A Markov chain model for traffic equilibrium problems

Giandomenico Mastroeni

RAIRO - Operations Research (2010)

  • Volume: 36, Issue: 3, page 209-226
  • ISSN: 0399-0559

Abstract

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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 be effective 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 the already travelled part. The developed model is a homogeneous Markov chain, whose stationary distributions (if any) characterize the equilibrium.

How to cite

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Mastroeni, Giandomenico. "A Markov chain model for traffic equilibrium problems." RAIRO - Operations Research 36.3 (2010): 209-226. <http://eudml.org/doc/105271>.

@article{Mastroeni2010,
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 be effective 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 the already travelled part. The developed model is a homogeneous Markov chain, whose stationary distributions (if any) characterize the equilibrium. },
author = {Mastroeni, Giandomenico},
journal = {RAIRO - Operations Research},
keywords = {Traffic assignment problems; Markov chains; network flows.; traffic assignment problems; network flows},
language = {eng},
month = {3},
number = {3},
pages = {209-226},
publisher = {EDP Sciences},
title = {A Markov chain model for traffic equilibrium problems},
url = {http://eudml.org/doc/105271},
volume = {36},
year = {2010},
}

TY - JOUR
AU - Mastroeni, Giandomenico
TI - A Markov chain model for traffic equilibrium problems
JO - RAIRO - Operations Research
DA - 2010/3//
PB - EDP Sciences
VL - 36
IS - 3
SP - 209
EP - 226
AB - 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 be effective 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 the already travelled part. The developed model is a homogeneous Markov chain, whose stationary distributions (if any) characterize the equilibrium.
LA - eng
KW - Traffic assignment problems; Markov chains; network flows.; traffic assignment problems; network flows
UR - http://eudml.org/doc/105271
ER -

References

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  11. J.F. Nash, Non-Cooperative games. Ann. Math.54 (1951) 286-295.  Zbl0045.08202
  12. S. Nguyen and S. Pallottino, Equilibrium traffic assignment for large scale transit networks. Eur. J. Oper. Res.37 (1988) 176-186.  Zbl0649.90049
  13. M. Patriksson, Nonlinear Programming and Variational Inequality Problems. Kluwer Academic Publishers, Dordrecht, Boston, London (1999).  Zbl0913.65058
  14. E. Seneta, Non-negative Matrices and Markov Chains. Springer Verlag, New York,Heidelberg, Berlin (1981).  Zbl0471.60001
  15. J.G. Wardrop, Some Theoretical Aspects of Road Traffic Research, in Proc. of the Institute of Civil Engineers, Part II (1952) 325-378.  

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