Networks and Spatial Economics

, Volume 8, Issue 4, pp 383–406

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


DOI: 10.1007/s11067-007-9019-6

Cite this article as:
Ukkusuri, S.V. & Waller, S.T. Netw Spat Econ (2008) 8: 383. doi:10.1007/s11067-007-9019-6


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.


Dynamic traffic assignment Equilibrium Linear programming Network design Recourse Stochastic programming Transportation networks 

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Transportation Systems Engineering, Department of Civil & Environmental EngineeringRensselaer Polytechnic InstituteTroyUSA
  2. 2.Department of Civil EngineeringUniversity of Texas at AustinAustinUSA

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