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Stochastic quasi-gradient algorithm for the off-line stochastic dynamic traffic assignment problem

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  • Peeta, Srinivas
  • Zhou, Chao

Abstract

This paper proposes a stochastic quasi-gradient (SQG) based algorithm to solve the off-line stochastic dynamic traffic assignment (DTA) problem that explicitly incorporates randomness in O-D demand, as part of a hybrid DTA deployment framework for real-time operations. The problem is formulated as a stochastic programming DTA model with multiple user classes. Due to the complexities introduced by real-time traffic dynamics and system characteristics, well-behaved properties cannot be guaranteed for the resulting formulation and analytical functional forms that adequately capture traffic realism typically do not exist for the associated objective functions. Hence, a simulation-based SQG method that is applicable for a generalized differentiable (locally Lipschitz) non-convex objective function and non-convex constraint set is proposed to solve the problem. Simulation is used to estimate quasi-gradients that are stochastic to incorporate demand randomness. The solution approach is a generalization of the deterministic DTA solution methodology; under it, deterministic DTA models are special cases. Of practical significance, it provides a robust solution for the field deployment of DTA, or an initial solution for hybrid real-time strategies. The solution algorithm searches a larger feasible domain of the solution space, leading to a potentially more robust and computationally more efficient solution than its deterministic counterparts. These advantages are highlighted through simulation experiments.

Suggested Citation

  • Peeta, Srinivas & Zhou, Chao, 2006. "Stochastic quasi-gradient algorithm for the off-line stochastic dynamic traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 40(3), pages 179-206, March.
  • Handle: RePEc:eee:transb:v:40:y:2006:i:3:p:179-206
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    2. Yannis Pavlis & Markos Papageorgiou, 1999. "Simple Decentralized Feedback Strategies for Route Guidance in Traffic Networks," Transportation Science, INFORMS, vol. 33(3), pages 264-278, August.
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    Cited by:

    1. Sumalee, A. & Zhong, R.X. & Pan, T.L. & Szeto, W.Y., 2011. "Stochastic cell transmission model (SCTM): A stochastic dynamic traffic model for traffic state surveillance and assignment," Transportation Research Part B: Methodological, Elsevier, vol. 45(3), pages 507-533, March.
    2. Lu, Chung-Cheng & Liu, Jiangtao & Qu, Yunchao & Peeta, Srinivas & Rouphail, Nagui M. & Zhou, Xuesong, 2016. "Eco-system optimal time-dependent flow assignment in a congested network," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 217-239.
    3. Laval, Jorge A., 2009. "Graphical solution and continuum approximation for the single destination dynamic user equilibrium problem," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 108-118, January.

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