Linear Programming Models for the User and System Optimal Dynamic Network Design Problem: Formulations, Comparisons and Extensions

In this paper we formulate a network design model in which the traffic flows satisfy dynamic user equilibrium conditions for a single destination. The model presented here incorporates the Cell Transmission Model (CTM); a traffic flow model capable of capturing shockwaves and link spillovers. Comparisons are made between the properties of the Dynamic User equilibrium Network Design Problem (DUE NDP) and an existing Dynamic System Optimal (DSO) NDP formulation. Both network design models have different objective functions with similar constraint sets which are linear and convex. Numerical demonstrations are made on multiple networks to demonstrate the efficacy of the model and demonstrate important differences between the DUE and DSO NDP approaches. In addition, the flexibility of the approach is demonstrated by extending the formulation to account for demand uncertainty. This is formulated as a stochastic programming problem and initial test results are demonstrated on test networks. It is observed that not accounting for demand uncertainty explicitly, provides sub-optimal solution to the DUE NDP problem.

[1]  Carlos F. Daganzo,et al.  THE CELL TRANSMISSION MODEL, PART II: NETWORK TRAFFIC , 1995 .

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

[3]  S. Travis Waller,et al.  Comparison of System- and User-Optimal Stochastic Dynamic Network Design Models Using Monte Carlo Bounding Techniques , 2005 .

[4]  Julia L. Higle,et al.  An Introductory Tutorial on Stochastic Linear Programming Models , 1999, Interfaces.

[5]  David E. Boyce,et al.  A bilevel programming algorithm for exact solution of the network design problem with user-optimal flows , 1986 .

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

[7]  Satish V. Ukkusuri,et al.  Selectorecombinative Genetic Algorithm to Relax Computational Complexity of Discrete Network Design Problem , 2006 .

[8]  C. Daganzo.  THE CELL TRANSMISSION MODEL.. , 1994 .

[9]  S. Travis Waller,et al.  Combinatorial Approach for Multiple-Destination User Optimal Dynamic Traffic Assignment , 2004 .

[10]  John R. Birge,et al.  Introduction to Stochastic Programming , 1997 .

[11]  Larry J. LeBlanc,et al.  CONTINUOUS EQUILIBRIUM NETWORK DESIGN MODELS , 1979 .

[12]  P. Marcotte.  Network Optimization with Continuous Control Parameters , 1983 .

[13]  Gwo-Hshiung Tzeng,et al.  Application of multiple criteria decision making for network improvement , 1997 .

[14]  Hani S. Mahmassani,et al.  DYNAMIC TRAFFIC ASSIGNMENT WITH MULTIPLE USER CLASSES FOR REAL-TIME ATIS/ATMS APPLICATIONS , 1993 .

[15]  John R. Birge,et al.  Optimal Flows in Stochastic Dynamic Networks with Congestion , 1993, Oper. Res..

[16]  S. Travis Waller,et al.  A Combinatorial user optimal dynamic traffic assignment algorithm , 2006, Ann. Oper. Res..

[17]  Clermont Dupuis,et al.  An Efficient Method for Computing Traffic Equilibria in Networks with Asymmetric Transportation Costs , 1984, Transp. Sci..

[18]  Thomas L. Magnanti,et al.  Network Design and Transportation Planning: Models and Algorithms , 1984, Transp. Sci..

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

[20]  Athanasios K. Ziliaskopoulos,et al.  Stochastic Dynamic Network Design Problem , 2001 .

[21]  Athanasios K. Ziliaskopoulos,et al.  A Linear Programming Model for the Single Destination System Optimum Dynamic Traffic Assignment Problem , 2000, Transp. Sci..

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

[23]  S. Travis Waller,et al.  A Decomposition Scheme for System Optimal Dynamic Traffic Assignment Models , 2003 .

[24]  Hani S. Mahmassani,et al.  Uncertainty in transportation systems evaluation: issues and approaches , 1984 .

[25]  B. Heydecker.  Dynamic Equilibrium Network Design , 2002 .

[26]  Hai Yang,et al.  Models and algorithms for road network design: a review and some new developments , 1998 .

[27]  Athanasios K. Ziliaskopoulos,et al.  Foundations of Dynamic Traffic Assignment: The Past, the Present and the Future , 2001 .