Headway Variation Research Articles

Planning-Level Optimisation of Headway Regularity

Headway variability has a negative impact on the public transport passengers’ perception of service quality. However, most of the existing methods aimed at improving the headway regularity operate in real time and require precise vehicle location data, making it difficult to implement them in practice. On the other hand, planning-level methods can be used to increase the resilience of public passenger transport (PPT) to the accumulation of headway disturbances. As this is typically done from the operator’s perspective, the passengers’ perspective tends to be overlooked, motivating the current work. In this article, an optimisation procedure for evaluating the viability of diametrical line splitting in terms of passenger travel time and headway regularity is proposed. The aim is to increase the robustness/resistance of the PPT system to the propagation of headway disturbances without reducing the service quality. The developed optimisation procedure was validated by applying it to real data pertaining to an urban PPT line. The results show that there is a positive correlation between the transport demand and the effects of the optimisation procedure, whereby an increase in the primary headway disturbance increases the sensitivity of the optimisation procedure to the transport demand.

Headway regularity as an attribute for classifying bus drivers

Different indices have been proposed in the literature to characterize headway regularity. These metrics aggregate the headway variability for a service, but none can be directly associated with a specific driver. This paper seeks to understand drivers' influence on a service's regularity. To do so, we propose four regularity indices related to a driver's performance and use the Hierarchical Clustering Analysis method to generate a classification of drivers according to their contribution to the headway regularity during the operation of a service. We characterize each class based on the driver's attributes such as age, years of experience as a driver, and years in the bus company, and those attributes associated with the operation, such as number of services per day and period of the day. The results show consistency in the classification obtained, with nearly 90% of drivers remaining in the same regularity classes regardless of the index.

Probabilistic Forecasting of Bus Travel Time with a Bayesian Gaussian Mixture Model

Accurate forecasting of bus travel time and its uncertainty is critical to service quality and operation of transit systems: it can help passengers make informed decisions on departure time, route choice, and even transport mode choice, and it also support transit operators on tasks such as crew/vehicle scheduling and timetabling. However, most existing approaches in bus travel time forecasting are based on deterministic models that provide only point estimation. To this end, we develop in this paper a Bayesian probabilistic model for forecasting bus travel time and estimated time of arrival (ETA). To characterize the strong dependencies/interactions between consecutive buses, we concatenate the link travel time vectors and the headway vector from a pair of two adjacent buses as a new augmented variable and model it with a mixture of constrained multivariate Gaussian distributions. This approach can naturally capture the interactions between adjacent buses (e.g., correlated speed and smooth variation of headway), handle missing values in data, and depict the multimodality in bus travel time distributions. Next, we assume different periods in a day share the same set of Gaussian components, and we use time-varying mixing coefficients to characterize the systematic temporal variations in bus operation. For model inference, we develop an efficient Markov chain Monte Carlo (MCMC) algorithm to obtain the posterior distributions of model parameters and make probabilistic forecasting. We test the proposed model using the data from two bus lines in Guangzhou, China. Results show that our approach significantly outperforms baseline models that overlook bus-to-bus interactions, in terms of both predictive means and distributions. Besides forecasting, the parameters of the proposed model contain rich information for understanding/improving the bus service, for example, analyzing link travel time and headway correlation using covariance matrices and understanding time-varying patterns of bus fleet operation from the mixing coefficients. Funding: This research is supported in part by the Fonds de Recherche du Quebec-Societe et Culture (FRQSC) under the NSFC-FRQSC Research Program on Smart Cities and Big Data, the Canadian Statistical Sciences Institute (CANSSI) Collaborative Research Teams grants, and the Natural Sciences and Engineering Research Council (NSERC) of Canada. X. Chen acknowledges funding support from the China Scholarship Council (CSC). Supplemental Material: The e-companion is available at https://doi.org/10.1287/trsc.2022.0214 .

Deep Reinforcement Learning Two-Way Transit Signal Priority Algorithm for Optimizing Headway Adherence and Speed

Transit Signal Priority (TSP) is a broadly used traffic signal control strategy designed for reducing transit delays at signalized intersections. Although recent TSP systems began to consider more objectives, TSPs that addressed transit reliability issues commonly focused on improving schedule adherence and were only able to reduce schedule delays by expediting buses. Buses running ahead of the schedule were not considered. This paper proposed a dual-objective two-way TSP algorithm (D2 TSP) using Deep Reinforcement Learning (DRL). D2 TSP concurrently optimizes transit delays and reliability (i.e., headway adherence) by expediting late buses or delaying early buses. Further, the DRL agents were enhanced with a coordination algorithm for an optimized solution balancing opposite directions. This D2 TSP reacts adaptively and efficiently to real-time bus performance using data provided by readily available technology (loop detector) at low communication frequencies. We trained and tested this algorithm in a stochastic microsimulation environment in Aimsun Next that modelled a transit route segment with reliability issues in the City of Toronto. The performance of D2 TSP was compared with four baseline scenarios, one without TSP, one with the current TSP algorithm used in the field in the City of Toronto, one conditional TSP with an arrival prediction model, and one using DRL agents with a First-Come-First-Served logic. D2 TSP demonstrated its advantages in providing an efficient and balanced solution in reducing headway variability and travel time for both directions.

The adverse impact of headway variability on bus transit ridership: Evidence from Bengaluru, India

This study examines the impact of bus service headway variability on bus transit ridership using direct demand models at different levels of spatial aggregation – route level and stop-route level – using transit demand and supply data from the city of Bengaluru, India. In addition, auxiliary models are developed to understand the determinants of service frequency and headway variability and to address the endogeneity of these service characteristics in the demand models. This is perhaps the first study in the public transit literature to compare and contrast the endogeneity and non-linearity effects of service frequency and headway variability in transit demand models using both a conceptual framework and empirical evidence from a large transit system. The empirical results offer evidence that variability in headways adversely impacts transit ridership and passenger-kilometres. The strength of the adverse effect increases with increasing variability. On the other hand, the influence of service frequency decreases with increasing frequency. Furthermore, it is shown conceptually and demonstrated empirically that ignoring the endogeneity of service variability results in an underestimation of its adverse effect on transit demand. On the other hand, the empirical results suggest that ignoring the endogeneity of service frequency would result in an overestimation of its beneficial effect. An important takeaway from these results and additional policy simulations is that transit agencies can potentially gain greater ridership and revenue by reducing headway variability rather than simply allocation more buses and crew to high-frequency routes.

Stochastic capacity analysis for a distributed connected automated vehicle virtual car-following control strategy

Capacity analysis of the pure connected automated vehicle (CAV) traffic remains a challenging problem due to the high-dimensional factors involved in the control design. Especially, the communication loss and communication topology greatly impact the headway variation of CAVs and hence capacity with stochastic properties. This study provides a stochastic framework to mathematically derive multiple factors’ impact including free-flow speed, control gains, communication loss, and traffic arrival pattern on the pure CAV traffic capacity based on a virtual car-following control strategy targeting a single-lane highway and merging section. To begin with, we first mathematically derive the stochastic capacity for a single-lane highway based on a multi-predecessor-based linear feedback and feedforward car-following model for generic stochastic communication loss models. For a further illustration, a detailed analysis is conducted based on a well-known Signal-to-Interference-plus-Noise Ratio (SINR) communication loss model. We then extend the derivation to a merging section by a virtual car-following concept considering traffic arrival pattern’s stochasticity. Numerical sensitivity analyses have been conducted to systematically evaluate the impact of multiple factors mentioned. As the result indicated, the stochastic communication loss and traffic arrival pattern do have a significant impact on the pure CAV traffic capacity of the above scenarios.

Train following model for urban rail transit performance analysis

In this paper we introduce a mesoscopic Train Following Model which accurately captures train interactions and predicts delays based on spacing between consecutive trains. The Train Following Model is applied recursively block by block estimating train trajectories given initial conditions (i.e. the trajectory of an initial train and dispatching headways of following trains from the terminal station). We validate the proposed model using data from the Red Line of the Massachusetts Bay Transportation Authority (MBTA). The results indicate that it accurately represents train operations under both normal and disrupted conditions. Based on the model developed, the impacts of factors such as service frequency, headway variations, passenger demand, and initial train delays on line performance (i.e. line throughput and train knock-on delays) are explored. The proposed Train Following Model is generic and can be developed based on readily available historical train tracking data. It is not as resource intensive as micro simulation models, while it can efficiently address the drawbacks of macro-scale analytical models and complex discrete algebraic models. The proposed model can be used to predict system performance either off-line or in real-time.

Application of modular vehicle technology to mitigate bus bunching

The stochastic nature of public transport systems leads to headway variability and bus bunching, causing both operator and passenger cost to increase significantly. Traditional strategies to counter bus bunching, including bus-holding, stop-skipping, and bus substitution/insertion, suffer from trade-offs and shortcomings. Autonomous modular vehicle (AMV) technology provides an additional level of flexibility in bus dispatching and operations, which can offer significant benefits in mitigating bus bunching compared to strategies available with conventional buses. This paper introduces a novel alternative to stop-skipping by leveraging the new capabilities offered by AMVs (in particular, en-route coupling and decoupling of modular units). We develop a simple bus-splitting strategy that directs a modular bus to decouple into individual units when it experiences a headway longer than a given threshold. We then use a macroscopic simulation to present a proof-of-concept evaluation of the proposed modular strategy compared to a benchmark traditional stop-skipping strategy and the base (no control) case. We find that the proposed strategy outperforms the benchmark in decreasing each of the three travel time components: waiting time, in-vehicle time, and walking time (which it eliminates completely). It therefore reduces the overhead of bus bunching and thus the travel cost by more than twice as much as the benchmark for busy bus lines. Simultaneously, it also reduces headway variability to a comparable degree. Furthermore, we analyze different control thresholds for applying the proposed strategy, and show that it is most effective when applied proactively, i.e. with the control action being triggered even by small headway deviations.

Travel Time Reliability Analysis Considering Bus Bunching: A Case Study in Xi’an, China

Bus bunching occurring at stops has an unstable impact on bus travel time. In order to evaluate urban bus travel time effectively, the travel time reliability (TTR) addressing bus bunching is analyzed. This paper focuses on the delayed time caused by bus bunching in the dwelling process at bus stops and uses the coefficient of variation of time headway to evaluate the degree of bus bunching. Moreover, the travel time deviation (TTD) indicator and travel time on-time accuracy (OTA) model are proposed to evaluate the bus TTR. The proposed model is used to analyze 113 runs of a bus route in Xi’an city, China. Real-time GPS data are used to analyze the operation of each run from the origin to the destination stops. The results show that 74.34% of the runs are delayed. When the value of TTD is higher than |0.1|, 64.2% of runs are delayed with bus bunching. Based on the measuring of OTA in two situations, the value of TTR considering bus bunching is reduced by 20%. In addition, the number of stopping routes at peak periods has a significant impact on the occurrence of bus bunching. The research results would have practical implications for the operation and management of buses.

Negative mood mind wandering and unsafe driving in young male drivers

ObjectiveRoad traffic crash fatalities disproportionately affect young male drivers. Driver distraction is a leading contributor to crashes. Mind wandering (MW) is a prevalent form of driver distraction that is linked to certain unsafe driving behaviours that are associated with increased crash risk (e.g., faster driving). Negative mood can lead to MW, and thus may represent a causal pathway to MW-related unsafe driving. This preliminary pre-post (T1, T2), randomized, controlled, single-blinded experiment tested whether negative mood, compared to neutral mood, increases MW while driving as well as unsafe driving and emotional arousal during MW. It also tested the moderating contribution of trait rumination and inhibitory control to this proposed causal pathway. MethodsForty healthy male drivers aged 20 to 24 were randomly allocated to a negative or neutral mood manipulation involving deception. Individual differences in trait rumination and inhibitory control were measured at T1. At T1 and T2, participants drove in a driving simulator measuring driving speed, headway distance, steering behaviour, and overtaking. Heart rate and thought probes during simulation measured emotional arousal and MW, respectively. ResultsNegative mood exposure led to more MW while driving (Odds Ratio = 1.79, p = .022). Trait rumination positively moderated the relationship between negative mood and MW (Odds Ratio = 2.11, p = .002). Negative versus neutral mood exposure led to increases in headway variability (Cohen’s d = 1.46, p = .026) and steering reversals (Rate Ratio = 1.33, p = .032) during MW relative to focused driving. Between-group differences in emotional arousal were not significant. ConclusionResults support a causal pathway from negative mood to unsafe driving via MW, including the moderating contribution of trait rumination. If replicated, these preliminary findings may inform the development of interventions targeting this potential crash-risk pathway in vulnerable young driver subgroups.

Dynamic Multi-Bus Dispatching Strategy With Boarding and Holding Control for Passenger Delay Alleviation and Schedule Reliability: A Combined Dispatching-Operation System

The continuing increase of the on-road private cars is contributing to a deterioration of the urban traffic system. Public transportation is widely used to tackle this issue due to its large ridership. In this paper, we propose a multi-bus dispatching strategy combined with the boarding and holding control (MBDBH) to improve bus utilization and further decrease the passenger excess delay. Dispatching adjustments and operation control are taken into account in the system. At the dispatching level, on the one hand, either a bus platoon or a single bus can be dispatched for each trip to provide adaptive bus capacity to match the highly-fluctuated stop demands, on the other hand, we adjust the bus dispatching time based on the existing timetable to minimize passenger excess waiting time to a large extent. Meanwhile, the operation level incorporates both holding strategy and boarding limit strategy to bring more flexible adjustments in improving bus service. Besides the efficiency, we also minimize the headway variation in order to maintain a high system reliability. The problem is formulated as a Mixed Integer Nonlinear Programming (MINP) problem, which is solved by the commercial solver Gurobi. With the computational complexity as a concern, we propose a distributed algorithm to implement dual decomposition based on the partial Lagrangian relaxation. Finally, numerical examples are investigated to illustrate the significant time reduction of distributed algorithm and the efficiency of our proposed strategy: The proposed MBDBH model can reduce roughly 50% and 30% of remaining passenger volumes when compared with the timetable-based fixed schedule and the optimized single-bus dispatching schedule, respectively.

Use of an Improved Car-Following Model to Explain the Influence of Traffic Composition on Saturation Headway at Signalized Intersections

Previous studies mainly used statistical methods to analyze the impact of traffic composition on saturation flow rate from the mesolevel, and there is insufficient research on how traffic composition affects driving behavior. Thus, the purpose of this paper is to establish a more accurate car-following model, establish the relationship between microbehavior and mesostatistical regularity, and explain the influence of vehicle composition on saturation headway. In this paper, an improved full velocity difference (FVD) model is proposed, which abstracts the driver characteristics of a heterogeneous flow into four scenarios: car-car, car-bus, bus-car, and bus-bus. The measured data are used to calibrate and verify the basic FVD and the improved FVD models. The performance of the improved model is significantly improved. The RMSE and RMSPE are reduced by 15.29% and 22.32%, respectively. Finally, through numerical simulation experiments, the variation of saturation headway with different proportions of buses is analyzed. The saturation headway increases with the increase of the proportion of heavy vehicles. Moreover, another important finding is that the saturation headway is not significantly influenced by the position of the buses but only by the proportion of the buses. The research results could provide theoretical support for the control and management of fleets composed of different vehicles at intersections.

Bus Predictive-Control Method considering the Impact of Traffic Lights

Amid the COVID-19 pandemic, many travelers have switched from public transit to other modes. How to maintain the stability and service quality of the bus system under regular pandemic prevention and control, so as to maintain the attractiveness of the bus, is an important research direction. Predicting operation states and adopting appropriate control measures for running buses are effective means of improving the bus system’s schedule reliability and service quality. Focusing on the impacts of intersection traffic lights on the link’s travel time durations, we establish a probabilistic prediction model for bus headways, classifying the bus headways into three states: bunching, stable, and big gap states. Based on the prediction of bus headways, the most suitable control strategy is selected by the proposed method from the plan set, such as holding control, speed-adjusting control, and stop-skipping control to minimize the bus headway deviation. Simulation experiments were employed to verify the effectiveness of the proposed method. Compared with the no-control situation, the expected headway variation, average passenger waiting time, and bus bunching frequency for 100 simulations by the proposed method are reduced by 77.73%, 41.66%, and 87.11%, respectively. Compared with some control methods without prediction, the proposed method is more robust, maintains good control performance, and reduces bus bunching despite significant variations in environmental parameters. In addition, the model still performs well when considering the execution errors of bus drivers.

Charging operations in battery electric bus systems considering fleet size variability along the service

This paper analyzes the new operations induced by the energy range limitation in battery electric bus (BEB) systems to ensure the service provision along the whole day. An operating model has been developed to estimate the number of resources to be deployed (extra vehicles and charging facilities) for two charging schemes: charging at bus garage facility and opportunity charging at on-street chargers. Firstly, the model calculates the entrance and exit time of buses in service assuming an unlimited battery capacity, caused by demand and headway variations in different time periods along day. Then, based on the previous results, the model estimates the moment when vehicles will run out of energy and proposes a charging schedule as well as new vehicle movements between chargers, bus garage and routes to maintain the targeted headway. Consequently, the model is able to calculate the number of resources needed and the total cost for a given route and battery size, allowing cost and performance comparison to diesel and hybrid powertrains. The estimated results in two bus routes in Barcelona indicate that the purchasing cost of BEB vehicles (670,000 euros/veh for articulated, 500,000Euros/veh for standard vehicles, both depreciated over a lifetime of 15 years), battery packs (231 Euro/kWh purchased, depreciated over a lifetime of 10 years), as well as the investment in chargers, are still high to clearly justify their cost-competitiveness against diesel or hybrid counterparts. Nevertheless, if the acquisition cost of both vehicles and battery pack are only reduced by 9%, the BEB technology may present cost savings for transit agencies. It only happens if the fleet size is as large as the corresponding to diesel and hybrid technologies. Opportunity charging is resulted to be more cost- efficient than charging at bus garage for small battery packs, routes with acceptable time headway adherence and, specially, when fast chargers are located very close to terminal stops. Nevertheless, when the real bus route design and operation do not fulfill these standards, charging scheme at bus garage is preferable.

The effects of cannabis and alcohol on driving performance and driver behaviour: a systematic review and meta-analysis.

Cannabis and alcohol are frequently detected in fatal and injury motor vehicle crashes. While epidemiological meta-analyses of cannabis and alcohol have found associations with an increase in crash risk, convergent evidence from driving performance measures is insufficiently quantitatively characterized. Our objectives were to quantify the magnitude of the effect of cannabis and alcohol-alone and in combination-on driving performance and behaviour. Systematic review and meta-analysis. We systematically searched Academic Search Complete, CINAHL, Embase, Scopus, Google Scholar, MEDLINE, PsycINFO, SPORTDiscus and TRID. Of the 616 studies that underwent full-text review, this meta-analysis represents 57 studies and 1725 participants. We extracted data for hazard response time, lateral position variability, lane deviations or excursions, time out of lane, driving speed, driving speed variability, speed violations, time speeding, headway, headway variability and crashes from experimental driving studies (i.e. driving simulator, closed-course, on-road) involving cannabis and/or alcohol administration. We reported meta-analyses of effect sizes using Hedges' g and r. Cannabis alone was associated with impaired lateral control [e.g. g = 0.331, 95% confidence interval (CI) = 0.212-0.451 for lateral position variability; g = 0.198, 95% CI = 0.001-0.395 for lane excursions) and decreased driving speed (g = -0.176, 95% CI = -0.298 to -0.053]. The combination of cannabis and alcohol was associated with greater driving performance decrements than either drug in isolation [e.g. g = 0.480, 95% CI = 0.096-0.865 for lateral position variability (combination versus alcohol); g = 0.525, 95% CI = 0.049-1.002 for time out of lane (versus alcohol); g = 0.336, 95% CI = 0.036-0.636 for lateral position variability (combination versus cannabis; g = 0.475, 95% CI = 0.002-0.949 for time out of lane (combination versus cannabis)]. Subgroup analyses indicated that the effects of cannabis on driving performance measures were similar to low blood alcohol concentrations. A scarcity of data and study heterogeneity limited the interpretation of some measures. This meta-analysis indicates that cannabis, like alcohol, impairs driving, and the combination of the two drugs is more detrimental to driving performance than either in isolation.

Adaptive Threshold Adjustment Strategy Based on Fuzzy Logic Control for Ground Energy Storage System in Urban Rail Transit

The installation of a ground energy storage system (ESS) in the substation can improve the recovery and utilization of regenerative braking energy. This paper proposes an energy management strategy (EMS) of adaptive threshold adjustment for ground ESS. In this regard, this paper analyzes the energy flow in traction power supply system (TPSS) with different headways and no-load voltage. According to the influence of charge and discharge threshold on the energy flow in TPSS, the laws of energy flow are formulated. Subsequently, an EMS based on fuzzy logic control (FLC) is designed. The proposed EMS is adaptive to the variation of headway and no-load voltage. By monitoring the charge-discharge effect of ESS and the variation of substation output energy within two adjacent periods, the charge-discharge threshold is adjusted adaptively to guarantee the recovery effect of regenerative braking energy. Finally, the simulation and field experiment of proposed EMS are carried out with ground energy storage device and actual line conditions of Beijing Batong line. The experiment results indicate the good performance of proposed EMS in terms of energy saving.

Headway variability in public transport: a review of metrics, determinants, effects for quality of service and control strategies

ABSTRACT The most relevant issues related to headway variability in public transport planning, operations and quality of service are reviewed in this paper. We discuss the causes and consequences of headway variability, the alternative metrics that have been proposed to measure it, the preventive and reactive strategies to control headway variability in both research and practice, including the role of drivers and of present and future technology, and how service provision contracts might deal with headway variability through metrics and financial incentives. The most influential elements that explain headway variability along a route are the irregularity at which vehicles are dispatched, the scheduled frequency, the distance travelled or route length, the passenger demand and associated dwell times, and the number of stops. We conclude that there is a large gap between the state-of-the-art and the state-of-practice in terms of identification of headway variability issues, as well as in the development of mitigation and control measures. It is therefore paramount that future research will contribute to closing this gap by addressing organisational, contractual and technological barriers in the implementation of measures aimed at mitigating headway variability in public transport services.

A continuous traffic flow model considering predictive headway variation and preceding vehicle’s taillight effect

The car taillights in the deceleration process of preceding vehicle may greatly affect the acceleration and deceleration processes of the following vehicle. Additionally, the driver can predict the headway at the next time period from surrounding traffic information, and adjust the vehicle acceleration based on the difference between the predicted headway and the current headway information. To analyze these combined effects, we propose a new continuous traffic flow model taking into account the predictive headway variation and preceding vehicle’s taillight. The stability condition and KdV–Burgers equation of the continuum model are derived in linear and nonlinear stability analysis. The density wave solution obtained by solving the KdV–Burgers equation can be used to describe the formation and propagation mechanism of traffic jams near stable conditions. The complex traffic phenomena such as shock waves, rarefaction waves and local cluster effects are reproduced by simulation. Results show that the taillight information of preceding vehicle and the driver’s prediction time step both contribute greatly to the stability of the traffic flow and energy consumption.

Modeling Bus Capacity for Bus Stops Using Queuing Theory and Diffusion Approximation

For bus service quality and line capacity, one critical influencing factor is bus stop capacity. This paper proposes a bus capacity estimation method incorporating diffusion approximation and queuing theory for individual bus stops. A concurrent queuing system between public transportation vehicles and passengers can be used to describe the scenario of a bus stop. For most of the queuing systems, the explicit distributions of basic characteristics (e.g., waiting time, queue length, and busy period) are difficult to obtain. Therefore, the diffusion approximation method was introduced to deal with this theoretical gap in this study. In this method, a continuous diffusion process was applied to estimate the discrete queuing process. The proposed model was validated using relevant data from seven bus stops. As a comparison, two common methods— Highway Capacity Manual (HCM) formula and M/M/S queuing model (i.e., Poisson arrivals, exponential distribution for bus service time, and S number of berths)—were used to estimate the capacity of the bus stop. The mean absolute percentage error (MAPE) of the diffusion approximation method is 7.12%, while the MAPEs of the HCM method and M/M/S queuing model are 16.53% and 10.23%, respectively. Therefore, the proposed model is more accurate and reliable than the others. In addition, the influences of traffic intensity, bus arrival rate, coefficient of variation of bus arrival headway, service time, coefficient of variation of service time, and the number of bus berths on the capacity of bus stops are explored by sensitivity analyses.

Analysis of the Determinants of Service Headway Variability at Tollbooths Under Mixed Traffic Scenario in Emerging Countries

This study makes an effort to model service-headway distribution at manually operated toll plazas (MTC) under mixed traffic conditions. To identify the most suitable probability distribution among the selected candidate distributions, Kolmogorov–Smirnov, Ander-son–Darling, and chi-squared tests were performed. It was found that the generalized extreme value (GEV) was the most suited distribution for modelling service-headway distribution at tollbooths. The results show that GEV distribution parameters can capture possi-ble variations in service headway at tollbooths under MTC reasonably well. The study results can also be used for capacity and level-of-service estimation and the development of warrants for converting MTC to electronic lanes.