**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.

Corresponding technical report: pdf file (257 KB)

@inproceedings{Kervan:13-015,

author={B. Kersbergen and T. van den Boom and B. {D}e Schutter},

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}

}

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