Reference
B. Kersbergen, T. van den Boom, and B. De Schutter, "On implicit versus
explicit max-plus modeling for the rescheduling of trains,"
Proceedings of the 5th International Seminar on Railway Operations
Modelling and Analysis (RailCopenhagen), Copenhagen, Denmark, 15 pp.,
May 2013.
Abstract
In this paper a new railway traffic model is introduced. This model is
determined by rewriting the model introduced in the papers "A
permutation-based algorithm to optimally reschedule trains in a railway traffic
network" by T.J.J. van den Boom, N. Weiss, W. Leune, R.M.P. Goverde, and B. De
Schutter (
Proceedings of the 18th IFAC World Congress,
pages 9537-9542, Milan, Italy, August-September 2011) and "Structured modeling,
analysis, and control of complex railway operations." by T.J.J. van den Boom,
B. Kersbergen, and B. De Schutter (
Proceedings of the 51st
IEEE Conference on Decision and Control, pages 7366-7371, Maui, Hawaii,
December 2012). The models are both macroscopic, contain the same level of
details, allow the rescheduling of trains, and are formulated as Switching
Max-Plus-Linear (SMPL) models, the difference being that the first model is an
implicit SMPL model and the second one is an explicit SMPL model. In this paper
a method is detailed for rewriting an implicit SMPL model into an explicit
SMPL. Both models are used to solve the rescheduling problem. By solving the
rescheduling problem a schedule for all trains in the network is found that
minimizes the total delay. The rescheduling problem will be written as a Mixed
Integer Linear Programming (MILP) problem and solved using the standard solver
available in the Multi-Parametric Toolbox for Matlab. The time needed to solve
the rescheduling problem using either the implicit and explicit model is
compared.
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BibTeX
@inproceedings{Kervan:13-015,
author = {Kersbergen, Bart and van den Boom, Ton and De Schutter, Bart},
title = {On Implicit versus Explicit Max-Plus Modeling for the
Rescheduling of Trains},
booktitle = {Proceedings of the 5th International Seminar on Railway
Operations Modelling and Analysis (RailCopenhagen)},
address = {Copenhagen, Denmark},
month = may,
year = {2013}
}