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A (max, plus) modelling approach for the evaluation of travelling times in a public transportation system.

Manier, Marie-Ange; el Moudni, Abdellah; Manier, Herve; Nait-Sidi-Moh, A.

In: Proceedings of the second IEEE International Conference on Systems, Man and Cybernetics (SMC'02), October 6-9, 2002, Hammamet, Tunisia, Volume 3. IEEE Computer Society Press, October 2002.

Abstract: This paper extends the simple transportation network model proposed before. We are interested in a public transportation system composed of several lines and several connection stops. The performance analysis and the evaluation of the travelling times at the connection stops are the main objectives of this study. Then to reach these goals we use a subclass of Petri nets to model our transportation network. By taking into account the network working, some structural conflicts appear in the graphical model. Then we solve them by determining routing equations. We represent our model by a non-stationary linear (max, plus) system in the (max, plus) algebra. The resolution of this state model enables us to evaluate the system performances. Finally a numerical example is presented to illustrate the proposed model.

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