (MAPE) measures error as apercentage of the true value (Equation 5.8):𝑀𝐴𝑃𝐸 =1𝑛𝑛∑︁𝑖=1|𝑦𝑖 − ?ˆ? |𝑦𝑖(5.8)• R-squared: R-squared or 𝑅2 score is the Coefficient of Determination andevaluates the goodness of fit. It indicates how well the input variables in themodel can explain the variability in the output variable (Equation 5.9).𝑅2 = 1 −∑𝑛𝑖=1(𝑦𝑖 − ?ˆ?)2∑𝑛𝑖=1(𝑦𝑖 − ?¯?)2(5.9)Lower values of MSE, RMSE, MAE, and MAPE imply higher accuracy ofa regression model. 𝑅2 normally ranges between 0 and 1 with the higher valuehaving a better fit to observations.625.4. Results and Discussion5.4 Results and DiscussionThis section presents and analyzes the results obtained from training andevaluating the different ML regression models on the work zone delay predictiontask. All models were trained using 437,204 samples and evaluated on 48,579samples with each input vector having a dimension of 27. The code is implementedusing Python 3.11 in PyTorch 2.0.1 and scikit-learn 1.3.0 with CUDA 11.7. Theinference time for each model is less than 0.6 seconds.Table 5.1 and the bar plots in Figure 5.3 show the comparison of differentevaluation metrics across multiple ML models. These visualizations provideinsights into the relative performance of each regression model based on variousevaluation metrics.In examining the performance of various ML regression models for work zoneFigure 5.3: Comparison of 𝑅2 across regression models. Each bar represents thevalue of a specific evaluation metric for a particular model. The x-axis showsthe names of the regression models, while the y-axis represents the values of theevaluation metric. The color of the bars distinguishes between different evaluationmetrics, allowing for easy visual comparison.635.4. Results and DiscussionTable 5.1: Comparison of Evaluation Metrics Across Regression ModelsModel R-squared MSE RMSE MAE MAPERidge Regression 0.824 0.073 0.270 0.171 0.074Support Vector Regression 0.795 0.086 0.292 0.184 0.080Gradient Boosting Regression 0.899 0.042 0.205 0.115 0.049Decision Tree Regression 0.994 0.002 0.049 0.006 0.002Feed-Forward Neural Network 0.945 0.022 0.151 0.092 0.041travel time prediction, the ANN and non-linear tree-based models (i.e. GradientBoosting and Decision Tree) outperform the linear Ridge and SVR models. InFigure 5.4, the plot illustrates the comparison between true and predicted valuesfor various regression models. This visualization provides insight into the per-formance and accuracy of different regression models in predicting the outcomevariable.The results show that the Decision Tree model achieved the best performanceamong all the compared models, followed closely by the ANN achieving 𝑅2 of0.99 and 0.95, respectively. Gradient Boosting also achieved good performancescoring 𝑅2 = 0.89. The tree-based models are known for their ability to capturecomplex non-linear relationships in structured data. It achieved the lowest MSE,RMSE, MAE, and MAPE values, and the highest R-squared value, indicating abetter fit to the data and higher prediction accuracy compared to other models.Regularized linear regression, namely Ridge and Support Vector Regressiongenerally performed well, but they did not achieve the same level of accuracy asthe ANN and Decision Tree models. This could be due to several reasons, suchas the limitations of these models in capturing complex non-linear relationships.Additionally, these models perform better when given a small number of variables.645.4. Results and DiscussionFigure 5.4: Comparison of True vs. Predicted Values Across Regression Models.Each point represents a data instance, with the x-coordinate denoting the true valueand the y-coordinate representing the corresponding predicted value. The dashedblack line indicates perfect prediction, where true and predicted values align. Theopacity of markers indicates the density of data points at each location.655.4. Results and DiscussionAdvantages and DisadvantagesWhile both tree-based models (i.e. Decision Tree and Gradient BoostingRegression) and ANNs achieved impressive results in predicting work zone traveltimes, there are several limitations that should be considered. A summary of theadvantages and disadvantages of the different regression models is provided inTable 5.2.In ML when a model achieves high accuracy on training data but strugglesto generalize to unseen instances [84], the model is overfitted. It reflects themodel’s ability to handle new, unseen instances effectively which is the ultimatecrucial goal. This could be due to three primary reasons: (i) the presence of noisyinstances with incorrect labels, (ii) insufficient training examples, leading to aninadequate representation of the true target function, and (iii) overtraining, wherethe model captures noise or irrelevant patterns in the training data [85].In addition to the preprocessing techniques applied to data, there are some tech-niques used while training to improve the performance and generalization abilityof ANNs on efficient learning from high-dimensional data and avoid overfitting.For instance, dropout works by randomly ignoring a subset of nodes in a givenlayer during training, which forces the network to learn redundant representationsof the data [86]. This, in turn, makes the model more robust and prevents it fromrelying too much on specific weights. In practice, a dropout layer is added aftereach dense layer, and it randomly sets a fraction of input units to 0 at each updateduring training. Additionally, early stopping is also used to prevent overfitting.Specifically, the early stopping was used with validation loss as the monitoredmetric to track on a validation set after each training epoch.Furthermore, ANNs can continuously refine their predictions through iterativelearning (through a process known as fine-tuning) without the need to be trainedfrom the beginning. Fine-tuning can be applied only to some certain layers andfreezing the rest of the network. This allows them to adapt to potential changes intraffic patterns or work zone dynamics over time, potentially maintaining accuracyeven as conditions evolve and alter.665.4. Results and DiscussionTable 5.2: Summary of Advantages and Disadvantages of ModelsModel Advantages and DisadvantagesRidgeRegression• Simple and efficient to train• Provides some regularization to reduce overfitting• Limited to modeling linear relationships• Performance degrades with high dimensionalitySupport VectorRegression• Effective for a small number of features• Robust to noise and outliers• Limited to modeling linear relationships• Difficulty scaling to high-dimensional data• Sensitive to parameters like kernel choiceGradientBoostingRegression• Models complex non-linear relationships effectively• Robust to outliers• Can handle high dimensionality• Prone to overfitting if not regularized properly• Computationally expensive for large datasetsDecision TreeRegression• Models non-linear relationships intuitively• Prone to high variance and overfitting• Struggles with high-dimensional data (curse of dimensionality)• Hierarchical constraints on feature interactionsFeed-ForwardNeural Network• Can model complex non-linear relationships• Learns relevant feature interactions from data patterns• Can be fine-tuned on new data without retraining from scratch• Potential to overfit without proper regularization• Requires careful hyperparameter tuning• Computationally expensive to train675.4. Results and DiscussionIt is worth noting that ANN can theoretically approximate any continuousfunction to arbitrary precision due to its universal function approximation property[87, 88].ANN ValidationGiven the ANN’s superior performance, flexibility, and ability to effectivelymodel complex relationships in the data, as well as the employed regularizationand validation techniques, further validation efforts were focused on this model.The other models, while valuable for comparative purposes, did not demonstratethe same level of accuracy and robustness as the ANN approach.ANNs are favored for predictive modelling due to their inherent strengths.When the goal is to obtain an accurate prediction model, and a big set of datais available for the task, ANNs can learn the complex pattern through the use oftheir hidden layers and their connections. Through back-propagation and gradientdescent optimization, ANN continually adapts to refine predictions based on thedata. This iterative learning allows them to improve generalization and makereasonable inferences on new data points without any prior assumption about thedataset’s distribution.The model was trained for 800 epochs with a batch size of 1024. The de-veloped model used a mode of minimization and patience of 200 epochs, whichallowed sufficient training iterations for the model to converge while preventingexcessive training. Training was automatically stopped if the validation loss didnot decrease for 200 consecutive epochs. On an NVIDIA GeForce RTX 3090GPU, model training took approximately 43 minutes. Once trained, the modelcan rapidly provide work zone delay predictions, with an average inference timeof 150 milliseconds per query.Once trained, as illustrated earlier, the model achieved an RMSE of 0.150minutes in predicting under-construction travel time. The reported values areMSE = 0.023, MAE = 0.092, MAPE = 0.041, and 𝑅2 = 0.945 evaluated on thetest set. Figure 5.5 plots model predictions (y-axis) versus true (x-axis) under-685.4. Results and DiscussionFigure 5.5: Actual vs Predicted Under-Construction Travel Times (in minutes).Orange dots represent each sample, while the blue fitted line characterizes thecorrelation trend. Proximity to the 45-degree red line signals strong model perfor-mance.construction travel times. The scatter plot with regression line depicts the re-lationship between actual and predicted delay times. The close alignment of thescattered plot to the diagonal line (𝑥 = 𝑦) indicates the model’s ability to accuratelyestimate work zone travel times considering input features.In fact, besides estimating the RMSE and 𝑅2 variables, the model was evaluatedspecifically on scenarios that led to high under-construction time, resulting in695.4. Results and Discussionpredictions close to observed travel time. This is also confirmed and apparentin Figure 5.5. Increased deviations at higher travel times could be attributed toa relative lack of data points for very high travel times compared with moderatetravel times. In cases where there are fewer examples to train on, the model’sability to predict outliers could be less certain.In addition to the primary training approach, the impact of the k-fold cross-validation method during training was also evaluated. K-fold cross-validation canbe used to assess if a ML model is overfitting to the training data [89–91]. Forthat, the original training set is randomly partitioned into k equal-sized subsets orfolds. The model is then trained k times, with each iteration using a different foldas the validation set and the remaining k-1 folds as the training set. This processensures that each data point is used for both training and validation, and that alldata points are used for validation exactly once. This approach helps mitigateissues like overfitting, as the model is evaluated on different subsets of the data,providing a more reliable estimate of its performance on unseen data.The model underwent 5-fold cross-validation, with each fold trained for 200epochs using batches of 1024 samples. The choice of k=5 for the k-fold cross-validation is a common standard in ML, offering a good balance between bias,variance, and computational efficiency while ensuring sufficient folds for reliablevalidation [92]. Early stopping with a patience of 100 epochs was also applied ineach fold. On the test set, the model achieved an RMSE of 0.161 minutes, MSEof 0.026, MAE of 0.102, MAPE of 0.047, and 𝑅2 of 0.940. Figure 5.6 illustratesthe model’s predictions versus true under-construction travel times when trainedusing k-fold cross-validation. These obtained metrics with cross-validation furtherconfirm the model’s robustness and its ability to generalize to new data.705.5. ConclusionFigure 5.6: Actual vs Predicted Under-Construction Travel Times (in minutes)using K-Fold Cross-Validation5.5 ConclusionThis chapter developed ML models to reliably predict work zone travel timedelays and worked on comparing the different algorithms for this prediction task.The results demonstrated that non-linear models like artificial neural networks,decision trees, and gradient-boosting regression outperformed linear models likeridge regression and support vector regression. This highlights their effective-715.5. Conclusionness in capturing the complex, non-linear relationships between the many inputvariables impacting travel time delays in work zones.Among the models evaluated, the decision tree regressor achieved the bestoverall performance with the lowest error rates and highest R-squared value of0.99, closely followed by the neural network at 0.95 R-squared.The neural network also showcased advantages, such as making fewer assump-tions about the underlying data distribution, the ability to train large models andgeneralize well, and capturing intricate patterns in a large dataset with numerousfeatures. Moreover, in the event of new data becoming available, the ANN modelcan be efficiently fine-tuned without the need to be rebuilt and trained from scratch,as is often required for tree-based models. Additionally, the trained ANN modelcan potentially be adapted and applied to other regions or contexts through transferlearning techniques, leveraging the learned representations and patterns.Ultimately, the selection of the most suitable model depends on the specific re-quirements of the use case, balancing factors like prediction performance, trainingtime, model complexity, interpretability needs, and robustness to noise in the data.This analysis provides valuable insights to guide the selection of delay predictionmodels for future work zone scenarios.72Chapter 6Discussion, Conclusion, andLimitationsThe objective of this thesis was to (i) identify the effects and relationshipsbetween work zone attributes and delays and (ii) compare the performance ofdifferent machine learning (ML) models in predicting delays at highway workzones. A comprehensive framework was adopted involving data integration, ex-ploratory analysis, and predictive modelling phases. Here, we highlight the keycontributions and takeaways, acknowledge the inherent limitations, and providesome future direction in this domain.6.1 Conclusion and TakeawaysContributionThis thesis has made several significant contributions to the understanding andprediction of work zone delays. These contributions include:I. The compilation of a dataset containing approximately 15 million travel timeobservations across 674 work zones provides a remarkable level of detail.This dataset, combining traffic data, weather conditions, temporal factors,and precise work zone characteristics, facilitates more in-depth analysis ofwork zone congestion dynamics than previously possible.II. By using mixed-effects models, the thesis quantifies the influence of bothobservable factors (e.g., traffic volume, weather) and unobserved character-736.1. Conclusion and Takeawaysistics of work zones. This approach enhances understanding of the complexrelationship among variables contributing to delays.III. The thesis developed various ML models capable of reliably predicting workzone delays. It demonstrated the superiority of non-linear methods (neuralnetworks, decision trees, gradient boosting) over linear models for this task.Further analysis revealed that decision trees achieved the overall best perfor-mance. However, neural networks offer distinct advantages like flexibility,generalization, adaptability with new data, and potential for transfer learningto different regions.Comprehensive Data Analysis and ML ModellingThe large-scale and integrated diverse dataset enabled comprehensive analy-ses that addressed limitations of prior work zone delay studies relying on smalldatasets, simulations, or excluding key variables. Clustering provided an assumption-free approach to explore variables impacting delay at work zone attributes, unliketraditional methods that make strict assumptions about variable relationships. Or-dinal logistic regression was then used to quantify the odds of delays occurringbased on a set of predictor variables often overlooked, like weather and tempo-ral factors. Additionally, mixed-effects regression modelled unobserved hetero-geneity across work zones through random effects - accounting for unmeasuredsite-specific characteristics impacting delays that prior models did not account for.This rigorous application of statistical learning methods on the vast dataset en-abled identifying and quantifying relationships between delays and various factors.Moreover, a comprehensive comparative evaluation of ML models was conducted.A range of models from linear to non-linear models, artificial neural networks, tree-based, and ensemble techniques were leveraged. The strengths and weaknesses ofmodels for this delay prediction task, particularly artificial neural networks, werediscussed further.746.1. Conclusion and TakeawaysInsights into Work Zone DelaysThe key findings from this thesis provide valuable insights into the factorsinfluencing delays at highway work zones and demonstrate the effectiveness ofadvanced ML techniques in accurately predicting these delays from real-worlddata.Work zone characteristics like longer segment lengths and higher traffic vol-umes were found to be associated with increased delays. Interestingly, the specificlength of transition areas into/out of the work zone did not significantly impactdelays after accounting for other variables. This suggests that minimizing transi-tion lengths may not be as critical compared to other work zone design elements.Environmental conditions exhibited considerable impacts on delay levels. Workzones experienced substantially higher delays during inclement weather scenarios(i.e. low temperature and high wind speed). This underscores the importanceof accounting for environmental factors in work zone planning and schedulingactivities. Temporal patterns were evident as well, with delays peaking duringdaytime hours and weekdays when traffic volumes are typically highest. Certainseasonal effects were also captured, with spring months tending to have higherdelays, potentially due to increased travel demand during that period.In terms of predictive capabilities, the analysis evaluated multiple ML modelsusing the comprehensive real-world dataset compiled in this study. Among thetechniques assessed, decision trees and artificial neural networks (ANNs) demon-strated superior performance, achieving a respective RMSE of 0.05 and 0.150minutes and an exceptional 𝑅2 of 0.99 and 0.945 in predicting delays on the testset. This high accuracy highlights the models’ ability to effectively capture com-plex non-linear relationships between the multitude of input variables and delayoutputs.The results of trained ANN can be applied to other regions with minimaladjustments. For that, local data on traffic volume, weather conditions, and workzone characteristics relevant to the new region should be incorporated. Afterward,the model should be adjusted and fine-tuned on the local data to account for756.1. Conclusion and Takeawaysregional differences in traffic patterns and work zone management practices.Practical Applications and ImplicationsThe practical applications and the findings on work zone delays can havesignificant implications in work zone delay management and planning in severalways. The findings can be used in the creation and assessment of traffic mitigationand flow management plans.A primary application is leveraging the predictive models to conduct simula-tions and assess the potential impacts of different work zone design alternativeseven before implementation. By adjusting parameters, such as lane closures, sig-nage placement, transition area configurations in the models, transportation pro-fessionals can evaluate which layouts minimize anticipated delays without costlyreal-world trial-and-error experimentation. This virtual testing enables data-drivendesign optimization.The models and quantified delay determinants also allow agencies to strategi-cally allocate resources like personnel and equipment across work zones based onpredicted congestion. Work zones anticipated to experience higher delays can beprioritized for additional deployment of traffic control personnel, portable signalsetc. This optimization ensures efficient use of resources dynamically matched todemand, resulting in substantial cost savings.Additionally, the models can be used for strategic planning of the start andend times of work zones. Leading to minimizing the impact on traffic flow, andreducing the likelihood of project delays. It can serve as a tool to improve safetyand facilitate proactive traffic control by helping planners predict and addresscongestion in in planning and scheduling phase.Finally, the predictive capabilities enable precise calculation of contractorpenalties related to cost overruns. The high accuracy of predictive models allowsproject managers to ensure that delays and their financial impacts can be evaluatedobjectively and considered before or during the operation phase.766.2. Limitations and Future Work6.2 Limitations and Future WorkWhile this thesis made a significant contribution, several limitations should beacknowledged.Challenges and LimitationsAccessing detailed work zone layout plans proved highly challenging due toprivacy and security constraints, as these plans were internal and restricted and notreadily available to third parties like academic researchers. The process of gainingaccess took considerable effort and time. Ultimately, only a limited set of PDFlayout plans corresponding to the work zones where travel time observations wereavailable could be obtained.A major bottleneck was then extracting relevant geometric parameters liketransition lengths, lane closure configurations, etc. from these PDFs. This highlymanual process was tedious since the plans did not follow consistent formats. Theparameters and information on work zone layouts were not collected in a digital,tabulated format like CSV files.As with any data-driven model, the performance and generalizability are in-herently conditioned by the quality and diversity represented in the training data.While measures like regularization were adopted, the models may still need furthertraining for scenarios that are underrepresented in the dataset used.The exclusion of certain variables like unexpected incidents within work zonesis another limiting factor on the models’ predictive capabilities under all possibleconditions. The dataset also currently lacks direct measurements of driver behav-ioral responses like braking profiles which could further enhance predictions.Finally, the regional focus on British Columbia constrains direct generalizationto other regions which may have distinct traffic patterns, driver behavior, and workzone practices. While the models should generalize reasonably well to otherregions, some degree of transfer learning or fine-tuning using local data wouldbe beneficial. Despite these limitations, the research makes concerted efforts to776.2. Limitations and Future Workdevelop robust models from the available data sources.Future DirectionsRegarding future directions, the are several approaches to enhance the capa-bilities of work zone delay prediction and build upon this thesis.Expanding the dataset to include a wider range of variables, such as moredetailed weather data, real-time incident reports, and real-time daily traffic volume,could enhance the model’s accuracy and applicability. Additionally, integratingadditional data sources, such as social media feeds or Internet of Things (IoT)sensors can enrich the dataset and uncover new insights into traffic dynamics.Expanding the geographic scope of the work would further help validate themodel’s generalizability and refine its predictive capabilities. Transfer learningtechniques could leverage models trained on data from one region to acceleratethe training process in new geographic areas with limited historical data.Exploring the integration of other ML techniques, such as reinforcement learn-ing or deep learning models that can dynamically adapt to changing traffic condi-tions, may offer improvements in predictive performance.Conducting comparative studies of multiple deep and shallow ML algorithmswith traditional simulation approaches provides useful insights into their relativestrengths and weaknesses for predicting travel time and delays in different situa-tions. This comprehensive analysis will clarify the trade-offs between accuracy,interpretability, and computational efficiency of different methods. 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Thesis/Dissertation
eng
Civil Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-ShareAlike 4.0 International
Graduate
Gargoum, Suliman
Using big data and machine learning for microscopic delay modelling at construction work zones
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