User-equilibrium properties of fixed points in dynamic traffic assignment 1 1 This research was supp

Abstract This paper considers the problem of dynamic traffic assignment under the principle that individual drivers will choose fastest paths, in the dynamic situation where path durations consist of time-dependent link travel times. Rather than constructing a unified model encompassing traffic dynamics and route choice, we decompose the model into an assignment mapping, which identifies the link travel times resulting from an input routing policy, and a routing mapping, which yields fastest-path routings associated with input link travel times. Since time-dynamic link travel times are influenced by route choice, this dynamic situation therefore encompasses predictive routing strategies. We establish that user-equilibrium routing policies are fixed points of the composition of the routing and assignment functions. After discussing difficulties associated with establishing existence of fixed points under discrete-time modeling and all-or-nothing routing, we present instead new iterative routing mappings for continuous-time multipath routing (the splitting of a single-class flow onto multiple paths), which adjust routing policies more incrementally. We provide sufficient conditions for existence of fixed points in various routing policy domains and offer some suggestions on the computation of these fixed-point policies.

[1]  R. M. Oliver,et al.  Flows in transportation networks , 1972 .

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

[3]  M. J. Smith,et al.  A continuous day-to-day traffic assignment model and the existence of a continuous dynamic user equilibrium , 1995, Ann. Oper. Res..

[4]  Robert L. Smith,et al.  Fastest Paths in Time-dependent Networks for Intelligent Vehicle-Highway Systems Application , 1993, J. Intell. Transp. Syst..

[5]  Anthony Chen,et al.  A DYNAMIC TRAFFIC ASSIGNMENT MODEL WITH TRAFFIC-FLOW RELATIONSHIPS , 1995 .

[6]  S-Y Wong.  TRAF-NETSIM: HOW IT WORKS, WHAT IT DOES , 1990 .

[7]  D.E. Kaufman,et al.  An iterative routing/assignment method for anticipatory real-time route guidance , 1991, Vehicle Navigation and Information Systems Conference, 1991.

[8]  Robert L. Smith,et al.  Link travel time prediction techniques for convergent iterative anticipatory route guidance methods , 1997 .

[9]  Mike Smith,et al.  A model for the dynamic system optimum traffic assignment problem , 1995 .

[10]  Robert L. Smith,et al.  A MIXED INTEGER LINEAR PROGRAMMING MODEL FOR DYNAMIC ROUTE GUIDANCE , 1998 .

[11]  Robert L. Smith,et al.  DYNAMIC SYSTEM-OPTIMAL TRAFFIC ASSIGNMENT USING A STATE SPACE MODEL , 1993 .

[12]  Terry L. Friesz,et al.  A COMPARISON OF SYSTEM OPTIMUM AND USER EQUILIBRIUM DYNAMIC TRAFFIC ASSIGNMENTS WITH SCHEDULE DELAYS , 1995 .

[13]  James R. Munkres,et al.  Topology; a first course , 1974 .

[14]  Bin Ran,et al.  A New Class of Instantaneous Dynamic User-Optimal Traffic Assignment Models , 1993, Oper. Res..

[15]  Bruce N Janson,et al.  Dynamic traffic assignment for urban road networks , 1991 .

[16]  M Van Aerde.  AN INTEGRETATED APPROACH TO MANAGING TRAFFIC CONGESTION IN COMBINED FREEWAY AND TRAFFIC SIGNAL NETWORKS , 1989 .

[17]  J. Schwartz,et al.  Linear Operators. Part I: General Theory. , 1960 .

[18]  Stella Dafermos,et al.  Traffic Equilibrium and Variational Inequalities , 1980 .

[19]  Hai-Jun Huang,et al.  Dynamic user optimal traffic assignment model for many to one travel demand , 1995 .

[20]  Bruce N Janson,et al.  NETWORK DESIGN EFFECTS OF DYNAMIC TRAFFIC ASSIGNMENT , 1995 .

[21]  Terry L. Friesz,et al.  A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem , 1993, Oper. Res..

[22]  Ajay K. Rathi,et al.  Urban Network Traffic Simulation:TRAF-NETSIM Program , 1990 .

[23]  Robert L. Smith,et al.  A mixed integer-linear programming model for dynamic traffic assignment , 1992 .