Passenger Assignment Model Based on Common Route in Congested Transit Networks
Publication: Journal of Transportation Engineering
Volume 138, Issue 12
Abstract
In this paper, the common line problem and passengers’ choice behaviors in transit networks are revisited and discussed. The concept of the common line problem is extended to represent a common route problem in transit networks. The transit routes are classified into various levels of attractive route sets according to route fixed costs and route frequencies. The transit passenger assignment problem on congested transit networks is defined to assign passenger flows on attractive route sets and is formulated as a variational inequality (VI) problem. In the proposed model, the effective frequency approach is applied to reflect the effects of passenger congestion on the waiting time at the stations. Compared with traditional models, the proposed passenger flow assignment model does not require a modification to the transit network nor a constant recomputation of the changing attractive line set. Finally, a simple example is used to illustrate the difference between common line and common route methods, and the passengers’ travel behaviors under various transit conditions are demonstrated on the Sioux Falls transit network.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors would like to thank the anonymous referees for their helpful comments on revising this paper. The work in this paper was supported by the National Basic Research Program of China (2012CB725401), the National Natural Science Foundation of China (70801004, 71171013, 71131001), and the Fundamental Research Funds for the Central Universities (2011JBM059).
References
Bekhor, S., Ben-Akiva, M. E., and Ramming, M. S. (2006). “Evaluation of choice set generation algorithms for route choice models.” Ann. Oper. Res., 144(1), 235–247.
Bekhor, S., and Toledo, B. (2005). “Investigating path-based solution algorithms to the stochastic user equilibrium problem.” Transportation Research Part B, 39(3), 279–295.
Bouzaïene-Ayari, B., Gendreau, M., and Nguyen, S. (2001). “Modeling bus stops in transit networks: A survey and new formulations.” Transp. Sci., 35(3), 304–321.
Cepeda, M., Cominetti, R., and Florian, M. (2006). “A frequency-based assignment model for congested transit networks with strict capacity constraints: Characterization and computation of equilibria.” Transp. Res. B, 40(6), 437–459.
Chriqui, C., and Robillard, P. (1975). “Common bus lines.” Transp. Sci., 9(2), 115–121.
Cominetti, R., and Correa, J. (2001). “Common lines and passenger assignment in congested transit networks.” Transp. Sci., 35(3), 250–267.
De Cea, J., and Fernández, E. (1993). “Transit assignment for congested public transport system: An equilibrium model.” Transp. Sci., 27(2), 133–147.
Dial, R. B. (1967). “Transit pathfinder algorithms.” Highway Res. Record, 205, 67–85.
Dial, R. B. (1971). “A probabilistic multipath traffic assignment model which obviates path enumeration.” Transp. Res., 5(2), 83–111.
Fearnside, K., and Draper, D. P. (1971). “Public transport assignment—a new approach.” Traffic Eng. Control, 13(7), 298–299.
Florian, M. (1977). “A traffic equilibrium model of travel by car and public transit modes.” Transp. Sci., 11(2), 166–179.
Florian, M., and Spiess, H. (1983). “On binary mode choice/assignment models.” Transp. Sci., 17(1), 32–47.
Gao, Z. Y., Sun, H. J., and Shan, L. L. (2003). “A continuous equilibrium network design model and algorithm for transit systems.” Transp. Res. B, 38(3), 235–250.
Guan, J. F., Yang, H., and Wirasinghe, S. C. (2006). “Simultaneous optimization of transit line configuration and passenger line assignment.” Transp. Res. B, 40(10), 885–902.
Han, S. (2007). “A route-based solution algorithm for dynamic user equilibrium assignments.” Transp. Res. B, 41(10), 1094–1113.
Kurauchi, F., Bell, M. G. H., and Schmöcker, J. D. (2003). “Capacity constrained transit assignment with common lines.” J. Math. Model. Algorithms, 2(4), 309–327.
Lampkin, W., and Saalmans, P. D. (1967). “The design of routes, service frequencies and schedules for a municipal bus undertaking: A case study.” J. Oper. Res. Q., 18(4), 375–397.
LeBlanc, L. J. (1988). “Transit system network design.” Transp. Res. B, 22(5), 383–390.
Le Clercq, F. (1972). “A public transport assignment model.” Traffic Eng. Control, 14(1), 91–96.
Li, Z. C., Lam, W. H. K., and Wong, S. C. (2009). “The optimal transit fare structure under different market regimes with uncertainty in the network.” Networks Spatial Econ., 9(2), 191–216.
Nguyen, S., and Pallotino, S. (1988). “Equilibrium traffic assignment in large scale transit networks.” Eur. J. Oper. Res., 37(2), 176–186.
Nguyen, S., Pallottino, S., and Malucelli, F. (2001). “A modeling framework for passenger assignment on a transport network with timetables.” Transp. Sci., 35(3), 238–249.
Nuzzolo, A., and Wilson, N. H. M., eds. (2004). Schedule-based dynamic transit modeling: Theory and applications. Operations Research/Computer Science Interfaces Series, Band 28, Springer-Verlag, Berlin.
Rapp, M. H., Mattenberger, P., Piguet, S., and Robert-Grandpierre, A. (1976). “Interactive graphic system for transit route optimization.” Transp. Res. Rec., 559, 73–88.
Ren, H. L. (2007). “Origin-destination demands estimation in congested dynamic transit networks.” 14th Proc., 2007 Int. Conf. on Management Science & Engineering, IEEE, 3, 2247–2252.
Ren, H. L., and Gao, Z. Y. (2006). “Bilevel model and solution algorithm for dynamic transit schedule planning problem.” 13th Proc., 2006 Int. Conf. on Management Science & Engineering, IEEE, 1–3, 2115–2119.
Ren, H. L., Gao, Z. Y., Lam, W. H. K., and Long, J. C. (2009). “Assessing the benefits of integrated en-route transit information systems and time-varying transit pricing systems in a congested transit network.” Transp. Plann.Technol., 32(3), 215–237.
Ren, H. L., and Lam, W. H. K. (2007). “Modeling transit passenger travel behaviors in congested network with en-route transit information systems.” J. East. Asia Soc. Transp. Stud., 7, 670–685.
Spiess, H., and Florian, M. (1989). “Optimal strategies: A new assignment model for transit networks.” Transp. Res. B, 23(2), 83–102.
Tong, C. O., and Wong, S. C. (1998). “A stochastic transit assignment model using a dynamic schedule-based network.” Transp. Res. B, 33(2), 107–121.
Wong, S. C., and Tong, C. O. (1998). “Estimation of time-dependent origin-destination matrices for transit networks.” Transp. Res. B, 32(1), 35–48.
Wu, J., Florian, M., and Marcotte, P. (1994). “Transit equilibrium assignment: A model and solution algorithms.” Transp. Sci., 28(3), 193–203.
Information & Authors
Information
Published In
Journal of Transportation Engineering
Volume 138 • Issue 12 • December 2012
Pages: 1484 - 1494
Copyright
© 2012 American Society of Civil Engineers.
History
Received: Aug 17, 2009
Accepted: Jun 4, 2012
Published online: Aug 20, 2012
Published in print: Dec 1, 2012
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.