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Finding the reliable shortest path with correlated link travel times in signalized traffic networks under uncertainty

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  • Shen, Liang
  • Shao, Hu
  • Wu, Ting
  • Fainman, Emily Zhu
  • Lam, William H.K.

Abstract

This article proposes an innovative path finding algorithm to achieve on-time arrival reliability on road networks under uncertainty with stochastic delays at signalized intersections. Typically, we extend conventional path-finding algorithms to signalized traffic networks of 1) random and correlated running travel time along links (RTTL), 2) delays at intersections and traffic signals (DITS) and their correlations, as well as 3) correlations between RTTL and DITS. We first discuss the theoretical foundations concerning the existence of the optimal solutions and analyze the efficient convergence speed of our proposed algorithm. Lastly, we conduct numerical studies to demonstrate efficiency and effectiveness of the proposed algorithm.

Suggested Citation

  • Shen, Liang & Shao, Hu & Wu, Ting & Fainman, Emily Zhu & Lam, William H.K., 2020. "Finding the reliable shortest path with correlated link travel times in signalized traffic networks under uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:transe:v:144:y:2020:i:c:s1366554520308048
    DOI: 10.1016/j.tre.2020.102159
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    as
    1. Arslan, Okan & Yıldız, Barış & Karaşan, Oya Ekin, 2015. "Minimum cost path problem for Plug-in Hybrid Electric Vehicles," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 80(C), pages 123-141.
    2. Srinivasan, Karthik K. & Prakash, A.A. & Seshadri, Ravi, 2014. "Finding most reliable paths on networks with correlated and shifted log–normal travel times," Transportation Research Part B: Methodological, Elsevier, vol. 66(C), pages 110-128.
    3. A. Arun Prakash & Karthik K. Srinivasan, 2018. "Pruning Algorithms to Determine Reliable Paths on Networks with Random and Correlated Link Travel Times," Transportation Science, INFORMS, vol. 52(1), pages 80-101, January.
    4. Luigi Di Puglia Pugliese & Francesca Guerriero, 2016. "On the shortest path problem with negative cost cycles," Computational Optimization and Applications, Springer, vol. 63(2), pages 559-583, March.
    5. Güner, Ali R. & Murat, Alper & Chinnam, Ratna Babu, 2017. "Dynamic routing for milk-run tours with time windows in stochastic time-dependent networks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 97(C), pages 251-267.
    6. Hall, Randolph W., 1983. "Travel outcome and performance: The effect of uncertainty on accessibility," Transportation Research Part B: Methodological, Elsevier, vol. 17(4), pages 275-290, August.
    7. Anthony Chen & Zhong Zhou, 2009. "A Stochastic α-reliable Mean-excess Traffic Equilibrium Model with Probabilistic Travel Times and Perception Errors," Springer Books, in: William H. K. Lam & S. C. Wong & Hong K. Lo (ed.), Transportation and Traffic Theory 2009: Golden Jubilee, chapter 0, pages 117-145, Springer.
    8. D.R. Han & H.K. Lo, 2002. "New Alternating Direction Method for a Class of Nonlinear Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 112(3), pages 549-560, March.
    9. Jenelius, Erik & Koutsopoulos, Haris N., 2013. "Travel time estimation for urban road networks using low frequency probe vehicle data," Transportation Research Part B: Methodological, Elsevier, vol. 53(C), pages 64-81.
    10. Bi Chen & William Lam & Agachai Sumalee & Qingquan Li & Hu Shao & Zhixiang Fang, 2013. "Finding Reliable Shortest Paths in Road Networks Under Uncertainty," Networks and Spatial Economics, Springer, vol. 13(2), pages 123-148, June.
    11. 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.
    12. Wu, Xing, 2015. "Study on mean-standard deviation shortest path problem in stochastic and time-dependent networks: A stochastic dominance based approach," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 275-290.
    13. Raj A. Sivakumar & Rajan Batta, 1994. "The Variance-Constrained Shortest Path Problem," Transportation Science, INFORMS, vol. 28(4), pages 309-316, November.
    14. Ravi Seshadri & Karthik K. Srinivasan, 2012. "An Algorithm for the Minimum Robust Cost Path on Networks with Random and Correlated Link Travel Times," Transportation Research, Economics and Policy, in: David M. Levinson & Henry X. Liu & Michael Bell (ed.), Network Reliability in Practice, edition 1, chapter 0, pages 171-208, Springer.
    15. Liu, Zhiyuan & Chen, Xinyuan & Meng, Qiang & Kim, Inhi, 2018. "Remote park-and-ride network equilibrium model and its applications," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 37-62.
    16. Xing, Tao & Zhou, Xuesong, 2011. "Finding the most reliable path with and without link travel time correlation: A Lagrangian substitution based approach," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1660-1679.
    17. 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.
    18. Liang Shen & Hu Shao & Long Zhang & Jian Zhao, 2017. "The Global Optimal Algorithm of Reliable Path Finding Problem Based on Backtracking Method," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-10, October.
    19. Chen, Yen-Liang & Yang, Hsu-Hao, 2000. "Shortest paths in traffic-light networks," Transportation Research Part B: Methodological, Elsevier, vol. 34(4), pages 241-253, May.
    20. Chen, Huey-Kuo & Feng, Ginny, 2000. "Heuristics for the stochastic/dynamic user-optimal route choice problem," European Journal of Operational Research, Elsevier, vol. 126(1), pages 13-30, October.
    21. Clark, Stephen & Watling, David, 2005. "Modelling network travel time reliability under stochastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 39(2), pages 119-140, February.
    22. Qureshi, A.G. & Taniguchi, E. & Yamada, T., 2009. "An exact solution approach for vehicle routing and scheduling problems with soft time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 45(6), pages 960-977, November.
    23. Watling, David, 2006. "User equilibrium traffic network assignment with stochastic travel times and late arrival penalty," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1539-1556, December.
    24. Lo, Hong K. & Luo, X.W. & Siu, Barbara W.Y., 2006. "Degradable transport network: Travel time budget of travelers with heterogeneous risk aversion," Transportation Research Part B: Methodological, Elsevier, vol. 40(9), pages 792-806, November.
    25. Yang, Lixing & Zhou, Xuesong, 2014. "Constraint reformulation and a Lagrangian relaxation-based solution algorithm for a least expected time path problem," Transportation Research Part B: Methodological, Elsevier, vol. 59(C), pages 22-44.
    26. Ravindra K. Ahuja & James B. Orlin & Stefano Pallottino & Maria Grazia Scutellà, 2002. "Minimum Time and Minimum Cost-Path Problems in Street Networks with Periodic Traffic Lights," Transportation Science, INFORMS, vol. 36(3), pages 326-336, August.
    27. Wang, Li & Yang, Lixing & Gao, Ziyou, 2016. "The constrained shortest path problem with stochastic correlated link travel times," European Journal of Operational Research, Elsevier, vol. 255(1), pages 43-57.
    28. Fangfang Zheng & Henk van Zuylen & Xiaobo Liu, 2017. "A Methodological Framework of Travel Time Distribution Estimation for Urban Signalized Arterial Roads," Transportation Science, INFORMS, vol. 51(3), pages 893-917, August.
    29. Chen, Yen-Liang & Yang, Hsu-Hao, 2003. "Minimization of travel time and weighted number of stops in a traffic-light network," European Journal of Operational Research, Elsevier, vol. 144(3), pages 565-580, February.
    30. Meng, Qiang & Liu, Zhiyuan & Wang, Shuaian, 2012. "Optimal distance tolls under congestion pricing and continuously distributed value of time," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(5), pages 937-957.
    31. Shi, Ning & Zhou, Shaorui & Wang, Fan & Tao, Yi & Liu, Liming, 2017. "The multi-criteria constrained shortest path problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 101(C), pages 13-29.
    32. H. Frank, 1969. "Shortest Paths in Probabilistic Graphs," Operations Research, INFORMS, vol. 17(4), pages 583-599, August.
    33. Chen, Anthony & Lo, Hong K. & Yang, Hai, 2001. "A self-adaptive projection and contraction algorithm for the traffic assignment problem with path-specific costs," European Journal of Operational Research, Elsevier, vol. 135(1), pages 27-41, November.
    34. Zhang, Yuli & Max Shen, Zuo-Jun & Song, Shiji, 2017. "Lagrangian relaxation for the reliable shortest path problem with correlated link travel times," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 501-521.
    35. Yang, Lixing & Zhou, Xuesong, 2017. "Optimizing on-time arrival probability and percentile travel time for elementary path finding in time-dependent transportation networks: Linear mixed integer programming reformulations," Transportation Research Part B: Methodological, Elsevier, vol. 96(C), pages 68-91.
    36. Chen, Bi Yu & Li, Qingquan & Lam, William H.K., 2016. "Finding the k reliable shortest paths under travel time uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 189-203.
    37. Wang, David Z.W. & Lo, Hong K., 2010. "Global optimum of the linearized network design problem with equilibrium flows," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 482-492, May.
    38. 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.
    39. Chen, Anthony & Zhou, Zhong, 2010. "The [alpha]-reliable mean-excess traffic equilibrium model with stochastic travel times," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 493-513, May.
    40. Wang, Shuaian & Meng, Qiang & Sun, Zhuo, 2013. "Container routing in liner shipping," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 49(1), pages 1-7.
    41. Nie, Yu (Marco) & Wu, Xing, 2009. "Shortest path problem considering on-time arrival probability," Transportation Research Part B: Methodological, Elsevier, vol. 43(6), pages 597-613, July.
    42. Ziliaskopoulos, Athanasios K. & Mahmassani, Hani S., 1996. "A note on least time path computation considering delays and prohibitions for intersection movements," Transportation Research Part B: Methodological, Elsevier, vol. 30(5), pages 359-367, October.
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