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Deriving Link Travel-Time Distributions via Stochastic Speed Processes

Author

Listed:
  • Jeffrey P. Kharoufeh

    (Department of Operational Sciences, Air Force Institute of Technology, AFIT/ENS, 2950 Hobson Way, Wright-Patterson AFB, Ohio 45433-7765)

  • Natarajan Gautam

    (Harold and Inge Marcus Department of Industrial and Manufacturing Engineering, The Pennsylvania State University, 310 Leonhard Building, University Park, Pennsylvania 16802)

Abstract

We derive an analytical expression for the cumulative distribution function of travel time for a vehicle traversing a freeway link of arbitrary length. The vehicle's speed is assumed to be modulated by a random environment that can be modeled as a stochastic process. We first present a partial differential equation (PDE) describing the travel time distribution and obtain a solution in terms of Laplace transforms. Next, we present a numerical inversion algorithm to invert the transforms. The technique is demonstrated on two example problems. Numerical results indicate great promise for this approach to the link travel-time problem.

Suggested Citation

  • Jeffrey P. Kharoufeh & Natarajan Gautam, 2004. "Deriving Link Travel-Time Distributions via Stochastic Speed Processes," Transportation Science, INFORMS, vol. 38(1), pages 97-106, February.
    • Handle: RePEc:inm:ortrsc:v:38:y:2004:i:1:p:97-106
    DOI: 10.1287/trsc.1030.0048
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    References listed on IDEAS

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    1. 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.
    2. Rajat Jain & J. Macgregor Smith, 1997. "Modeling Vehicular Traffic Flow using M/G/C/C State Dependent Queueing Models," Transportation Science, INFORMS, vol. 31(4), pages 324-336, November.
    3. H. Frank, 1969. "Shortest Paths in Probabilistic Graphs," Operations Research, INFORMS, vol. 17(4), pages 583-599, August.
    4. Coifman, Benjamin, 2002. "Estimating travel times and vehicle trajectories on freeways using dual loop detectors," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(4), pages 351-364, May.
    5. Joseph Abate & Gagan L. Choudhury & Ward Whitt, 1996. "On the Laguerre Method for Numerically Inverting Laplace Transforms," INFORMS Journal on Computing, INFORMS, vol. 8(4), pages 413-427, November.
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    Citations

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    Cited by:

    1. Verbeeck, C. & Vansteenwegen, P. & Aghezzaf, E.-H., 2016. "Solving the stochastic time-dependent orienteering problem with time windows," European Journal of Operational Research, Elsevier, vol. 255(3), pages 699-718.
    2. LECLUYSE, C. & VAN WOENSEL, Tom & PEREMANS, Herbert, 2007. "Vehicle routing with stochastic time-dependent travel times," Working Papers 2007018, University of Antwerp, Faculty of Business and Economics.
    3. Yeon, Jiyoun & Elefteriadou, Lily & Lawphongpanich, Siriphong, 2008. "Travel time estimation on a freeway using Discrete Time Markov Chains," Transportation Research Part B: Methodological, Elsevier, vol. 42(4), pages 325-338, May.
    4. Andrew M. Ross, 2009. "Distribution sensitivity in a highway flow model," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(6), pages 769-786, November.
    5. Zhaoqi Zang & Xiangdong Xu & Kai Qu & Ruiya Chen & Anthony Chen, 2022. "Travel time reliability in transportation networks: A review of methodological developments," Papers 2206.12696, arXiv.org, revised Jul 2022.
    6. Hu Shao & William Lam & Mei Tam, 2006. "A Reliability-Based Stochastic Traffic Assignment Model for Network with Multiple User Classes under Uncertainty in Demand," Networks and Spatial Economics, Springer, vol. 6(3), pages 173-204, September.
    7. Vodopivec, Neža & Miller-Hooks, Elise, 2017. "An optimal stopping approach to managing travel-time uncertainty for time-sensitive customer pickup," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 22-37.
    8. Saif Eddin Jabari & Nikolaos M. Freris & Deepthi Mary Dilip, 2020. "Sparse Travel Time Estimation from Streaming Data," Transportation Science, INFORMS, vol. 54(1), pages 1-20, January.
    9. Levering, Nikki & Boon, Marko & Mandjes, Michel & Núñez-Queija, Rudesindo, 2022. "A framework for efficient dynamic routing under stochastically varying conditions," Transportation Research Part B: Methodological, Elsevier, vol. 160(C), pages 97-124.

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