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A Markov chain modelfor traffic equilibrium problems

Published online by Cambridge University Press:  15 April 2003

Giandomenico Mastroeni
Giandomenico Mastroeni*
Affiliation:
Department of Mathematics, via Buonarroti 2, 56127 Pisa, Italy; mastroen@dm.unipi.it.
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Abstract

We consider a stochastic approach in order to define an equilibrium model for a traffic-network problem. In particular, we assume a Markovian behaviour of the users in their movements throughout the zones of the traffic area. This assumption turns out to beeffective at least in the context of urban traffic, where, in general, the users tend to travel by choosing the path they find more convenient and not necessarily depending on thealready travelled part.The developed model is a homogeneous Markov chain, whosestationarydistributions (if any) characterize the equilibrium.

Keywords

Traffic assignment problemsMarkov chainsnetwork flows.
Type
Research Article
Information
RAIRO - Operations Research , Volume 36 , Issue 3 , July 2002 , pp. 209 - 226
Copyright
© EDP Sciences, 2002

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References

Barnes, J.A. and Disney, R.L., Traffic processes in a class of finite Markov queues. Queueing Systems Theory Appl. 9 (1990) 311-326. CrossRef
R. Bellman, Dynamic Programming. Princeton University Press, Princeton, New Jersey (1957).
Dafermos, S., Traffic equilibria and variational inequalities. Math. Programming 26 (1980) 40-47. CrossRef
Harker, P.T. and Pang, J.S., Finite-Dimensional Variational Inequalities and Nonlinear Complementarity Problem: A Survey of Theory, Algorithms and Appl. Math. Programming 48 (1990) 161-220. CrossRef
K.J. Hastings, Introduction to the mathematics of operations research. Dekker, New York (1989).
M. Iosifescu, Finite Markov Processes and Their Applications. John Wiley and Sons (1980).
T. Kurasugi and K. Kobayashi, A Markovian model of coded video traffic which exhibits long-range dependence in statistical analysis. J. Oper. Res. Soc. Japan 42 (1999) 1-17.
J. Kemeni and J. Snell, Finite Markov Chains. Van Nostrand, Princeton, New Jersey (1960).
W. Leontief, Environmental Repercussions and the Economic Structure: An Input-Output Approach. Rev. Econom. Statist. 52 (1970).
Mihoc, G., General Properties, On of Dependent Statistical Variables. Bull. Math. Soc. Roumaine Sci. 37 (1935) 37-82.
Nash, J.F., Non-Cooperative games. Ann. Math. 54 (1951) 286-295. CrossRef
Nguyen, S. and Pallottino, S., Equilibrium traffic assignment for large scale transit networks. Eur. J. Oper. Res. 37 (1988) 176-186. CrossRef
M. Patriksson, Nonlinear Programming and Variational Inequality Problems. Kluwer Academic Publishers, Dordrecht, Boston, London (1999).
E. Seneta, Non-negative Matrices and Markov Chains. Springer Verlag, New York,Heidelberg, Berlin (1981).
J.G. Wardrop, Some Theoretical Aspects of Road Traffic Research, in Proc. of the Institute of Civil Engineers, Part II (1952) 325-378.