Train scheduling for minimizing passenger waiting time with time-dependent demand and skip-stop patterns: Nonlinear integer programming models with linear constraints

Niu, Huimin; Zhou, Xuesong; Gao, Ruhu

doi:10.1016/j.trb.2015.03.004

Cited by 382 publications

(191 citation statements)

References 22 publications

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“…Linear piecewise curve is used to approximate the energy per unit mass of train i in segment x: (4) where and are two parameters, and l x is the length of segment . The values of and can be estimated by the mean squared error (MSE) method.…”

Section: Energy Consumptionmentioning

confidence: 99%

“…Urban rail transit, which has large capacity and utilizes energy more efficiently than automobiles, becomes one of the busiest transportation systems in large cities. However, current metro systems usually set uniform timetables in certain periods [1,2], while passenger demands vary from time to time [3,4]. Such uniform timetables are less efficient and economic than the non-uniform ones.…”

Section: Introductionmentioning

confidence: 99%

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A Numerical Optimization Technique for Scheduling Non-uniform Metro Trains under Time-varying Passenger Demands

Huang¹,

Li²

2017

dtcse

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Urban rail transit is costly and often overloaded. Thus, the motivation of this paper is to develop specific operating strategies to reduce cost and improve service level. This paper proposed a numerical optimization technique to optimize non-uniform metro train timetables with time-varying passenger demands, where the total monetary cost of time and energy is minimized. The problem was formulated with a constrained, non-smooth, nonlinear programming model, and transformed into an unconstrained one by the proposed Augmented Lagrangian (AL) algorithm. Then, the Pattern Search (PS) algorithm was designed to search for an optimal solution in each iteration step of AL. The case study shows that the proposed technique is effective to obtain non-uniform timetables that significantly outperform uniform ones reducing cost at most 34.92%, and provides decision-making support.

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Section: Energy Consumptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Numerical Optimization Technique for Scheduling Non-uniform Metro Trains under Time-varying Passenger Demands

Huang¹,

Li²

2017

dtcse

View full text Add to dashboard Cite

show abstract

“…Passenger waiting time is one of the most crucial factors for transit design and planning, related to passenger satisfaction and to measure public transport (PT) quality of service [1][2][3][4]. However, it was significant at the trip level in urban PT, and the ratio of passenger actual waiting time to actual journey time was between 10 and 30% [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

On Individual Repositioning Distance along Platform during Train Waiting

Leurent

Xie

2018

Journal of Advanced Transportation

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Out of waiting times spent in rail stations on boarding platforms, some part can be reinvested by the trip-makers to optimize their positions of boarding and save on travel time for the rest of their trips. This paper provides a stochastic model, in which user's journey is decomposed into phases of, successively, walking in the access station, platform positioning, waiting for boarding, train riding, and walking in the egress station. Walking speed and target position are modeled as individual factors, and in-station distances as random variables. Service timetable is exogenous. This makes egress times and exit instants random variables that are characterized by distribution and mass probability functions under closed-forms, for both single and distributed walking speeds. Specific statistical distributions are shown to ease computation. The resulting PDF formulae make likelihood functions of the model parameters. Maximum likelihood estimation is proposed and applied to a case study of commuter rail line in Paris: journeys between stations Vincennes and La Défense along line A of the Regional Express Railways. Based on data from Automated Fare Collection and Automatic Vehicle Location systems and pertaining to an individual user, satisfactory results were obtained.

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“…Researchers have devoted themselves to optimize the train schedule to assist help dispatchers make better decisions meeting passengers and operators expectations. The objective functions are most concentrated on enhancing passengers satisfaction in terms of degree of crowdedness [1][2][3], passengers waiting time [2,4,5] and passengers travel time [6,7] or reducing operation costs in terms of energy consumption [6,[8][9][10], trains [11,12], train travel time [13], etc. Not only does the urban rail transit systems expand fast, but also the passenger demand rises significantly.…”

Section: Introductionmentioning

confidence: 99%

A Short Turning Strategy for Train Scheduling Optimization in an Urban Rail Transit Line: The Case of Beijing Subway Line 4

Zhang

Wang

et al. 2018

Journal of Advanced Transportation

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In urban rail transit systems, train scheduling plays an important role in improving the transport capacity to alleviate the urban traffic pressure of huge passenger demand and reducing the operation costs for operators. This paper considers the train scheduling with short turning strategy for an urban rail transit line with multiple depots. In addition, the utilization of trains is also taken into consideration. First, we develop a mixed integer nonlinear programming (MINLP) model for the train scheduling, where short turning train services and full-length train services are optimized based on the predefined headway obtained by the passenger demand analysis. The MINLP model is then transformed into a mixed integer linear programming (MILP) model according to several transformation properties. The resulting MILP problem can be solved efficiently by existing solvers, e.g., CPLEX. Two case studies with different scales are constructed to assess the performance of train schedules with the short turning strategy based on the data of Beijing Subway line 4. The simulation results show that the reduction of the utilization of trains is about 20.69%.

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Train scheduling for minimizing passenger waiting time with time-dependent demand and skip-stop patterns: Nonlinear integer programming models with linear constraints

Cited by 382 publications

References 22 publications

A Numerical Optimization Technique for Scheduling Non-uniform Metro Trains under Time-varying Passenger Demands

A Numerical Optimization Technique for Scheduling Non-uniform Metro Trains under Time-varying Passenger Demands

On Individual Repositioning Distance along Platform during Train Waiting

A Short Turning Strategy for Train Scheduling Optimization in an Urban Rail Transit Line: The Case of Beijing Subway Line 4

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