Abstract  
In this paper, we propose a new model for the multi-class multi-modal network equilibrium problem, which is a route utility based model, and transfer flows for combined modes are considered specially. The model is formulated as a general fixed point problem. The choice behaviors are assumed regular, which include the common features of deterministic and of continuous with continuous first derivatives additive probabilistic choice models. Users of different classes permit different choice behaviors (including routes, modes, and interchanges), as well as different sets of available routes, modes, and interchanges. Different choice models are explicitly considered; in addition, travel demand of the network can be dealt without using its inverse-unlike the mathematical programming, variational inequality, or complementarity formulations. Existence and uniqueness of the model are analyzed, which extend those conclusions in existed literature.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bajwa, S., Bekhor, S., Kuwahara, M. and Cheng E. (2008). Discrete choice modeling of combined mode and departure time. Transportmetrica, 4(2), 155-177.
Bekhor, S., Toledo, T. and Prashker, J.N. (2008). Effects of choice set size and route choice models on route-based traffic assignment. Transportmetrica, 4(2), 117-133.
Bar-Gera, H. and Boyce, D. (2004). A combined distribution, hierarchical mode choice, and assignment network model with multiple user and mode classes. Urban and Regional Transportation Modeling: Essays in Honor of David Boyce, 43-57.
Border, K.C. (1989). Fixed Point Theorems with Applications to Economics and Game Theory. Cambridge University Press.
Bottom, J., Ben-Akiva, M., Bierlaire, M., Chabini, I., Koutsopoulos, H. and Yang, Q. (1999). Investigation of route guidance generation issues by simulation with DynaMIT. Proceedings of International Symposium on Transportation and Traffic Theory,577-600.
Boyce, D. and Bar-Gera, H. (2001). Network equilibrium models of travel choices with multiple Classes. Regional Science Perspectives in Economic Analysis, 85–98.
Boyce, D. and Bar-Gera, H. (2003). Validation of urban travel forecasting models combining origin-destination, mode and route choices. Journal of Regional Science, 43(6), 517–540.
Boyce, D. and Bar-Gera, H. (2004). Multiclass combined models for urban travel forecasting. Networks and Spatial Economics, 4(1), 115-124.
Boyce, D. and Xiong, C. (2007). Forecasting travel for very large cities: challenges and opportunities for China. Transportmetrica, 3(1), 1-19.
Bliemer, M.C.J. and Bovy, P.H.L. (2003). Quasi-variational inequality formulation of the multiclass dynamic traffic assignment problem. Transportation Research Part B, 34 (5), 501-519.
China Academy of Urban Planning and Design (CAUPD). (2002). Final Report of Travel Surveys in Beijing 2000.
Cascetta, E. (2001). Transportation System Engineering: Theory and Methods. Kluwer Academic.
Cascetta, E. and Postorino, M.N. (2001). Fixed point approaches to the estimation of O/D matrices using traffic counts on congested networks. Transportation Science, 35(2), 134-147.
Cantarella, G.E. (1997). A general fixed-point approach to multimode multi-user equilibrium assignment with elastic demand. Transportation Science, 31(2), 107–128.
Daganzo, C.F. (1983). Stochastic network equilibrium with multiple vehicles types and asymmetric, indefinite link cost Jacobians. Transportation Science, 17(4), 282-300.
De Cea, J. and Fernandez, J.E. (1993). Transit assignment for congested public transport systems: an equilibrium model. Transportation Science, 27(2), 133-147.
De Cea, J., Fernandez, J.E., Soto, A. and Dekock, V. (2005). Solving network equilibrium on multimodal urban transportation networks with multiple user classes. Transport Reviews, 25(3), 293-317.
Fernandez, E., Cea, J.D., Florian, M. and Cabrera, E. (1994). Network equilibrium models with combined modes. Transportation Science, 28(3), 182–192.
Ferrari, P. (1999). A model of urban transport management. Transportation Research Part B, 33(2), 43–61.
Florian, M. (1977). A traffic equilibrium model of travel by car and public transit modes. Transportation Science, 11(2), 166–179.
Florian, M., Nguyen, S. and Ferland, S. (1977). On the combined distribution-assignment of traffic. Transportation Science, 9(1), 43–53.
Florian, M., and Los, H. (1978). Determining intermediate origin–destination matrices for the analysis of composite mode trips. Transportation Research Part B, 13(1), 91–103.
Florian, M., Wu, J. H. and He, S.G. (2002). A multi-class multi-mode variable demand network equilibrium model with hierarchical Logit structures. Transportation and Network Analysis: Current Trends. Kluwer Academic Publishers, London.
Garcia, R. and Marin, A. (2001). Urban multimodal interchange design methodology. Mathematical methods on optimization in transportation Systems, 49-79.
Garcia, R. and Marin, A. (2005). Network equilibrium with combined modes: models and solution algorithms. Transportation Research Part B, 39(2), 223–254.
Hoogendoorn, S.P. and Bovy, P.H.L. (2004). Pedestrian route-choice and activity scheduling theory and models. Transportation Research Part B, 38 (3), 169-190.
Hoogendoorn, S., Bovy, P.H.L. and Nes, R.V. (2007). Application of constrained enumeration approach to multi-modal choice set generation. The 86 th Annual Meeting of Transportation Research Board, Washington.
Hoogendoorn, S., Nes, R.V. and Bovy, P.H.L. (2005). Path size modeling in multi-modal route choice analysis. Transportation Research Record, 1921, 27-34.
Hoogendoorn, S. and Bovy, P.H.L. (2007). Modeling overlap in multi-modal route choice by inclusion of trip part specific path size factors. The 86 th Annual Meeting of Transportation Research Board, Washington.
Huang, H.J. and Lam, W.H.K. (2005). A stochastic model for combined activity/destination/route choice problems. Annals of Operations Research, 135(2), 111-125.
Lam, W.H.K. and Huang, H.J. (2002). A combined activity/travel choice model for congested road networks with queues. Transportation, 29(1), 5-29.
Lam,W.H.K. and Huang, H.J. (1992a). A combined trip distribution and assignment model for multiple user classes. Transportation Research Part B, 26(4), 275–287.
Lam, W.H.K. and Huang, H.J. (1992b). Calibration of the combined trip distribution and assignment model for multiple user classes. Transportation Research Part B, 26(4), 289–305.
Lam, W.H.K. and Huang, H.J. (1994). Comparison of results of two models of transportation demand in Hong Kong: CDAM and a version of MicroTRIPS. Journal of Advanced Transportation, 28(2), 107–126.
Liu, G. (2007). A behavioral model of work-trip mode choice in Shanghai. China Economic Review, 18(4), 456-486.
Patriksson, M. (1994). The Traffic Assignment Problem: Models and Methods. VSP, Utrecht.
Sakano, R. and Benjamin, J.M. (2008). A structural equations analysis of revealed and stated travel mode and activity choices. Transportmetrica, 4(2), 97-115.
Sheffi, Y. (1985). Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods. Prentice Hall, New Jersey.
Toint, P. and Wynter, L. (1995). Asymmetric multiclass traffic assignment: a coherent formulation. Proceedings of International Symposium on Transportation and Traffic Theory. Amsterdam: Elsevier Science.
Wong, S.C. (1998). Multicommodity traffic assignment by continuum approximation of network flow with variable demand. Transportation Research B, 32 (8), 567–581.
Wong, K.I., Wong, S.C., Wu, J.H., Yang, H. and Lam, W.H.K. (2004). A combined distribution, hierarchical mode choice, and assignment network model with multiple user and mode classes. Urban and Regional Transportation Modeling, 25-42.
Wu, Z.X. and Lam, W.H.K. (2003a). A combined modal split and stochastic assignment model for congested networks with motorized and non-motorized transport modes. Transportation Research Record, 1831, 57-64.
Wu, Z.X. and Lam, W.H.K. (2003b). Network equilibrium for congested multi-mode networks with elastic demand. Journal of Advanced Transportation, 37, 295-318.
Acknowledgments
The first author is indebted to Professor David Boyce for his comments and support. We would like to express our gratitude to the anonymous referees whose comments have contributed to improve both the clarity and contents of this paper. The study is supported by the National Basic Research Program of China (Project No. 2006CB705503), the National Natural Science Foundation of China (Grant No. 70771005, 70631001), and the Ministry of Education Foundation of China (20070004045).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag US
About this chapter
Cite this chapter
Xu, M., Gao, Z. (2009). Multi-class Multi-modal Network Equilibrium with Regular Choice Behaviors: A General Fixed Point Approach. In: Lam, W., Wong, S., Lo, H. (eds) Transportation and Traffic Theory 2009: Golden Jubilee. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-0820-9_15
Download citation
DOI: https://doi.org/10.1007/978-1-4419-0820-9_15
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-0819-3
Online ISBN: 978-1-4419-0820-9
eBook Packages: Business and EconomicsBusiness and Management (R0)