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Zbl 1162.90515
Ukkusuri, Satish V.; Waller, S.Travis
Linear programming models for the user and system optimal dynamic network design problem: Formulations, comparisons and extensions. (English)
[J] Netw. Spat. Econ. 8, No. 4, 383-406 (2008). ISSN 1566-113X; ISSN 1572-9427/e

Summary: 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.
MSC 2000:
*90C05 Linear programming
90B18 Communication networks
90B20 Highway traffic
90C15 Stochastic programming

Keywords: dynamic traffic assignment; equilibrium; linear programming; network design; recourse; stochastic programming; transportation networks

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