Dynamic Traffic Assignment under Uncertainty: A Distributional Robust Chance-Constrained Approach

This paper provides a chance-constrained programming approach for transportation planning and operations under uncertainty. The major contribution of this paper is to approximate a joint chance-constrained Cell Transmission Model based System Optimum Dynamic Traffic Assignment with only partial distributional information about uncertainty as a linear program which is computationally efficient. Numerical experiments have been conducted to show the performance of the proposed approach compared with other two workable approaches based on a cumulative distribution function and a sampling method. This new approach can be used as a pragmatic tool for system optimum dynamic traffic control and management.

[1]  Steven T Waller,et al.  Integrated Network Capacity Expansion and Traffic Signal Optimization Problem: Robust Bi-level Dynamic Formulation , 2010 .

[2]  Tao Yao,et al.  Evacuation Transportation Planning Under Uncertainty: A Robust Optimization Approach , 2009 .

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

[4]  A. Charnes,et al.  Cost Horizons and Certainty Equivalents: An Approach to Stochastic Programming of Heating Oil , 1958 .

[5]  Alexander Shapiro,et al.  Convex Approximations of Chance Constrained Programs , 2006, SIAM J. Optim..

[6]  S. Travis Waller,et al.  A Chance-Constrained Based Stochastic Dynamic Traffic Assignment Model: Analysis, Formulation and Solution Algorithms , 2006 .

[7]  Yu Nie.  A Cell-based Merchant-Nemhauser Model for the System Optimum Dynamic Traffic Assignment Problem , 2010 .

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

[9]  James R. Luedtke,et al.  A Sample Approximation Approach for Optimization with Probabilistic Constraints , 2008, SIAM J. Optim..

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

[11]  G. Calafiore,et al.  On Distributionally Robust Chance-Constrained Linear Programs , 2006 .

[12]  Kaan Ozbay,et al.  Evacuation Network Modeling via Dynamic Traffic Assignment with Probabilistic Demand and Capacity Constraints , 2010 .

[13]  Melvyn Sim,et al.  Goal-Driven Optimization , 2009, Oper. Res..

[14]  Garud Iyengar,et al.  Ambiguous chance constrained problems and robust optimization , 2006, Math. Program..

[15]  Giuseppe Carlo Calafiore,et al.  Uncertain convex programs: randomized solutions and confidence levels , 2005, Math. Program..

[16]  Robert J. Vanderbei,et al.  Robust Optimization of Large-Scale Systems , 1995, Oper. Res..

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

[18]  Carlos F. Daganzo,et al.  The Cell Transmission Model. Part I: A Simple Dynamic Representation Of Highway Traffic , 1992 .

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

[20]  Giuseppe Carlo Calafiore,et al.  The scenario approach to robust control design , 2006, IEEE Transactions on Automatic Control.

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

[22]  S. Travis Waller,et al.  Robust Dynamic Continuous Network Design Problem , 2007 .