Abstract
Traffic assignment models attempt to determine the usage of each route and/or link in a transportation network, given information about the number of trips being taken between various locations, the characteristics of the network, and the characteristics of the vehicles on the network. Though the term “assignment” seems to connote a prescriptive process in which vehicles are assigned to particular routes, there are both descriptive/positive and prescriptive/normative traffic assignment models.
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.
Similar content being viewed by others
References
Beckmann, M., McGuire, C. and Winsten, C. (1956), Studies in the Economics of Transportation, Yale University Press, New Haven, CT.
Ben-Akiva, M., de Palma, A. and Kaysi, I. (1991) ‘Dynamic network models and driver information systems’, Transportation Research, vol. 25A, pp. 251–266.
Bernstein, D., Friesz, T.L., Tobin, R.L., Shenoi, R. and Wie, B.W. (1992), ‘Solving a variational inequality formulation of the simultaneous route and departure-time choice equilibrium problem’, presented at the 39th North American Meetings of the Regional Science Association International.
Bernstein, D., Friesz, T.L., Tobin, R.L. and Wie, B.-W. (1993), ‘Variational control models of dynamic network traffic equilibrium’, Proceedings of the 12th International Symposium on Transportation and Traffic Theory, Elsevier, Amsterdam, pp. 107–126.
Bernstein, D. (1994) ‘Non-existence of nash equilibria to the departure-time choice problem’, presented at the Joint National Meetings of ORSA/TIMS.
Boardman, A.E. and Lave, L.B. (1977), ‘Highway congestion and congestion tolls’, Journal of Urban Economics, vol. 4, pp. 340–359.
Branston, D. (1976), ‘Link capacity functions: A review’, Transportation Research, vol. 10, pp. 223–236.
Carey, M. and Srinivasan, A. (1988), ‘Congested network flows: Time varying demands and start-time policies’, European Journal of Operational Research, vol. 36, pp. 227–240.
Cascetta, E. (1991), ‘A day-to-day and within-day dynamic stochastic assignment model’, Transportation Research, vol. 25A, pp. 277–291.
Chang, G-L. and Mahmassani, H.S. (1988), ‘Travel time prediction and departure time adjustment behavior dynamics in a congested traffic system’, Transportation Research, vol. 22B, pp. 217–232.
Dafermos, S.C. (1980), ‘Traffic equilibria and variational inequalities’, Transportation Science, vol. 14, pp. 42–54.
Dupuis, P. and Nagumey, A. (1993), ‘Dynamical systems and variational inequalities’, Annals of Operations Research, vol. 44, pp. 9–42.
Drissi-Kaitouni, O. (1990), ‘A model for the dynamic traffic assignment problem’, Centre de Recherche sur les Transports, Publication No. 702, Universite de Montreal.
Friesz, T.L., Luque, J., Tobin, R.L. and Wie, B.W. (1989), ‘Dynamic network traffic assignment considered as a continuous time optimal control problem,’ Operations Research, vol. 37, pp. 893–901.
Friesz, T.L., Bernstein, D. and Stough, R. (1992), ‘Variational inequalities, dynamical systems, and control theoretic models for predicting time-varying urban network flows’, presented at the North American Meetings of the Regional Science Association International.
Friesz, T.L., Bernstein, D., Smith, T.E., Tobin, R.L. and Wie, B.-W. (1993), ‘A variational inequality formulation of the dynamic network user equilibrium problem’, Operations Research, vol. 41, 1993, pp. 179–191.
Friesz, T.L., Mehta, N., Tobin, R.L., Bernstein, D. and Ganjalizadeh, S. (1994), ‘Day-today adjustments in the presence of an imperfect driver information system’, Operations Research, forthcoming.
Istratescu, V.I. (1981) Fixed Point Theory, Riedel Publishing, Dordrecht.
Janson, B.N. (1991) ‘Dynamic traffic assignment for urban road networks’, Transportation Research, vol. 25B, pp. 143–161.
Jauffred, F. and Bernstein, D. (1996), ‘An alternative formulation of the simultaneous route and departure-time choice equilibrium problem’, Transportation Research C, vol. 4, pp. 339–357.
Mahmassani, H.S. and Peeta, S. (1992), ‘Dynamic assignment for route guidance decisions’, presented at the 39th North American Meetings of the Regional Science Association International.
Merchant, D.K. and Nemhauser, G.L. (1978a) ‘A Model and an Algorithm for the Dynamic Traffic Assignment Problem’, Transportation Science, vol. 12, pp. 183–199.
Merchant, D.K. and Nemhauser, G.L. (1978b) ‘Optimality Conditions for a Dynamic Traffic Assignment Model’, Transportation Science, vol. 12, pp. 200–207.
Ran, B., Boyce, D.E. and LeBlanc, L.J. (1993), ‘Towards a new class of instantaneous dynamic user-optimal traffic assignment models’, Operations Research, vol. 41, pp. 192–202.
Smith, M.J. (1979) ‘Existence, uniqueness, and stability of traffic equilibria’, Transportation Research, vol. 13B, pp. 295–304.
Smith, M.J. and Ghali, M.O. (1990) ‘The dynamics of traffic assignment and traffic control: A theoretical study’, Transportation Research, vol. 24B, pp. 409–422.
Vickrey, W.S. (1969) ‘Congestion theory and transport investment’, Papers and Proceedings of the American Economic Review, vol. 59, pp. 251–261.
Wardrop, J. (1952), ‘Some theoretical aspects of road traffic research’, Proceedings of Institute of Civil Engineers, vol. 1, part II, pp. 325–378.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin · Heidelberg
About this paper
Cite this paper
Bernstein, D., Friesz, T.L. (1998). Infinite Dimensional Formulations of Some Dynamic Traffic Assignment Models. In: Lundqvist, L., Mattsson, LG., Kim, T.J. (eds) Network Infrastructure and the Urban Environment. Advances in Spatial Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72242-4_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-72242-4_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-72244-8
Online ISBN: 978-3-642-72242-4
eBook Packages: Springer Book Archive