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Optimal routing policy problems in stochastic time-dependent networks

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  • Gao, Song
  • Chabini, Ismail

Abstract

We study optimal routing policy problems in stochastic time-dependent networks, where link travel times are modeled as random variables with time-dependent distributions. These are fundamental network optimization problems for a wide variety of applications, such as transportation and telecommunication systems. The routing problems studied can be viewed as counterparts of shortest path problems in deterministic networks. A routing policy is defined as a decision rule that specifies what node to take next at each decision node based on realized link travel times and the current time. We establish a framework for optimal routing policy problems in stochastic time-dependent networks, which we believe is the first in the literature. We give a comprehensive taxonomy and an in-depth discussion of variants of the problem. We then study in detail one variant that is particularly pertinent in traffic networks, where both link-wise and time-wise stochastic dependencies of link travel times are considered and online information is represented. We give an exact algorithm to this variant, analyze its complexity and point out the importance of finding good approximations to the exact solution. We then overview several approximations, and present a summary of a theoretical and computational analysis of their effectiveness against the exact algorithm.

Suggested Citation

  • Gao, Song & Chabini, Ismail, 2006. "Optimal routing policy problems in stochastic time-dependent networks," Transportation Research Part B: Methodological, Elsevier, vol. 40(2), pages 93-122, February.
    • Handle: RePEc:eee:transb:v:40:y:2006:i:2:p:93-122
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    1. Fu, Liping & Rilett, L. R., 1998. "Expected shortest paths in dynamic and stochastic traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 32(7), pages 499-516, September.
    2. Fu, Liping, 2001. "An adaptive routing algorithm for in-vehicle route guidance systems with real-time information," Transportation Research Part B: Methodological, Elsevier, vol. 35(8), pages 749-765, September.
    3. Elise D. Miller-Hooks & Hani S. Mahmassani, 2000. "Least Expected Time Paths in Stochastic, Time-Varying Transportation Networks," Transportation Science, INFORMS, vol. 34(2), pages 198-215, May.
    4. Randolph W. Hall, 1986. "The Fastest Path through a Network with Random Time-Dependent Travel Times," Transportation Science, INFORMS, vol. 20(3), pages 182-188, August.
    5. Harilaos N. Psaraftis & John N. Tsitsiklis, 1993. "Dynamic Shortest Paths in Acyclic Networks with Markovian Arc Costs," Operations Research, INFORMS, vol. 41(1), pages 91-101, February.
    6. James L. Bander & Chelsea C. White, 2002. "A Heuristic Search Approach for a Nonstationary Stochastic Shortest Path Problem with Terminal Cost," Transportation Science, INFORMS, vol. 36(2), pages 218-230, May.
    7. Yang, Baiyu & Miller-Hooks, Elise, 2004. "Adaptive routing considering delays due to signal operations," Transportation Research Part B: Methodological, Elsevier, vol. 38(5), pages 385-413, June.
    8. Pretolani, Daniele, 2000. "A directed hypergraph model for random time dependent shortest paths," European Journal of Operational Research, Elsevier, vol. 123(2), pages 315-324, June.
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