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A Cumulative Perceived Value-Based Dynamic User Equilibrium Model Considering the Travelers’ Risk Evaluation on Arrival Time

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  • Li-Jun Tian
  • Hai-Jun Huang
  • Zi-You Gao

Abstract

This paper presents a cumulative perceived value-based dynamic user equilibrium model by applying the prospect theory to formulate the travelers’ risk evaluation on arrival time. The network uncertainty caused by link exit capacity degradation is incorporated into the analysis. The model which considers departure time and route choices simultaneously is expressed by a variational inequality in a discrete time space. Numerical results show that the travelers’ risk preference indeed has big influence on flow distribution. Our study constitutes a deepening of cognition in developing more realistic dynamic traffic assignment technologies. Copyright Springer Science+Business Media, LLC 2012

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  • Li-Jun Tian & Hai-Jun Huang & Zi-You Gao, 2012. "A Cumulative Perceived Value-Based Dynamic User Equilibrium Model Considering the Travelers’ Risk Evaluation on Arrival Time," Networks and Spatial Economics, Springer, vol. 12(4), pages 589-608, December.
  • Handle: RePEc:kap:netspa:v:12:y:2012:i:4:p:589-608
    DOI: 10.1007/s11067-011-9168-5
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    1. Yang, Hai & Hai-Jun, Huang, 1997. "Analysis of the time-varying pricing of a bottleneck with elastic demand using optimal control theory," Transportation Research Part B: Methodological, Elsevier, vol. 31(6), pages 425-440, November.
    2. Erel Avineri, 2006. "The Effect of Reference Point on Stochastic Network Equilibrium," Transportation Science, INFORMS, vol. 40(4), pages 409-420, November.
    3. 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.
    4. 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.
    5. Lam, William H.K. & Shao, Hu & Sumalee, Agachai, 2008. "Modeling impacts of adverse weather conditions on a road network with uncertainties in demand and supply," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 890-910, December.
    6. Malachy Carey, 1987. "Optimal Time-Varying Flows on Congested Networks," Operations Research, INFORMS, vol. 35(1), pages 58-69, February.
    7. Wie, Byung-Wook & Tobin, Roger L., 1998. "Dynamic congestion pricing models for general traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 32(5), pages 313-327, June.
    8. Chow, Andy H.F., 2009. "Properties of system optimal traffic assignment with departure time choice and its solution method," Transportation Research Part B: Methodological, Elsevier, vol. 43(3), pages 325-344, March.
    9. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    10. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    11. Agachai Sumalee & Richard D. Connors & Paramet Luathep, 2009. "Network Equilibrium under Cumulative Prospect Theory and Endogenous Stochastic Demand and Supply," Springer Books, in: William H. K. Lam & S. C. Wong & Hong K. Lo (ed.), Transportation and Traffic Theory 2009: Golden Jubilee, chapter 0, pages 19-38, Springer.
    12. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    13. Noland, Robert B. & Small, Kenneth A. & Koskenoja, Pia Maria & Chu, Xuehao, 1998. "Simulating travel reliability," Regional Science and Urban Economics, Elsevier, vol. 28(5), pages 535-564, September.
    14. Terry L. Friesz & Javier Luque & Roger L. Tobin & Byung-Wook Wie, 1989. "Dynamic Network Traffic Assignment Considered as a Continuous Time Optimal Control Problem," Operations Research, INFORMS, vol. 37(6), pages 893-901, December.
    15. Wie, Byung-Wook & Tobin, Roger L. & Carey, Malachy, 2002. "The existence, uniqueness and computation of an arc-based dynamic network user equilibrium formulation," Transportation Research Part B: Methodological, Elsevier, vol. 36(10), pages 897-918, December.
    16. Xiaoning Zhang & H. Zhang, 2010. "Simultaneous Departure Time/Route Choices in Queuing Networks and a Novel Paradox," Networks and Spatial Economics, Springer, vol. 10(1), pages 93-112, March.
    17. Siu, Barbara W.Y. & Lo, Hong K., 2008. "Doubly uncertain transportation network: Degradable capacity and stochastic demand," European Journal of Operational Research, Elsevier, vol. 191(1), pages 166-181, November.
    18. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    19. Chen, Huey-Kuo & Hsueh, Che-Fu, 1998. "A model and an algorithm for the dynamic user-optimal route choice problem," Transportation Research Part B: Methodological, Elsevier, vol. 32(3), pages 219-234, April.
    20. Gitakrishnan Ramadurai & Satish Ukkusuri, 2010. "Dynamic User Equilibrium Model for Combined Activity-Travel Choices Using Activity-Travel Supernetwork Representation," Networks and Spatial Economics, Springer, vol. 10(2), pages 273-292, June.
    21. Bell, Michael G. H. & Cassir, Chris, 2002. "Risk-averse user equilibrium traffic assignment: an application of game theory," Transportation Research Part B: Methodological, Elsevier, vol. 36(8), pages 671-681, September.
    22. Wie, Byung-Wook & Friesz, Terry L. & Tobin, Roger L., 1990. "Dynamic user optimal traffic assignment on congested multidestination networks," Transportation Research Part B: Methodological, Elsevier, vol. 24(6), pages 431-442, December.
    23. Byung Chung & Tao Yao & Chi Xie & Andreas Thorsen, 2011. "Robust Optimization Model for a Dynamic Network Design Problem Under Demand Uncertainty," Networks and Spatial Economics, Springer, vol. 11(2), pages 371-389, June.
    24. Lim, Yongtaek & Heydecker, Benjamin, 2005. "Dynamic departure time and stochastic user equilibrium assignment," Transportation Research Part B: Methodological, Elsevier, vol. 39(2), pages 97-118, February.
    25. Robert B. Noland & John W. Polak, 2002. "Travel time variability: A review of theoretical and empirical issues," Transport Reviews, Taylor & Francis Journals, vol. 22(1), pages 39-54, January.
    26. Henn, Vincent & Ottomanelli, Michele, 2006. "Handling uncertainty in route choice models: From probabilistic to possibilistic approaches," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1526-1538, December.
    27. David Watling, 2002. "A Second Order Stochastic Network Equilibrium Model, I: Theoretical Foundation," Transportation Science, INFORMS, vol. 36(2), pages 149-166, May.
    28. Terry L. Friesz & David Bernstein & Tony E. Smith & Roger L. Tobin & B. W. Wie, 1993. "A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem," Operations Research, INFORMS, vol. 41(1), pages 179-191, February.
    29. W. Szeto & L. O'Brien & M. O'Mahony, 2006. "Risk-Averse Traffic Assignment with Elastic Demands: NCP Formulation and Solution Method for Assessing Performance Reliability," Networks and Spatial Economics, Springer, vol. 6(3), pages 313-332, September.
    30. Jou, Rong-Chang & Kitamura, Ryuichi & Weng, Mei-Chuan & Chen, Chih-Cheng, 2008. "Dynamic commuter departure time choice under uncertainty," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(5), pages 774-783, June.
    31. B. G. Heydecker & J. D. Addison, 2005. "Analysis of Dynamic Traffic Equilibrium with Departure Time Choice," Transportation Science, INFORMS, vol. 39(1), pages 39-57, February.
    32. Byung-Wook Wie & Roger L. Tobin & Terry L. Friesz & David Bernstein, 1995. "A Discrete Time, Nested Cost Operator Approach to the Dynamic Network User Equilibrium Problem," Transportation Science, INFORMS, vol. 29(1), pages 79-92, February.
    33. Chen, H. K. & Chang, M. S. & Wang, C. Y., 2001. "Dynamic capacitated user-optimal departure time/route choice problem with time-window," European Journal of Operational Research, Elsevier, vol. 132(3), pages 603-618, August.
    34. Lo, Hong K. & Tung, Yeou-Koung, 2003. "Network with degradable links: capacity analysis and design," Transportation Research Part B: Methodological, Elsevier, vol. 37(4), pages 345-363, May.
    35. Barbara W.Y. Siu & Hong K. Lo, 2009. "Equilibrium Trip Scheduling in Congested Traffic under Uncertainty," Springer Books, in: William H. K. Lam & S. C. Wong & Hong K. Lo (ed.), Transportation and Traffic Theory 2009: Golden Jubilee, chapter 0, pages 147-167, Springer.
    36. 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.
    37. Bates, John & Polak, John & Jones, Peter & Cook, Andrew, 0. "The valuation of reliability for personal travel," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 37(2-3), pages 191-229, April.
    38. Ban, Xuegang (Jeff) & Liu, Henry X. & Ferris, Michael C. & Ran, Bin, 2008. "A link-node complementarity model and solution algorithm for dynamic user equilibria with exact flow propagations," Transportation Research Part B: Methodological, Elsevier, vol. 42(9), pages 823-842, November.
    39. Yu Nie & H. Zhang, 2010. "Solving the Dynamic User Optimal Assignment Problem Considering Queue Spillback," Networks and Spatial Economics, Springer, vol. 10(1), pages 49-71, March.
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    4. Geng, Kexin & Wang, Yacan & Cherchi, Elisabetta & Guarda, Pablo, 2023. "Commuter departure time choice behavior under congestion charge: Analysis based on cumulative prospect theory," Transportation Research Part A: Policy and Practice, Elsevier, vol. 168(C).
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