Dynamic Congestion Pricing in Disequilibrium
Tóm tắt
A theory of dynamic congestion pricing for the day-to-day time scale is presented which takes the form of a continuous time optimal control problem. The formulation accomodates elastic nonseparable travel demands and nonseparable travel costs. Necessary conditions for optimal congestion prices are analyzed to uncover bang-bang, singular and synthesized optimal control decison rules for setting network tolls in a dynamic environment. These decision rules are shown to be sufficient for optimality under plausible regularity conditions.
Tài liệu tham khảo
Bernstein, D. and T.E. Smith. (1994). “Network Equilibria with Lower Semicontinuous Costs: With an Application to Congestion Pricing.” Transportation Science 28, 221–235.
Bernstein, D. and J. Muller. (1993). “Understanding the Competing Short-Run Objectives of Peak Period Road Pricing.” Transportation Research Record 1395, 122–128.
Braid, R.M. (1989). “Uniform versus Peak-Load Pricing of a Bottleneck with Elastic Demand.” Journal of Urban Economics 26, 320–327.
Bryson, A.E. Jr., and Y.-C. Ho. (1975). Applied Optimal Control. Halsted Press.
Carey, M. (1980). “Stability of Competitive Regional Trade with Monotone Demand/Supply Functions.” J. Reg. Sci. 20, 489–501.
Carey, M. and A. Srinivasen. (1993). “Externalities, Average and Marginal Cost, and Tolls on Congested Networks with Time-Varying Flows.” Operations Research 41, 217–231.
Dafermos, S. (1971). “Optimal Resource Allocation and Toll Patterns in User Optimized Transportation Networks.” Journal of Transport Economics and Policy 5, 1–17.
Dial, R.B. (1997a). “Network Optimized Congestion Pricing, Part I: A Parable, Model, Algorithm and Heuristic.” Operations Research (forthcoming).
Dial, R.B. (1997b). “Network Optimized Congestion Pricing, Part II: Algorithms and Examples.” Operations Research (forthcoming).
Dial, R.B. (1997c). “Minimum-Revenue Congestion Pricing, Part I: A Fast Algorithm for the Single-Origin Case.” Transportation Research (forthcoming).
Fernandez, J.E. and T.L. Friesz. (1983). “Travel Market Equilibrium: The State of the Art.” Transportation Research 17B(2), 155–172.
Friesz, T. (1985). “Transportation Network Equilibrium, Design and Aggregation.” Transportation Research 19A(5/6), 413–427.
Friesz, T., D. Bernstein, T. Smith, R. Tobin, and B.W. Wie. (1993). “A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem.” Operations Research 41(1), 80–91.
Friesz, T., D. Bernstein, N. Mehta, R. Tobin and S. Ganjalizadeh. (1994). “Day-toDay Dynamic Network Disequilibrium and Idealized Driver Information Systems.” Operations Research 42(16), 1120–1136.
Friesz, T., D. Bernstein and R. Stough. (1996). “Dynamic Systems, Variational Inequalities and Control Theoretic Models for Predicting Time-Varying Urban Network Flows.” Transportation Science 30(1), 14–3.
Kydes, N.A. (2002). “A Multigrid Solution to the Continuous Dynamic Disequilibrium Network Design Problem.” Ph.D. Thesis in progress, George Mason University.
Jara-Diaz, S. and T. Friesz. (1982). “Measuring the Benefits of a Transportation Investment.” Transportation Research 16B(1), 57–77.
Seierstad, A. and K. Sydsaeter. (1977). “Sufficient Conditions in Optimal Control Theory.” International Economic Review 18(2), 367–391.
Yang, H. and M.G.H. Bell. (1998). “Models and Algorithms for Road Network Design: A Review and Some New Developments.” Transport Review 18, 257–278.
Huang, H.J. and M.G.H. Bell. (1998). “Continuous Equilibrium Network Design with Elastic Demand: Derivative-Free Solution Methods.” In Transportation Networks: Recent Methodological Advances, Elsevier Science Publishers, pp. 175–193.