A Stochastic Version of the Strategy-Based Congested Transit Assignment Model and a Technique by Smoothing Approximations
This paper develops a stochastic version for the strategy-based congested transit assignment problem stated by Cominetti and Correa (Trans. Sci. 35(3):250–267, 2001). As a distinctive approach, this stochastic version takes into account stochastic mean waiting times of passengers at stops and in-vehicle travel times. The model is formulated as a stochastic variational inequality derived from the formulation of the deterministic version of the problem, also stated as a variational inequality problem, for which only a single solution method is known uptodate. Closely related with the stochastic model, and as a special case of it, a consistent smoothing approximation to the deterministic model is developed and it is shown that this approximation provides an alternative way of solving the deterministic model. It is also shown that both, the stochastic model and the smoothed approximation, can be solved by means of an adaptation of a path based method for the asymmetric traffic assignment problem. Computational tests have been carried out on several medium-large scale networks showing the viability of the method and its applicability to large scale transit models.
KeywordsCongested transit assignment Stochastic variational inequalities Strategy-based transit equilibrium Smoothing approximation
Research supported under Spanish Research Projects TRA2008-06782-C02-02, TRA2014-52530-C3-3-P.
- 14.Gentile, G., Florian, M., Hamdouch, Y., Cats, O., Nuzzolo, A.: The theory of transit assignment: basic modelling frameworks. In: Gentile, G., Noekel, K. (eds.) Modelling Public Transport Passenger Flows in the Era of Intelligent Transport Systems. Springer Tracts on Transportation and Traffic, vol. 10, pp. 287–386. Springer, Cham (2016). doi: 10.1007/978-3-319-25082-3_6 CrossRefGoogle Scholar
- 17.Jiang, Y., Szeto, W.Y., Ng, T.M., Ho, S.C.: The reliability-based stochastic transit assignment problem with elastic demand. J. Eastern Asia Soc. Transp. Stud. 10, 831–850 (2013)Google Scholar
- 23.Peng, J.-M.: A smoothing function and its applications. In: Fukushima, M., Qi, L. (eds.) Reformulation: Nonsmooth, Piecewise Smooth and Smoothing Methods. Applied Optimization Series, pp. 293–316. Kluwer Academic Publishers, Dordrecht (1999)Google Scholar
- 25.Spiess, H.: Contribution à la théorie et aux outils de planification des réseaux de transport urbains. Ph D thesis, Département d’Informatique et Récherche Opérationnelle, Publication 382, CRT, U. de Montréal (1984)Google Scholar