A bi-level programming approach for trip matrix estimation and traffic control problems with stochastic user equilibrium link flows

This paper deals with two mathematically similar problems in transport network analysis: trip matrix estimation and traffic signal optimisation on congested road networks. These two problems are formulated as bi-level programming problems with stochastic user equilibrium assignment as the second-level programming problem. We differentiate two types of solutions in the combined matrix estimation and stochastic user equilibrium assignment problem (or the combined signal optimisation and stochastic user equilibrium assignment problem): one is the solution to the bi-level programming problem and the other the mutually consistent solution where the two sub-problems in the combined problem are solved simultaneously. In this paper, we shall concentrate on the bi-level programming approach, although we shall also consider mutually consistent solutions so as to contrast the two types of solutions. The purpose of the paper is to present a solution algorithm for the two bi-level programming problems and to test the algorithm on several networks.

[1]  C. S. Fisk,et al.  ON COMBINING MAXIMUM ENTROPY TRIP MATRIX ESTIMATION WITH USER OPTIMAL ASSIGNMENT , 1988 .

[2]  Jonathan F. BARD,et al.  Convex two-level optimization , 1988, Math. Program..

[3]  L G Willumsen,et al.  SATURN - A SIMULATION-ASSIGNMENT MODEL FOR THE EVALUATION OF TRAFFIC MANAGEMENT SCHEMES , 1980 .

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

[5]  Terry L. Friesz,et al.  A Simulated Annealing Approach to the Network Design Problem with Variational Inequality Constraints , 1992, Transp. Sci..

[6]  M. J. Smith,et al.  Traffic Equilibrium with Responsive Traffic Control , 1993, Transp. Sci..

[7]  Warrren B Powell,et al.  The Convergence of Equilibrium Algorithms with Predetermined Step Sizes , 1982 .

[8]  Hai Yang,et al.  Estimation of origin-destination matrices from link traffic counts on congested networks , 1992 .

[9]  J. D. Griffiths Mathematics in Transport Planning and Control , 1998 .

[10]  E. Cascetta Estimation of trip matrices from traffic counts and survey data: A generalized least squares estimator , 1984 .

[11]  Terry L. Friesz,et al.  Equilibrium Decomposed Optimization: A Heuristic for the Continuous Equilibrium Network Design Problem , 1987, Transp. Sci..

[12]  Warren B. Powell,et al.  Optimal Signal Settings Over Transportation Networks , 1983 .

[13]  F. Leurent Curbing the computational difficulty of the logit equilibrium assignment model , 1997 .

[14]  C. Fisk GAME THEORY AND TRANSPORTATION SYSTEMS MODELLING , 1984 .

[15]  T Van Vuren,et al.  Route Choice and Signal Control: The Potential for Integrated Route Guidance , 1992 .

[16]  Hai Yang Heuristic algorithms for the bilevel origin-destination matrix estimation problem , 1995 .

[17]  E. Cascetta,et al.  A MODIFIED LOGIT ROUTE CHOICE MODEL OVERCOMING PATH OVERLAPPING PROBLEMS. SPECIFICATION AND SOME CALIBRATION RESULTS FOR INTERURBAN NETWORKS , 1996 .

[18]  P. Hughes,et al.  A PROBIT-BASED STOCHASTIC USER EQUILIBRIUM ASSIGNMENT MODEL , 1997 .

[19]  T L Friesz,et al.  BOUNDING THE SOLUTION OF THE CONTINUOUS EQUILIBRIUM NETWORK DESIGN PROBLEM , 1984 .

[20]  Xiaoyan Zhang,et al.  AN ALGORITHM FOR THE SOLUTION OF BI-LEVEL PROGRAMMING PROBLEMS IN TRANSPORT NETWORK ANALYSIS , 1998 .

[21]  Sang Nguyen,et al.  A unified framework for estimating or updating origin/destination matrices from traffic counts , 1988 .

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

[23]  Mike Maher,et al.  Algorithms for logit-based stochastic user equilibrium assignment , 1998 .

[24]  M Maher,et al.  ALGORITHMS FOR THE SOLUTION OF THE CONGESTED TRIP MATRIX ESTIMATION PROBLEM , 1999 .

[25]  R. Kellogg,et al.  Pathways to solutions, fixed points, and equilibria , 1983 .

[26]  D Van Vliet,et al.  METHODS FOR THE SOLUTION OF THE COMBINED TRIP MATRIX ESTIMATION AND STOCHASTIC USER EQUILIBRIUM ASSIGNMENT PROBLEM , 1999 .

[27]  Hai Yang,et al.  Traffic assignment and signal control in saturated road networks , 1995 .

[28]  Terry L. Friesz,et al.  Sensitivity Analysis for Equilibrium Network Flow , 1988, Transp. Sci..