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Some Remarks on Stochastic User Equilibrium

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  • Hazelton, Martin L.

Abstract

The behavioural foundation of Stochastic User Equilibrium is that each traveller attempts to minimize his or her perceived travel costs, where these costs are composed of a deterministic measured cost and a random term which can be interpreted as perceptual error. In principle such a definition, which is in terms of random errors, should imply an equilibrium probability distribution over feasible flow patterns on the transport network. Such a probability distribution could potentially allow between day variability in network flows to be represented. However, traditionally a deterministic, large sample approximation has been used as the 'solution' of Stochastic User Equilibrium. In this paper a representation of Stochastic User Equilibrium as a probability distribution is developed. This distribution is defined by the conditional route selection of each individual given the choices of all other travellers. An interpretation of the resulting assignment model as the limit (in the infinite future) of a continuous time assignment process is discussed. The limiting behaviour as the travel demand becomes large is also investigated, and convergence to the traditional deterministic form of Stochastic User Equilibrium is proved.

Suggested Citation

  • Hazelton, Martin L., 1998. "Some Remarks on Stochastic User Equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 32(2), pages 101-108, February.
    • Handle: RePEc:eee:transb:v:32:y:1998:i:2:p:101-108
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    References listed on IDEAS

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    1. M. A. P. Taylor, 1982. "Travel Time Variability---The Case of Two Public Modes," Transportation Science, INFORMS, vol. 16(4), pages 507-521, November.
    2. Gary A. Davis & Nancy L. Nihan, 1993. "Large Population Approximations of a General Stochastic Traffic Assignment Model," Operations Research, INFORMS, vol. 41(1), pages 169-178, February.
    3. Carlos F. Daganzo & Yosef Sheffi, 1977. "On Stochastic Models of Traffic Assignment," Transportation Science, INFORMS, vol. 11(3), pages 253-274, August.
    4. Cascetta, Ennio, 1989. "A stochastic process approach to the analysis of temporal dynamics in transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 23(1), pages 1-17, February.
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    1. Hazelton, Martin L., 2000. "Estimation of origin-destination matrices from link flows on uncongested networks," Transportation Research Part B: Methodological, Elsevier, vol. 34(7), pages 549-566, September.
    2. Wei, Chong & Asakura, Yasuo & Iryo, Takamasa, 2014. "Formulating the within-day dynamic stochastic traffic assignment problem from a Bayesian perspective," Transportation Research Part B: Methodological, Elsevier, vol. 59(C), pages 45-57.
    3. Henn, Vincent & Ottomanelli, Michele, 2006. "Handling uncertainty in route choice models: From probabilistic to possibilistic approaches," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1526-1538, December.
    4. C. Robin Lindsey & Erik T. Verhoef, 1999. "Congestion Modelling," Tinbergen Institute Discussion Papers 99-091/3, Tinbergen Institute.
    5. Clark, Stephen & Watling, David, 2005. "Modelling network travel time reliability under stochastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 39(2), pages 119-140, February.
    6. Martin L. Hazelton & David P. Watling, 2004. "Computation of Equilibrium Distributions of Markov Traffic-Assignment Models," Transportation Science, INFORMS, vol. 38(3), pages 331-342, August.
    7. Hazelton, Martin L., 2010. "Bayesian inference for network-based models with a linear inverse structure," Transportation Research Part B: Methodological, Elsevier, vol. 44(5), pages 674-685, June.
    8. Yin, Yafeng & Yang, Hai, 2003. "Simultaneous determination of the equilibrium market penetration and compliance rate of advanced traveler information systems," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(2), pages 165-181, February.
    9. Xie, Chi & Liu, Zugang, 2014. "On the stochastic network equilibrium with heterogeneous choice inertia," Transportation Research Part B: Methodological, Elsevier, vol. 66(C), pages 90-109.

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