Summary
We present in this paper a traffic model based on Petri nets and minplus algebra. A Petri net is represented by two matrices one in standard algebra and the other in minplus algebra. Then a system point of view is developed based on a matrix product combining these two algebras. Introducing inputs and outputs on transitions and places we can link two Petri nets by associating outputs with inputs of the two systems. This linking corresponds to a contraction operator. Combining elementary systems with this contraction operator we can build large systems. This point of view is used to define the traffic dynamics of a regular town from three elementary Petri nets.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
T. Murata: Petri Nets: Properties, Analysis and Applications Proceedings of the IEEE, Vol. 77, No. 4, pp. 541-580, 1989.
F. Baccelli, G. Cohen, G.J. Olsder, and J.P. Quadrat: Synchronization and Linearity, Wiley, 1992 available http://maxplus.org.
D. Chowdhury, L. Santen, A. Shadschneider: Statistical physics of vehicular traffic and some related systems. Physics Report 329, pp. 199-329, 2000.
P. Lotito, E. Mancinelli, J.P. Quadrat: A Min-Plus Derivation of the Fundamental Car-Traffic Law, IEEE-AC V.50, N.5, pp. 699-705, 2005.
N. Farhi, M. Goursat, and J.P. Quadrat: Derivation of the fundamental traffic diagram..., 44th IEEE-CDC-ECC December 2005, Seville.
N. Farhi, M. Goursat, J.-P. Quadrat: Fundamental Traffic Diagram of Elementary Road Networks, in Proceedings ECC, 2006, Kos.
N. Farhi: PhD thesis, to appear, Paris 1, 2008.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Farhi, N., Goursat, M., Quadrat, JP. (2009). Road Traffic Models Using Petri Nets and Minplus Algebra. In: Appert-Rolland, C., Chevoir, F., Gondret, P., Lassarre, S., Lebacque, JP., Schreckenberg, M. (eds) Traffic and Granular Flow ’07. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77074-9_27
Download citation
DOI: https://doi.org/10.1007/978-3-540-77074-9_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77073-2
Online ISBN: 978-3-540-77074-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)