Two-Train Trajectory Optimization with a Green-Wave Policy

Abstract

The problem of train trajectory optimization of two successive trains on the same line is studied in this paper. The two-train optimal control problem is formulated by using the multiple-phase method of optimal control, in which the train schedules as well as train performance parameters and track gradients, curves and speed limits are taken into account. The objective is to ensure a smooth, safe, punctual, and energy-efficient train operation. A green-wave (GW) policy is adopted to ensure that the trains proceed safely under all green signals. Special objective functions and constraints are developed in case of train delays. The method is applied in a case study of two successive trains running on a railway line with various input delays showing the benefit of the GW policy and the ability of delay recovery.

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References

Howlett

Optimal Strategies for the Control of a Train. Automatica, Vol. 32, No. 4, 1996, pp. 519–532.

Howlett

P. G.

and Pudney

P. J.

. Energy-Efficient Train Control. Springer, Berlin, 1995.

Albrecht

, Koelewijn

, and Pudney

. Energy-Efficient Recovery of Delays in a Rail Network. In Proceedings, 2011 Australasian Transport Research Forum, 2011.

Wang

, Goverde

R. M. P.

, and Ma

. A Multiple Phase Train Trajectory Optimization Method Under Real-Time Rail Traffic Management. Presented at 18th IEEE International Conference on Intelligent Transportation Systems, Las Palmas, Spain, Sept. 15–18, 2015.

Wang

, Goverde

R. M. P.

, and Ma

. Train Trajectory Optimization with Signalling Constraints. Presented at Conference on Advanced Systems in Public Transport (CASPT 2015), Rotterdam, Netherlands, July 19–24, 2015.

ON-TIME. Best Practice, Recommendations and Standardisation. Deliverable ONT-WP01-DEL-003, EU ON-TIME project, 2014.

Albrecht

, Binder

, and Gassel

. Applications of Real-Time Speed Control in Rail-Bound Public Transportation Systems. Intelligent Transport Systems, IET, Vol. 7, No. 3, 2013, pp. 305–314.

Corman

, D’Ariano

, Pacciarelli

, and Pranzo

. Evaluation of Green Wave Policy in Real-Time Railway Traffic Management. Transportation Research Part C: Emerging Technologies, Vol. 17, No. 6, 2009, pp. 607–616.

Hansen

I. A.

, and Pachl

. Railway Timetabling and Operations. Eurailpress, 2014.

10.

Rao

A. V.

Extension of a Pseudospectral Legendre Method to Non-Sequential Multiple-Phase Optimal Control Problems. In Proceedings, AIAA Guidance, Navigation, and Control Conference and Exhibit, Vol. 3, 2003, pp. 1961–1979.

11.

Rao

A. V.

, Benson

D. A.

, Darby

, Patterson

M. A.

, Francolin

, Sanders

, and Huntington

G. T.

. Algorithm 902: GPOPS, a Matlab Software for Solving Multiple-Phase Optimal Control Problems Using the Gauss Pseudospectral Method. ACM Transactions on Mathematical Software, Vol. 37, No. 2, 2010, pp. 1–22.