Analysis of Dynamic Traffic Equilibrium with Departure Time Choice

We present and analyse a model of the combined choice of departure time and route in a congested road network. Using the property of equilibrium solutions that for each origin-destination pair the total cost associated with travel is identical for all travellers, we establish a general result that relates assignments to various components of cost. The analysis is developed to include time-varying tolls and to establish a formula that will induce any specified inflow profile as an equilibrium. We introduce an iteration operator to calculate equilibrium inflow profiles, and present the results of example calculations for a range of test problems.

[1]  Terry L. Friesz,et al.  A variational control formulation of the simultaneous route and departure-time choice equilibrium problem , 1993 .

[2]  W. Vickrey.  Congestion Theory and Transport Investment , 1969 .

[3]  Malachy Carey.  Nonconvexity of the dynamic traffic assignment problem , 1992 .

[4]  Benjamin Heydecker,et al.  An exact expression of dynamic traffic equilibrium , 1996 .

[5]  Deepak K. Merchant,et al.  A Model and an Algorithm for the Dynamic Traffic Assignment Problems , 1978 .

[6]  Vanolin F. Hurdle.  On a Paper by Andre de Palma, Moshe Ben-Akiva, Claude Lefèvre, and Nicolaos Litinas Entitled “Stochastic Equilibrium Model of Peak Period Traffic Congestion” , 1986 .

[7]  Hani S. Mahmassani,et al.  System Optimal Dynamic Assignment for Electronic Route Guidance in a Congested Traffic Network: Dynamic Flow Modelling and Control , 1995 .

[8]  Patrice Marcotte,et al.  On the Existence of Solutions to the Dynamic User Equilibrium Problem , 2000, Transp. Sci..

[9]  J. Wardrop.  ROAD PAPER. SOME THEORETICAL ASPECTS OF ROAD TRAFFIC RESEARCH. , 1952 .

[10]  M J Lighthill,et al.  On kinematic waves II. A theory of traffic flow on long crowded roads , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[11]  Bin Ran,et al.  MODELING DYNAMIC TRANSPORTATION NETWORKS , 1996 .

[12]  Kenneth A. Small,et al.  THE SCHEDULING OF CONSUMER ACTIVITIES: WORK TRIPS , 1982 .

[13]  J. G. Wardrop,et al.  Some Theoretical Aspects of Road Traffic Research , 1952 .

[14]  Bin Ran,et al.  Solving an Instantaneous Dynamic User-Optimal Route Choice Model , 1995, Transp. Sci..

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

[16]  Benjamin Heydecker,et al.  ANALYSIS OF TRAFFIC MODELS FOR DYNAMIC EQUILIBRIUM TRAFFIC ASSIGNMENT , 1998 .

[17]  Markos Papageorgiou,et al.  Dynamic modeling, assignment, and route guidance in traffic networks , 1990 .

[18]  Robin Lindsey,et al.  DEPARTURE TIME AND ROUTE CHOICE FOR THE MORNING COMMUTE , 1990 .

[19]  Y. W. Xu,et al.  Advances in the Continuous Dynamic Network Loading Problem , 1996, Transp. Sci..

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

[21]  Malachy Carey,et al.  An approach to modelling time-varying flows on congested networks , 2000 .

[22]  Chris Hendrickson,et al.  Schedule Delay and Departure Time Decisions in a Deterministic Model , 1981 .

[23]  D J Holden.  WARDROP'S THIRD PRINCIPLE: URBAN TRAFFIC CONGESTION AND TRAFFIC POLICY , 1989 .

[24]  T. Koopmans,et al.  Studies in the Economics of Transportation. , 1956 .

[25]  David E. Boyce,et al.  ROUTE FLOW ENTROPY MAXIMIZATION IN ORIGIN-BASED TRAFFIC ASSIGNMENT , 1999 .

[26]  G. F. Newell.  A simplified theory of kinematic waves in highway traffic, part I: General theory , 1993 .

[27]  Bin Ran,et al.  A link-based variational inequality model for dynamic departure time/route choice , 1996 .

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

[29]  Benjamin Heydecker,et al.  System Optimal Assignment with Departure Time Choice , 1998 .

[30]  Carlos F. Daganzo,et al.  Properties of link travel time functions under dynamic loads , 1995 .

[31]  C. B. Mcguire,et al.  Studies in the Economics of Transportation , 1958 .

[32]  Vittorio Astarita,et al.  A CONTINUOUS TIME LINK MODEL FOR DYNAMIC NETWORK LOADING BASED ON TRAVEL TIME FUNCTION , 1996 .