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A stochastic process approach to the analysis of temporal dynamics in transportation networks

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  • Cascetta, Ennio
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    Abstract

    Equilibrium analyses of transportation networks are by their nature "static," with equilibrium configuration defined as "fixed" or "autoreflexive" points, i.e. flow patterns reproducing themselves on the basis of the assumptions made on users' behavior once reached by the system. In this paper it is argued that no transportation system remains in the same state over successive periods because of the action of several causes (e.g. temporal fluctuation of level and composition of demand, users' choices, and travel costs). This implies that the sequence of states occupied by the system over successive epochs or times of similar characteristics (e.g. peak hour of working days) is the realization of a stochastic process, the type of which depends on, among other things, the choice mechanism followed by travelers. Stationarity of the stochastic process within fixed potential demand and network structures is considered to be a desirable property because it allows a flow pattern distribution to be associated to each demand-network system independently of its starting configuration and elapsed time. Furthermore, this stationarity makes it possible to define expected path and link flows and compare them with those of stochastic user equilibrium (SUE). In this paper rather general sufficient conditions for the process stationarity are given, essentially calling for a "stable" choice mechanism of potential users. In the following a particular model of temporal dynamics (STODYN), based upon a number of simplifying assumptions on users' behavior common to most assignment models, is described. Exact and approximate relationships between STODYN steady-state expected flows and SUE average flows are also analyzed both in the case of unique and multiple equilibria. The possible use of STODYN as an assignment model giving unique average flows along with their variances and covariances is then discussed. The model takes into account stochastic fluctuations of demand and can be easily extended to other "dimensions" such as distribution and modal choice. Some results of an empirical analysis comparing STODYN average flows with SUE and observed flows on two urban car networks are also reported.

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    Bibliographic Info

    Article provided by Elsevier in its journal Transportation Research Part B: Methodological.

    Volume (Year): 23 (1989)
    Issue (Month): 1 (February)
    Pages: 1-17

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    Handle: RePEc:eee:transb:v:23:y:1989:i:1:p:1-17

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    Cited by:
    1. Hazelton, Martin L., 1998. "Some Remarks on Stochastic User Equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 32(2), pages 101-108, February.
    2. Alessandro Innocenti & Patrizia Lattarulo & Maria Grazia Pazienza, 2009. "Heuristics and Biases in Travel Mode Choice," Labsi Experimental Economics Laboratory University of Siena 027, University of Siena.
    3. Hazelton, Martin L., 2002. "Day-to-day variation in Markovian traffic assignment models," Transportation Research Part B: Methodological, Elsevier, vol. 36(7), pages 637-648, August.
    4. Watling, David, 1999. "Stability of the stochastic equilibrium assignment problem: a dynamical systems approach," Transportation Research Part B: Methodological, Elsevier, vol. 33(4), pages 281-312, May.
    5. Watling, David, 1998. "Perturbation stability of the asymmetric stochastic equilibrium assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 32(3), pages 155-171, April.
    6. Watling, David, 1996. "Asymmetric problems and stochastic process models of traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 30(5), pages 339-357, October.
    7. He, Xiaozheng & Guo, Xiaolei & Liu, Henry X., 2010. "A link-based day-to-day traffic assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 597-608, May.
    8. 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.
    9. 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.
    10. Bie, Jing & Lo, Hong K., 2010. "Stability and attraction domains of traffic equilibria in a day-to-day dynamical system formulation," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 90-107, January.
    11. Guo, Xiaolei & Liu, Henry X., 2011. "Bounded rationality and irreversible network change," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1606-1618.
    12. Lo, H. & Hickman, M. & Walstad, M., 1996. "An Evaluation Taxonomy For Congestion Pricing," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt80g5s1km, Institute of Transportation Studies, UC Berkeley.
    13. Ye, Hongbo & Yang, Hai, 2013. "Continuous price and flow dynamics of tradable mobility credits," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 436-450.
    14. Lo, H. P. & Zhang, N. & Lam, W. H. K., 1999. "Decomposition algorithm for statistical estimation of OD matrix with random link choice proportions from traffic counts," Transportation Research Part B: Methodological, Elsevier, vol. 33(5), pages 369-385, June.
    15. Liu, Ronghui & Van Vliet, Dirck & Watling, David, 2006. "Microsimulation models incorporating both demand and supply dynamics," Transportation Research Part A: Policy and Practice, Elsevier, vol. 40(2), pages 125-150, February.
    16. Canca, David & Zarzo, Alejandro & Algaba, Encarnación & Barrena, Eva, 2013. "Macroscopic attraction-based simulation of pedestrian mobility: A dynamic individual route-choice approach," European Journal of Operational Research, Elsevier, vol. 231(2), pages 428-442.
    17. Cominetti, Roberto & Melo, Emerson & Sorin, Sylvain, 2010. "A payoff-based learning procedure and its application to traffic games," Games and Economic Behavior, Elsevier, vol. 70(1), pages 71-83, September.
    18. Parry, Katharina & Hazelton, Martin L., 2013. "Bayesian inference for day-to-day dynamic traffic models," Transportation Research Part B: Methodological, Elsevier, vol. 50(C), pages 104-115.

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