A dynamic traffic assignment model for solving overlapping path issues and perfectly rational issues under stochastic time-varying conditions

Dongmei Yan; Jianmei Cheng; Jing Gan; Yue Wang; Dongmei Yan; Jianmei Cheng; Jing Gan; Yue Wang

doi:10.3934/math.20251345

AIMS Mathematics

2025, Volume 10, Issue 12: 30661-30682. doi: 10.3934/math.20251345

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A dynamic traffic assignment model for solving overlapping path issues and perfectly rational issues under stochastic time-varying conditions

1.
School of Modern Posts, Nanjing University of Posts and Telecommunications, Nanjing, 210003, China
2.
Department of Traffic Engineering, Sichuan Police College, Intelligent Policing Key Laboratory of Sichuan Province, Luzhou, 646000, China

Received: 10 October 2025 Revised: 12 December 2025 Accepted: 15 December 2025 Published: 26 December 2025
MSC : 00A06, 00A71

To effectively handle the overlapping path issue in the multinomial logit (MNL) model and perfectly rational issue in the expected utility theory (EUT) while capturing the time-varying probabilistic distribution characteristics of origin—destination (OD) demand, this study develops a reliability-based dynamic traffic assignment (R-DTA) model, that is, a cumulative prospect value (CPV)-based generalized nested logit (GNL) stochastic user equilibrium (SUE) model under stochastic time-varying conditions. Specifically, the proposed R-DTA model is established by replacing the utility value with the CPV as the path performance within the GNL model framework. An equivalent variational inequality model is provided for the proposed R-DTA model, which is solved by the method of successive averages (MSA). Moreover, the existence and equivalence of the solution to the equivalent model are also proved. The proposed R-DTA model is tested on two networks to demonstrate its performance. The corresponding results demonstrate that the model can jointly deal with the perfectly rational issues and the overlapping path issues; also, the model can effectively capture the time-varying probabilistic distribution characteristics of OD demand.
- stochastic user equilibrium,
- cumulative prospect theory,
- generalized nested logit,
- method of successive averages,
- stochastic time-varying conditions
Citation: Dongmei Yan, Jianmei Cheng, Jing Gan, Yue Wang. A dynamic traffic assignment model for solving overlapping path issues and perfectly rational issues under stochastic time-varying conditions[J]. AIMS Mathematics, 2025, 10(12): 30661-30682. doi: 10.3934/math.20251345

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Abstract

To effectively handle the overlapping path issue in the multinomial logit (MNL) model and perfectly rational issue in the expected utility theory (EUT) while capturing the time-varying probabilistic distribution characteristics of origin—destination (OD) demand, this study develops a reliability-based dynamic traffic assignment (R-DTA) model, that is, a cumulative prospect value (CPV)-based generalized nested logit (GNL) stochastic user equilibrium (SUE) model under stochastic time-varying conditions. Specifically, the proposed R-DTA model is established by replacing the utility value with the CPV as the path performance within the GNL model framework. An equivalent variational inequality model is provided for the proposed R-DTA model, which is solved by the method of successive averages (MSA). Moreover, the existence and equivalence of the solution to the equivalent model are also proved. The proposed R-DTA model is tested on two networks to demonstrate its performance. The corresponding results demonstrate that the model can jointly deal with the perfectly rational issues and the overlapping path issues; also, the model can effectively capture the time-varying probabilistic distribution characteristics of OD demand.

References

[1]	A. A. Prakash, R. Seshadri, K. K. Srinivasan, A consistent reliability-based user-equilibrium problem with risk-averse users and endogenous travel time correlations: formulation and solution algorithm, Transp. Res. Part B., 114 (2018), 171–198. https://doi.org/10.1016/j.trb.2018.06.003 doi: 10.1016/j.trb.2018.06.003
[2]	Y. M. Nie, Multi-class percentile user equilibrium with flow-dependent stochasticity, Transp. Res. Part B., 45 (2011), 1641–1659. https://doi.org/10.1016/j.trb.2011.06.001 doi: 10.1016/j.trb.2011.06.001
[3]	L. Shen, Q. Yang, X. Xu, T. Wu, S. Zhang, H. Shao, A generalized three-stage optimization model for emergency medical services under uncertainties: Integrating rescue station locations, ambulance deployment, and vehicle dispatch, Transp. Res. Part E, 205 (2026), 104499. https://doi.org/10.1016/j.tre.2025.104499 doi: 10.1016/j.tre.2025.104499
[4]	H. K. Lo, X. W. Luo, B. W. Y. Siu, Degradable transport network: travel time budget of travelers with heterogeneous risk aversion, Transp. Res. Part B., 40 (2006), 792–806. https://doi.org/10.1016/j.trb.2005.10.003 doi: 10.1016/j.trb.2005.10.003
[5]	B. W. Y. Siu, H. K. Lo, Doubly uncertain transportation network: Degradable capacity and stochastic demand, Eur. J. Oper. Res., 191 (2008), 166–181. https://doi.org/10.1016/j.ejor.2007.08.026 doi: 10.1016/j.ejor.2007.08.026
[6]	A. Chen, Z. Zhou, The α-reliable mean-excess traffic equilibrium model with stochastic travel times, Transp. Res. Part B., 44 (2010), 493–513. https://doi.org/10.1016/j.trb.2009.11.003 doi: 10.1016/j.trb.2009.11.003
[7]	L. Han, H. Sun, D. Z. W. Wang, C. J. Zhu, A stochastic process traffic assignment model considering stochastic traffic demand, Transportmetrica B., 6 (2018), 169–189. https://doi.org/10.1080/21680566.2016.1240051 doi: 10.1080/21680566.2016.1240051
[8]	X. Xu, F. Li, T. Wu, X. R. Huang, X. L. Guan, T. Y. Zheng, et al., Location-routing optimization problem of pharmaceutical cold chain logistics with oil-electric mixed fleets under uncertainties, Comput. Ind. Eng., 201 (2025), 110932. https://doi.org/10.1016/j.cie.2025.110932 doi: 10.1016/j.cie.2025.110932
[9]	H. K. Lo, Y. K. Tung, Network with degradable links: capacity analysis and design, Transp. Res. Part B., 37 (2003), 345–363. https://doi.org/10.1016/s0191-2615(02)00017-6 doi: 10.1016/s0191-2615(02)00017-6
[10]	H. Shao, W. H. K. Lam, Q. Meng, M. L. Tam, Demand-driven traffic assignment problem based on travel time reliability, Transp. Res. Rec., 1985 (2006), 220–230. https://doi.org/10.1177/0361198106198500124 doi: 10.1177/0361198106198500124
[11]	R. D. Luce, Individual choice behavior: A theoretical analysis, Dover Publications, 2005. https://psycnet.apa.org/doi/10.1037/14396-000
[12]	D. M. Yan, J. H. Guo, A stochastic user equilibrium model solving overlapping path and perfectly rational issues, J. Cent. South. Univ., 28 (2021), 1584–1600. https://doi.org/10.1007/s11771-021-4718-6 doi: 10.1007/s11771-021-4718-6
[13]	J. Yao, H. Yuan, Y. A. Jiang, S. An, Z. H. Chen, Effect of route overlapping feature on stochastic assignment paradox, Transp. Lett., 15 (2023), 1430–1440. https://doi.org/10.1080/19427867.2022.2159058 doi: 10.1080/19427867.2022.2159058
[14]	X. Xu, A. Chen, C-logit stochastic user equilibrium model with elastic demand, Transport. Plan. Techn., 36 (2013), 463–478. https://doi.org/10.1080/03081060.2013.818275 doi: 10.1080/03081060.2013.818275
[15]	S. J. Lieu, S. Guhathakurta, Exploring pedestrian route choice preferences by demographic groups: Analysis of street attributes in Chicago, Transp. Res. Part A. Policy. Pract., 195 (2025), 104437. https://doi.org/10.1016/j.tra.2025.104437 doi: 10.1016/j.tra.2025.104437
[16]	P. H. L. Bovy, S. Bekhor, C. G. Prato, The factor of revisited path size: alternative derivation, Transp. Res. Rec., 2076 (2008), 132–140. https://doi.org/10.3141/2076-15 doi: 10.3141/2076-15
[17]	H. K. Lo, C. W. Yip, Q. K. Wan, Modeling competitive multi-modal transit services: a nested logit approach, Transp. Res. Part. C. Emerg. Technol., 12 (2004), 251–272. https://doi.org/10.1016/j.trc.2004.07.011 doi: 10.1016/j.trc.2004.07.011
[18]	R. Tanwar, P. K. Agarwal, Multinomial probit-improved nested logit regression model for examining travellers choices of access and egress modes in Bhopal city, Netw. Spat. Econ., 25 (2025), 717–756. https://doi.org/10.1007/s11067-025-09679-x doi: 10.1007/s11067-025-09679-x
[19]	J. Wang, S. Peeta, X. Z. He, J. B. Zhao, Combined multinomial logit modal split and paired combinatorial logit traffic assignment model, Transportmetrica A., 14 (2018), 737–760. https://doi.org/10.1080/23249935.2018.1431701 doi: 10.1080/23249935.2018.1431701
[20]	H. Zhang, P. Rusmevichientong, H. Topaloglu, Assortment optimization under the paired combinatorial logit model, Oper. Res., 68 (2020), 741–761. https://doi.org/10.2139/ssrn.3012401 doi: 10.2139/ssrn.3012401
[21]	S. Bekhor, T. Toledo, L. Reznikova, A path-based algorithm for the cross-nested logit stochastic user equilibrium traffic assignment, Comput. Aided. Civ. Infrastruct. Eng., 24 (2010), 15–25. https://doi.org/10.1111/j.1467-8667.2008.00563.x doi: 10.1111/j.1467-8667.2008.00563.x
[22]	L. Zhang, S. S. Azadeh, H. Jiang, Exact and heuristic algorithms for cardinality-constrained assortment optimization problem under the cross-nested logit model, Eur. J. Oper. Res., 324 (2025), 183–199. https://doi.org/10.1016/j.ejor.2024.12.037 doi: 10.1016/j.ejor.2024.12.037
[23]	Y. T. Wei, R. G. Zhou, J. Yang, Y. T. Chen, W. H. Li, Generalized nested logit-based stochastic user equilibrium considering static wayfinding instructions, Appl. Sci., 14 (2024), 9703. https://doi.org/10.3390/app14219703 doi: 10.3390/app14219703
[24]	D. Kahneman, A. Tversky, Prospect theory: An analysis of decision under risk, Econometrica, 47 (1979), 263–292. https://doi.org/10.2307/1914185 doi: 10.2307/1914185
[25]	A. Tversky, D. Kahneman, Advances in prospect theory: Cumulative representation of uncertainty, J. Risk Uncertainty, 5 (1992), 297–323. https://doi.org/10.1017/cbo9780511803475.004 doi: 10.1017/cbo9780511803475.004
[26]	R. D. Connors, A. Sumalee, A network equilibrium model with travelers' perception of stochastic travel times, Transp. Res. Part B., 43 (2009), 614–624. https://doi.org/10.1016/j.trb.2008.12.002 doi: 10.1016/j.trb.2008.12.002
[27]	H. L. Xu, Y. Y. Lou, Y. F. Yin, J. Zhou, A prospect-based user equilibrium model with endogenous reference points and its application in congestion pricing, Transp. Res. Part B., 45 (2011), 311–328. https://doi.org/10.1016/j.trb.2010.09.003 doi: 10.1016/j.trb.2010.09.003
[28]	W. Wang, H. J. Sun, Cumulative prospect theory-based user equilibrium model with stochastic perception errors, J. Cent. South Univ., 23 (2016), 2465–2474. https://doi.org/10.1007/s11771-016-3305-8 doi: 10.1007/s11771-016-3305-8
[29]	J. Yang, G. Jiang, Development of an enhanced route choice model based on cumulative prospect theory, Transp. Res. Part C. Emerg. Technol., 47 (2014), 168–178. https://doi.org/10.1016/j.trc.2014.06.009 doi: 10.1016/j.trc.2014.06.009
[30]	Z. Li, J. J. Zeng, Intra- and inter-individual risk attitude heterogeneity and the impact on road travel: Evidence from a dynamic procedural model, Appl. Econom., 56 (2024), 4177–4193. https://doi.org/10.1080/00036846.2023.2210821 doi: 10.1080/00036846.2023.2210821
[31]	S. Nakayama, D. Watling, Consistent formulation of network equilibrium with stochastic flows, Transp. Res. Part B., 66 (2014), 50–69. https://doi.org/10.1016/j.trb.2014.03.007 doi: 10.1016/j.trb.2014.03.007
[32]	L. E. Balan, R. Paleti, Misclassification in workers' telecommuting frequency choices using a generalized extreme value model, Transp. Res. Rec., 2679 (2025), 726–733. https://doi.org/10.1177/03611981241308867 doi: 10.1177/03611981241308867
[33]	Y. Sheffi, Urban transportation networks, New Jersey: Prentice-Hall, 1985.
[34]	W. B. Powell, Y. Sheffi, The convergence of equilibrium algorithms with predetermined step sizes, Transp. Sci., 16 (1982), 45–55. https://doi.org/10.1287/trsc.16.1.45 doi: 10.1287/trsc.16.1.45
[35]	D. Prelec, The probability weighting function, Econometrica, 66 (1998), 497–527. https://doi.org/10.2307/2998573 doi: 10.2307/2998573
[36]	X. F. Li, M. X. Lang, Multi-class and multi-criteria stochastic user equilibrium model based on generalized nested logit model, (in Chinese), J. Transp. Syst. Eng. Inf. Technol., 14 (2014), 139–145. https://doi.org/10.16097/j.cnki.1009-6744.2014.04.024 doi: 10.16097/j.cnki.1009-6744.2014.04.024
[37]	N. Jiang, C. Xie, Computing and analyzing mixed equilibrium network flows with gasoline and electric vehicles, Comput. Aided. Civ. Inf. Eng., 29 (2014), 626–641. https://doi.org/10.1111/mice.12082 doi: 10.1111/mice.12082

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