Turning Delay Stochastic User Equilibrium Model based on the Weibull Distribution

  • Jing Chen Hangzhou Dianzi University
  • Wenqiang Xu China Jiliang University
  • Weimin Peng Hangzhou Dianzi University
  • Baixi Xing Hangzhou Dianzi University
Keywords: distribution model, traffic forecast, node-link algorithm, road traffic planning,


With the continuous expansion of urban scales and the constant growth of traffic demands, it has become important to accurately predict the distribution of traffic flow so as to relieve the traffic jams and lower the energy consumption. This research mainly focuses on the distribution problem of traffic flow in the urban traffic network. A minimization program has been provided as an alternative formulation for the turning delay stochastic user equilibrium problem. The paper derives the Weibull distribution-based node-link random loading mechanism of turning delay for direct calculation of link and turning flows that are consistent with the
path flow, thus avoiding the enumeration of turning paths. Numerical examples are provided to illustrate the turning delay stochastic user equilibrium (SUE) model and the nodelink- based algorithm. The experiment demonstrates that the present method can reflect the relative performance of link and turning costs well, while presenting its advantages in the simulation of large-scale turning delay flow  ssignment.

Author Biographies

Jing Chen, Hangzhou Dianzi University
School of computer science and technology
Wenqiang Xu, China Jiliang University
College of Economics and Management
Weimin Peng, Hangzhou Dianzi University
School of computer science and technology
Baixi Xing, Hangzhou Dianzi University
School of computer science and technology


Long J, Szeto WY, Huang HJ. A bi-objective turning restriction design problem in urban road networks. Eur J Oper Res. 2014;237(2): 426-439.

Nielsen OA, Frederiksen RD, Simonsen N. Using expert system rules to establish data for intersections and turns in road networks. Int T Oper Res. 1998;5(6): 569-581.

Chen BY, Lam WHK, Sumalee A, et al. Reliable shortest path problems in stochastic time-dependent networks. J Intell Transport S. 2014;18(2): 177-189.

Daganzo CF, Sheffi Y. On stochastic models of traffic assignment. Transport Sci. 1977;11(3): 253-274.

McFadden D, Train K. Mixed MNL models for discrete response. J Applied Econometrics. 2000;15(5): 447-470.

Daganzo CF, Bouthelier F, Sheffi Y. Multinomial probit and qualitative choice: a computationally efficient algorithm. Transport Sci. 1977;11(4): 338-358.

Bhat CR, Dubey SK. A new estimation approach to integrate latent psychological constructs in choice modeling. Transport Res B-Meth. 2014;67: 68-85.

Bolduc D, Ben-Akiva M, Walker J, et al. Hybrid choice models with logit kernel: applicability to large scale models. In: Lee-Gosselin MEH, Doherty ST (eds.) Integrated Land-Use and Transportation Models. Elsevier; 2005. p. 275-302.

Wen CH, Koppelman FS. The generalized nested logit model. Transport Res B-Meth. 2001;35(7): 627-641.

Wen CH, Chen TN, Fu C. A factor-analytic generalized nested logit model for determining market position of airlines. Transport Res A-Pol. Apr 2014;62: 71-80.

Lai XJ, Li J, Li Z. A subpath-based logit model to capture the correlation of routes. Promet – Traffic & Transportation. 2016;28(3): 225-234.

Yang L, Zheng G, Zhu X. Cross-nested logit model for the joint choice of residential location, travel mode, and departure time. J Tongji University. 2013;38: 157-166.

Pravinvongvuth S, Chen A. Adaptation of the paired combinatorial logit model to the route choice problem. Transportmetrica. 2005 Jan;1(3): 223-240.

Chen A, Ryu S, Xu X, et al. Computation and application of the paired combinatorial logit stochastic user equilibrium problem. Comput Oper Res. 2014;43: 68-77.

Qin H, Gao J, Zhang G, et al. Nested logit model formation to analyze airport parking behavior based on stated preference survey studies. J Air Transport Manag. 2017;58:164-175.

Hou Y. Traffic congestion, polycentricity, and intraurban firm location choices: a nested logit model for the Los Angeles metropolitan area. J Regional Sci. 2016;56(4):683-716.

Ermagun A, Levinson D. Public transit, active travel, and the journey to school: a cross-nested logit analysis. Transportmetrica A. 2017;13(1): 24-37.

Lai X, Bierlaire M. Specification of the cross-nested logit model with sampling of alternatives for route choice models. Transport Res B-Meth. 2015;80: 220-234.

Haghani M, Shahhoseini Z, Sarvi M. Quantifying benefits of traveler information systems to performance of transport networks prior to implementation: a double-class structured-parameter stochastic trip assignment approach. Transp Lett. 2016;8(1): 1-12.

Cascetta E, Nuzzolo A, Russo F, et al. A modified logit route choice model overcoming path overlapping problems: specification and some calibration results for interurban networks. Proceedings of the 13th International Symposium on Transportation and Traffic Theory, Mar 1996, Lyon, France. Pergamon; 1996. p. 697-711.

Zhou Z, Chen A, Bekhor S. C-logit stochastic user equilibrium model: formulations and solution algorithm. Transportmetrica. 2012;8(1): 17-41.

Yao J, Chen A, Ryu S, et al. A general unconstrained optimization formulation for the combined distribution and assignment problem. Transport Res B-Meth. 2014;59: 137-160.

Hoogendoorn-Lanser S, Van-Ness R, Bovy PHL. Path size and overlap in multi-modal transport networks. Transportation and Traffic Theory. Flow, Dynamics and Human Interaction. 16th International Symposium on Transportation and Traffic Theory, Aug 2005, Maryland, United States. Elsevier; 2005. p. 63-84.

Prato CG. Expanding the applicability of random regret minimization for route choice analysis. Transportation. 2014;41(2): 351-375.

Zhong Z, Anthony C, Shlomo B. C-logit stochastic user equilibrium model: formulations and solution algorithm. Transportmetrica. 2012;8(1): 17-41.

Xiangdong X, Anthony C. C-logit stochastic user equilibrium model with elastic demand. Transport Plan Techn. 2013;36(5): 463-478.

Tan R, Adnan M, Lee DH, et al. New path size formulation in path size logit for route choice modeling in public transport networks. Transport Res Rec. 2015;2538: 11-16.

Castillo E, Menéndez JM, Jiménez P, et al. Closed form expressions for choice probabilities in the Weibull case. Transport Res B-Meth. 2008;42(4): 373-380.

Kitthamkesorn S, Chen A. Unconstrained weibit stochastic user equilibrium model with extensions. Transport Res B-Meth. 2014;59(1): 1-21.

Kitthamkesorn S, Chen A, Xu X. Elastic demand with weibit stochastic user equilibrium flows and application in a motorised and non-motorised network. Transportmetrica A. 2015;11(2): 158-185.

Yao J, Chen A. An analysis of logit and weibit route choices in stochastic assignment paradox. Transport Res B-Meth. 2014;69: 31-49.

Dial RB. A probabilistic multipath traffic assignment model which obviates path enumeration. Transport Res. 1971;5(2): 83-111.

Hua J, Ren G, Cheng Y, et al. Large-scale evacuation network optimization: a bi-level control method with uncertain arterial demand. Transport Plan Techn. 2015;38(7): 777-794.

How to Cite
Chen J, Xu W, Peng W, Xing B. Turning Delay Stochastic User Equilibrium Model based on the Weibull Distribution. Promet - Traffic&Transportation. 2018;30(2):131-40. DOI: 10.7307/ptt.v30i2.2321