Networks and Spatial Economics

, Volume 12, Issue 1, pp 167–181 | Cite as

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

  • Byung Do Chung
  • Tao Yao
  • Bo Zhang


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.


Dynamic traffic assignment Transportation planning Chance-constrained programming Joint chance constraint Data uncertainty 



This work was partially supported by the grant awards CMMI-0824640 and CMMI-0900040 from the National Science Foundation and the grant awards from the Mid-Atlantic Universities Transportation Center (MAUTC).


  1. Calafiore G, Campi MC (2005) Uncertain convex programs: randomized solutions and confidence levels. Math Program 102:25–46CrossRefGoogle Scholar
  2. Calafiore G, Campi MC (2006) The scenario approach to robust control design. IEEE Trans Autom Control 51:742–753CrossRefGoogle Scholar
  3. Calafiore G, El Ghaoui L (2006) On distributionally robust chance-constrained linear programs with applications. J Optim Theory Appl 130:1–22CrossRefGoogle Scholar
  4. Charnes A, Cooper WW, Symonds GH (1958) Cost horizons and certainty equivalents: an approach to stochastic programming of heating oil. Manag Sci 4:235–263CrossRefGoogle Scholar
  5. Chen W, Sim M (2009) Goal-driven optimization. Oper Res 57:342–357CrossRefGoogle Scholar
  6. Daganzo CF (1994) The cell transmission model part I: a simple dynamic representation of highway traffic. Transp Res B 28:269–287CrossRefGoogle Scholar
  7. Daganzo CF (1995) The cell transmission model part II: network traffic. Transp Res B 29:79–93CrossRefGoogle Scholar
  8. Ergodan G, Iyengar G (2006) Ambiguous chance constrained problems and robust optimization. Math Program 107:37–61CrossRefGoogle Scholar
  9. Karoonsoontawong A, Waller ST (2006) Comparison of system- and user-optimal stochastic dynamic network design models using Monte Carlo bounding techniques. J Transp Res Board 1923:91–102CrossRefGoogle Scholar
  10. Karoonsoontawong A, Waller ST (2007) Robust dynamic continuous network design problem. J Transp Res Board 2029:58–71CrossRefGoogle Scholar
  11. Karoonsoontawong A, Waller ST (2008) Integrated network capacity expansion and traffic signal optimization problem: robust bi-level dynamic formulation. Netw Spat Econ 10:525–550CrossRefGoogle Scholar
  12. Li Y, Waller ST, Ziliaskopoulos T (2003) A decomposition scheme for system optimal dynamic traffic assignment models. Netw Spat Econ 3:441–455CrossRefGoogle Scholar
  13. Luedtke J, Ahmed S (2008) A sample approximation approach for optimization with probabilistic constraints. SIAM J Optim 19:674–699CrossRefGoogle Scholar
  14. Mulvey JM, Vanderbei RJ, Zenios SA (1995) Robust optimization of large-scale systems. Oper Res 43:264–281CrossRefGoogle Scholar
  15. Nemirovski A, Shapiro A (2006) Convex approximation of chance constrained programs. SIAM J Optim 17:969–996CrossRefGoogle Scholar
  16. Nie Y (2011) A cell-based Merchant-Nemhauser model for the system optimum dynamic traffic assignment problem. Transp Res B 45:329–342CrossRefGoogle Scholar
  17. Peeta S, Ziliaskopoulos AK (2001) Foundations of dynamic traffic assignment: the past, the present and the future. Netw Spat Econ 1:233–265CrossRefGoogle Scholar
  18. Waller ST, Ziliaskopoulos AK (2006) A chance-constrained based stochastic dynamic traffic assignment model: analysis, formulation and solution algorithms. Transp Res C 14:418–427CrossRefGoogle Scholar
  19. Yao T, Mandala SR, Chung BD (2009) Evacuation transportation planning under uncertainty: A robust optimization approach. Netw Spat Econ 9:171–189CrossRefGoogle Scholar
  20. Yazici MA, Ozbay K (2010) Evacuation network modeling via dynamic traffic assignment with probabilistic demand and capacity constraints. J Transp Res Board 2196:10–20Google Scholar
  21. Ziliaskopoulos AK (2000) A linear programming model for the single destination system optimum dynamic traffic assignment problem. Transp Sci 34:37–49CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Industrial and Manufacturing EngineeringThe Pennsylvania State UniversityUniversity ParkUSA

Personalised recommendations