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On the system optimum of traffic assignment in M/G/c/c state-dependent queueing networks

Author

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  • Cruz, F.R.B.
  • van Woensel, T.
  • MacGregor Smith, J.
  • Lieckens, K.

Abstract

The classical Wardrop System Optimum assignment model assumes that the users will cooperate with each other in order to minimize the overall travel costs. The importance of the system optimum model lies on its well-recognized ability of producing solutions that correspond to the most efficient way of using the scarce resources represented by the street and road capacities. In this paper, we present a version of the system optimum model in which the travel costs incurred on each path come from M/G/c/c state-dependent queueing networks, a stochastic travel time estimation formula which takes into account congestion effects. A Differential Evolution algorithm is proposed to solve the model. We motivate this version of the problem in several ways and computational results show that the proposed approach is efficient.

Suggested Citation

  • Cruz, F.R.B. & van Woensel, T. & MacGregor Smith, J. & Lieckens, K., 2010. "On the system optimum of traffic assignment in M/G/c/c state-dependent queueing networks," European Journal of Operational Research, Elsevier, vol. 201(1), pages 183-193, February.
    • Handle: RePEc:eee:ejores:v:201:y:2010:i:1:p:183-193
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    Cited by:

    1. F. R. B. Cruz & A. R. Duarte & G. L. Souza, 2018. "Multi-objective performance improvements of general finite single-server queueing networks," Journal of Heuristics, Springer, vol. 24(5), pages 757-781, October.
    2. Smith, J. MacGregor & Cruz, F.R.B. & van Woensel, T., 2010. "Topological network design of general, finite, multi-server queueing networks," European Journal of Operational Research, Elsevier, vol. 201(2), pages 427-441, March.
    3. Hu, Lu & Zhao, Bin & Zhu, Juanxiu & Jiang, Yangsheng, 2019. "Two time-varying and state-dependent fluid queuing models for traffic circulation systems," European Journal of Operational Research, Elsevier, vol. 275(3), pages 997-1019.
    4. Celikoglu, Hilmi Berk, 2013. "Reconstructing freeway travel times with a simplified network flow model alternating the adopted fundamental diagram," European Journal of Operational Research, Elsevier, vol. 228(2), pages 457-466.
    5. Caixia Li & Sreenatha Gopalarao Anavatti & Tapabrata Ray, 2017. "A Path-Based Solution Algorithm for Dynamic Traffic Assignment," Networks and Spatial Economics, Springer, vol. 17(3), pages 841-860, September.
    6. Piotrowski, Adam P. & Napiorkowski, Jaroslaw J. & Kiczko, Adam, 2012. "Differential Evolution algorithm with Separated Groups for multi-dimensional optimization problems," European Journal of Operational Research, Elsevier, vol. 216(1), pages 33-46.
    7. MacGregor Smith, J. & Cruz, F.R.B., 2014. "M/G/c/c state dependent travel time models and properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 560-579.
    8. Cruz, F.R.B. & Van Woensel, T. & Smith, J. MacGregor, 2010. "Buffer and throughput trade-offs in M/G/1/K queueing networks: A bi-criteria approach," International Journal of Production Economics, Elsevier, vol. 125(2), pages 224-234, June.

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