Dynamic congestion pricing models for general traffic networks

Agneiv, 1977, The theory of congestion tolls, Journal of Regional Science, 17, 381, 10.1111/j.1467-9787.1977.tb00509.x Bergendorff, P., Hearn, D. W. and Ramana, M. V. (1997) Congestion toll pricing of traffic networks. In Network Optimization, Lecture Notes in Economics and Mathematical Systems. Springer–Verlag, Berlin. Bryson, A. E. and Ho, Y.-C. (1975) Applied Optimal Control: Optimization, Estimation, and Control. John Wiley and Sons, New York. Budelis, J. J. and Bryson, A. E. (1970) Some optimal control results for differential-difference systems. IEEE Transactions on Automatic Control, 237–241. Carey, 1987, Optimal time-varying flows on congested networks, Operations Research, 35, 58, 10.1287/opre.35.1.58 Carey, 1993, Externalities, average and marginal costs, and tolls on congested networks with time-varying flows, Operations Research, 41, 217, 10.1287/opre.41.1.217 Dafermos, 1973, Toll patterns for multiclass-user transportation networks, Transportation Science, 7, 211, 10.1287/trsc.7.3.211 Dafermos, 1971, Optimal resource allocation and toll patterns in user-optimized transport networks, Journal of Transport Economics and Policy, 5, 184 Daganzo, 1995, Properties of link travel time functions under dynamic loads, Transportation Research-B, 29, 95, 10.1016/0191-2615(94)00026-V Friesz, 1989, Dynamic network traffic assignment considered as a continuous time optimal control problem, Operations Research, 37, 893, 10.1287/opre.37.6.893 Friesz, 1993, A variational inequality formulation of the dynamic network user equilibrium problem, Operations Research, 41, 179, 10.1287/opre.41.1.179 Henderson, 1974, Road congestion: a reconsideration of pricing theory, Journal of Urban Economics, 1, 346, 10.1016/0094-1190(74)90012-6 Huang, H. J. and Yang, H. (1996) Optimal variable road-use pricing on a congested network of parallel routes with elastic demand. Proceedings of the 13th International Symposium on the Theory of Traffic Flow and Transportation, pp. 479–500. Kamien, M. I. and Schwartz, N. L. (1991) Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management. Elsevier Science, New York. Merchant, D. K. and Nemhauser, G. L. (1978a) A model and an algorithm for the dynamic traffic assignment problems. Transportation Science 12, 62–77. Merchant, D. K. and Nemhauser, G. L. (1978b) Optimality conditions for a dynamic traffic assignment model. Transportation Science 12, 200–207. Robertson, D. I. (1969) TRANSYT: A Traffic Network Study Tool. TRRL Report No. LR 253, Transport Road Research Laboratory, Ministry of Transport, Crowthorne, U.K. Seierstad, A. and Sydsaeter, K. (1987) Optimal Control Theory with Economic Applications. North Holland, New York. Smith, 1979, The marginal cost taxation of a transportation network, Transportation Research-B, 13, 237, 10.1016/0191-2615(79)90015-8 Walters, 1961, The theory and measurement of private and social cost of highway congestion, Econometrica, 29, 676, 10.2307/1911814 Wardrop, J. G. (1952) Some theoretical aspects of road traffic research. Proceedings, Institution of Civil Engineers II, 235–378. Wie, B. W. (1988) Dynamic models of network traffic assignment: a control theoretic approach. Ph.D. dissertation, University of Pennsylvania. Wie, 1990, Dynamic user optimal traffic assignment on congested multidestination networks, Transportation Research-B, 24, 431, 10.1016/0191-2615(90)90038-Z Wie, 1994, The augmented Lagrangian method for solving dynamic network traffic assignment models in discrete time, Transportation Science, 28, 204, 10.1287/trsc.28.3.204 Wie, 1995, A comparison of system optimum and user equilibrium traffic assignments with schedule delays, Transportation Research-C, 3, 389, 10.1016/0968-090X(95)00018-E Wie, 1995, A discrete time, nested cost operator approach to the dynamic network user equilibrium problem, Transportation Science, 29, 79, 10.1287/trsc.29.1.79 Wie, B. W. (1997) A convex control model of dynamic system optimal traffic assignment. Preprints of the 8th IFAC/IFIP/IFORS Symposium in Chania, Greece, Vol. II, pp. 540–545.