Sensitivity Analysis of Stochastic User Equilibrium Flows in a Bi-Modal Network with Application to Optimal Pricing

Sensitivity analysis methods for transport systems having an automobile road network and a physically separate transit network are studied. For the case that both the automobile and transit networks are congested in the sense that link cost functions increase with the flow, a general computational method is presented for sensitivity analysis. For another case where the automobile network is congested but the transit network simply consists of independent lines connecting Origin-Destination pairs and may have economies of scale with the increase of the passengers, conditions under which sensitivity analysis can be properly conducted are investigated. The sensitivity analysis algorithm is applied to the optimal pricing problem in a combined network with transit lines exhibiting economies of scale as well as congestion diseconomies.

[1]  Alan Wilson.  Catastrophe Theory and Urban Modelling: An Application to Modal Choice , 1976 .

[2]  Qiang Meng,et al.  Simultaneous Estimation of the Origin-Destination Matrices and Travel-Cost Coefficient for Congested Networks in a Stochastic User Equilibrium , 2001, Transp. Sci..

[3]  Y Iida,et al.  Transportation Network Analysis , 1997 .

[4]  William H. K. Lam,et al.  A capacity restraint transit assignment with elastic line frequency , 2002 .

[5]  Hai Yang,et al.  Sensitivity analysis for the elastic-demand network equilibrium problem with applications , 1997 .

[6]  Jiang Qian Ying,et al.  Sensitivity Analysis for Stochastic User Equilibrium Network Flows - A Dual Approach , 2001, Transp. Sci..

[7]  David G. Luenberger,et al.  Linear and Nonlinear Programming: Second Edition , 2003 .

[8]  Gary A. Davis,et al.  Exact local solution of the continuous network design problem via stochastic user equilibrium assignment , 1994 .

[9]  D. Watling.  STABILITY OF THE STOCHASTIC EQUILIBRIUM ASSIGNMENT PROBLEM: A DYNAMICAL SYSTEMS APPROACH , 1999 .

[10]  Hai Yang,et al.  System Optimum, Stochastic User Equilibrium, and Optimal Link Tolls , 1999, Transp. Sci..

[11]  Stephen D. Clark,et al.  Sensitivity analysis of the probit-based stochastic user equilibrium assignment model , 2002 .

[12]  M. Kraus.  Discomfort externalities and marginal cost transit fares , 1991 .

[13]  Robert B. Dial,et al.  Minimal-revenue congestion pricing part I: A fast algorithm for the single-origin case , 1999 .

[14]  Jiang Qian Ying.  Sensitivity Analysis Based Method for Optimal Road Network Pricing , 2005, Ann. Oper. Res..

[15]  David G. Luenberger,et al.  Linear and nonlinear programming , 1984 .

[16]  T. Abrahamsson,et al.  Formulation and Estimation of Combined Network Equilibrium Models with Applications to Stockholm , 1999, Transp. Sci..

[17]  H. Williams.  On the Formation of Travel Demand Models and Economic Evaluation Measures of User Benefit , 1977 .

[18]  Yosef Sheffi,et al.  Urban Transportation Networks: Equilibrium Analysis With Mathematical Programming Methods , 1985 .

[19]  Toshihiko Miyagi,et al.  A Ramsey Price Equilibrium Model for Urban Transit System: A Bilevel Programming Approach with Transportation Network Equilibrium Constraints. Volume 2: Modelling Transport Systems , 1996 .

[20]  Robert B. Dial,et al.  A PROBABILISTIC MULTIPATH TRAFFIC ASSIGNMENT MODEL WHICH OBVIATES PATH ENUMERATION. IN: THE AUTOMOBILE , 1971 .

[21]  Bethany L. Nicholson,et al.  Mathematical Programs with Equilibrium Constraints , 2021, Pyomo — Optimization Modeling in Python.

[22]  Giuseppe Bellei,et al.  Network pricing optimization in multi-user and multimodal context with elastic demand , 2002 .

[23]  Hai Yang,et al.  A stochastic user equilibrium assignment model for congested transit networks , 1999 .

[24]  Huang Hai-Jun,et al.  A BI-LEVEL FORMULATION AND QUASI-NEWTON ALGORITHM FOR STOCHASTIC EQUILIBRIUM NETWORK DESIGN PROBLEM WITH ELASTIC DEMAND , 2001 .