Departure Headway Research Articles

An energy‐efficient timetable optimization method for express/local train with on‐board passenger number considered

AbstractWith the expansion of the metropolitan area, the application of express/local mode is gradually increasing. In contrast to the normal mode, the express/local mode has advantages in reducing energy consumption and saving total travel time by having express trains skipping some stops. This paper aims to minimize the total energy consumption of express and local train throughout the day by optimizing the train operation strategy in the same power supply section and increasing the overlap time between train traction acceleration and train regenerative braking to obtain the optimal energy‐efficient timetable. As the consumed energy of a train is highly dependent on the rolling stock weight and the on‐board passengers’ weight. An integer programming model is proposed with on‐board passengers considered accurately, in which the dwell times, departure headway, and total turnaround time of express and local trains are determined. An improved grey wolf algorithm is designed by improving convergence factor and incorporating differential evolution to solve the proposed problem. The real data on Guangzhou Metro Line 18 is adopted for numerical studies. The results show that the optimized timetable increases the regenerative energy utilization rate by 21.37% and reduces the total energy consumption by 5.02% compared to the operational timetable.

An Adjustment Method for the Customized Trains of the Railway

The “customized train” is a train operated by the customized service of the passengers. The departure time, total travel time, and the travel classes are decided by passengers’ wishes. Successful operation of customized trains (CT) has a great significance to the future development in the relationship between the railway enterprise and the passenger service. In order to establish a comprehensive method for the CT operation plan, the paper proposes an intention survey method to obtain the passenger travel wishes data. Then, according to the existing timetable, the alternative set of CTs is built. The CT should satisfy the constraints of the passenger demand, the stop, and the train travel time. Based on the alternative set, a bilevel programming model for the maximum operation revenue of the CTs and minimum adjustment cost of existing timetable is established according to the passengers’ travel demands. The model also considers the constraints of actual travel time, arrival headway, departure headway, maximal adjustment time and capacity, and so on. The adjustment strategies for the train operation confliction are established. Finally, the method is proven through the analysis of actual cases, which can provide decision-making basis for future railway enterprises when operating the customized trains.

Does Roadway Performance Affect Transit Headway Unreliability? Evidence from Mixed-Traffic Transit Corridors in Toronto, Canada

This research assesses the links between roadway performance and transit headway unreliability. Frequent and reliable transit services are valued by transit users and feature as critical components affecting generalized travel costs. But retaining high quality and reliable transit services in mixed-traffic urban contexts is challenging because more and more users are competing for limited physical road space, making an understanding of service unreliability critical for effective transportation system management in growing urban contexts. This study focuses transit headway unreliability on three major downtown Toronto arterial transit corridors—King Street, Queen Street, and Dundas Street. These corridors are primarily served by streetcars but are also occasionally served by buses in cases of diversions or street closures. This research uses Inrix, Inc. probe data to measure traffic congestion and roadway service unreliability and to explore its links with transit headway reliability. Both inferential models and descriptive statistics are presented to identify patterns in transit headway reliability and estimate the strength of association with traffic congestion. Results indicate that roadway performance levels and terminus departure headway unreliability are linked with stop-level transit headway unreliability. Nevertheless, much of the variation in transit headway unreliability remains unexplained by inferential models. Results indicate that insofar as traffic management actions can affect congestion levels, this may improve transit headway reliability. However, one should temper expectations of congestion management affecting mixed-traffic transit services, particularly in a highly urbanized, mixed-traffic environment such as downtown Toronto. Instead, findings suggest meaningful improvements in stop-level headway reliability from better initial scheduling and headways at the beginning of these transit routes.

Discharge Characteristics Analysis of Queued-up Vehicles at Signal-Controlled Intersections Under Heterogeneous Traffic Conditions

Characteristics of discharge vehicle play a significant role in the concept of capacity estimation and designing of a signal-controlled intersection. Highway Capacity Manual (HCM) (Transportation Research Board of the National Academics, 5th edn, Washington, DC, 2000) presents a methodology for analysing signalized intersection considering details of each parameter for a lane-based car-dominated traffic stream, with limited applicability for the mixed traffic conditions. The present study analyses the departure headway characteristics of queued vehicles where a decreasing trend is observed with increase in vehicle position with a saturation headway of 2.05 s/veh. The distributions of departure headways are also analysed, and hypothesis result shows that the departure headways at each vehicle position follow a particular log-normal distribution with varying mean and variance. An optimization technique is framed to find out the discharge of vehicles through minimizing the difference between observed flow and ideal flow proposed by HCM (2000). Dynamic passenger car units (PCU) are also estimated through minimizing the Theil’s coefficient for accurate estimation of discharge pattern for mixed traffic conditions. The result shows that optimized discharge pattern is close to the ideal one with maximum saturation flow of 1908 PCUs/h (HCM proposed 1900 PCUs/h). A comparative analysis is done between the obtained flow value and flow value proposed by several guidelines and studies to check its suitability for mixed traffic stream.

Research on the Cooperative Train Control Strategy to Reduce Energy Consumption

Based on the mature energy-saving strategy of a single train, the optimization of multiple trains' trajectories is studied. A cooperative control model is formulated with the utilization of the regenerative energy considered, which is used to calculate the total energy consumption of an electric subway system under various energy-saving control strategies. Taking the cooperative operation of two trains within the same section of an electrical system as an example, the front one adopt the optimal driving strategy with four modes of movement, which are the maximum traction, cruising, coasting, and the maximum braking by sequence. The latter is controlled by the strategy with four movement modes (mentioned earlier) and five movement modes (namely, the maximum traction, cruising/coasting, the maximum traction, coasting, and the maximum braking), respectively. The minimum energy consumption under different departure headway is calculated by using a heuristic algorithm. It turned out that the optimal energy-saving control strategy can be obtained with the departure headway given, and an energy-saving control strategy corresponding to the minimum energy consumption can be worked out too. The proposed energy-saving strategy can reduce energy consumption by 19.2% at the most.

Revisiting distribution model of departure headways at signalised intersections

ABSTRACTThe departure headway is one of the critical parameters to optimise and evaluate the design and timing of signalised intersections. In order to provide a suitable method to accurately estimate saturation headway at signalised intersections, the distribution of departure headways and its characteristics were investigated based on field observation in Shanghai, China. Statistical analysis results reveal that (1) Shifted Log-Normal distribution can be used to capture the features of departure headways distribution at each position in a queue, including headways at the first position which are usually excluded in existing models; (2)Shifted Log-Normal is more suitable to capture the distribution of steady-flow headways which are approximately the headways at positions between the fifth vehicle and the last stopping vehicle in the queue; (3) the mode of steady-flow headway distribution, which reflects the real manipulative ability of drivers in a certain region, can be considered as theoretical saturation headway and the mean can be considered as practical saturation headway which is used for actual capacity analysis in practice; and (4) saturation headway distribution obeys four-sigma rule. These findings about departure headway distribution at signalised intersections will be helpful for driving behaviour understanding, capacity calculation, design, timing, as well as microscopic traffic simulation of signalised intersections.

A Bulk Queue Model for the Evaluation of Impact of Headway Variations and Passenger Waiting Behavior on Public Transit Performance

This paper demonstrates a model developed using the Markov chain technique, to ascertain the performance of public transit systems and examine the effects of stochastic variations in passenger arrival, waiting, boarding, and alighting behaviors on the regularity of headway along the route. The model addresses situations in which passengers abandon the system after a certain amount of waiting time. This accounts for the existence of a finite allowance of waiting time from the viewpoint of the passengers. The numerical examples included offer insights into factors that affect the reliability of public transit systems and presented analysis of the system performance measures such as mean counts of passengers served by transit systems, abandoned passengers, and unused space on vehicles. The impact of variability of departure headway on the utilization of public transit systems is illustrated. This model can be used as an analysis tool by transit planners to evaluate selection of system attributes.

Distribution models for start-up lost time and effective departure flow rate

Due to its importance, lots of investigations had been carried out in the last four decades to study the relationship between phase duration and vehicle departure amount. In this paper, we aim to build appropriate distribution models for start-up lost time and effective departure flow rate, by considering their relations with the frequently mentioned departure headway distributions. The motivation behind is that distribution models could provide richer information than the conventional mean value models and thus better serve the need of traffic simulation and signal timing planning. To reach this goal, we first check empirical data collected in Beijing, China. Tests show that the departure headways at each position in a discharging queue are very weakly dependent or almost independent. Based on this new finding, two distribution models are proposed for start-up lost time and effective flow rate, respectively. We also examine the dependences of departure headways that are generated by three popular traffic simulation software: VISSIM, PARAMICS and TransModeler. Results suggest that in VISSIM, the departure headways at different positions are almost deterministically dependent and may not be in accordance with empirical observations. Finally, we discuss how the dependence of departure headways may influence traffic simulation and signal timing planning.

Statistical estimation of railroad congestion delay

This research identifies factors that are the major contributors to freight rail congestion using statistical analysis. Total train running time is predicted based on free running time predictors (horsepower per ton, track topography and slow orders) and congestion-related factors (meets, passes, overtakes, prior time periods’ train counts, total train hours, train spacing variability, and train departure headway). Primary congestion predictive factors (meets, passes, overtakes) are consistently found to have the largest effect on congestion delay. The predictive equations are used to forecast average monthly train running time with a 4.6% mean absolute percent error.

Benefit Sensitivities of Adaptive Traffic Control Strategies at Isolated Traffic Signals

A study of the possible benefits of using traffic adaptive and actuated signal control strategies at traffic signals is described here. The study indicated that delay estimates produced by INTEGRATION closely matched the delay estimates of the 1997 revision to the U.S. Highway Capacity Manual. Second, benefits of time-of-day control and adaptive control became more pronounced as the level of demand peaking increased. Third, well-designed time-of-day plans easily outperform fixed-time and adaptive strategies when the prevailing traffic demands match the controller’s expectations. Adaptive strategies performed better than simple fixed-time control strategies, which were optimized only for the average demand level. It was also observed that all types of control strategies, especially adaptive control strategies, could be improved by introducing signal actuation. Finally, it was found that actuation improved the performance of the intersection for both uniform and random departure headways. Improvements were greatest when an adaptive control strategy was being implemented and the departure headway was random.

A capacity model for all-way stop-controlled intersections based on stream interactions

This paper presents a methodology for analyzing the capacity of all-way stop-controlled intersections and the data that have been collected to validate and support the methodology. The rate of departure from one approach of an all-way stop-controlled intersection is controlled by the presence or absence of vehicles on the other approaches. This degree of conflict is classified into a set of unique cases. Field measurements covering over 20,000 vehicle headways were classified into five degree of conflict cases. The model forecasts the mean departure headway based on the probability of occurrence of each degree of conflict case. ©

Distributions of queue lengths at fixed time traffic signals

This paper presents a new model which studies probability distributions of queue lengths at fixed time traffic signals. It extends Haight's model for Poisson arrivals that the arrival distribution during the effective red period is general and the headway between two successive departures is not less than the minimum departure headway. Moreover, the probability generating function of the queue length, at the end of the effective red period, is derived. The probabilities of the queue lengths, at the ends of the effective green, actual red and amber periods, are also obtained. Comparison is made with Haight's model. Finally a case study for the proposed model is reported.