Title: Side constrained traffic assignment problem for multiclass flow

Authors: Saeed Asadi Bagloee; Mohsen Asadi

Addresses: Smart Cities Transport Group, Department of Infrastructure Engineering, Melbourne School of Engineering, The University of Melbourne, Victoria 3010, Australia ' Centre for Transport Studies, Department of Civil and Environmental Engineering, Kharazmi University, P.O. Box 15614, Tehran, Iran

Abstract: Capacity constraints (or side constraints) - though representing realistic features - are largely overlooked in the traffic assignment due to the inherent mathematical complexities. To this end; we first relaxed the capacity constraints by an intuitive interpretation of their corresponding Lagrange values, that is, the amount of penalty imposed to the travel time of the oversaturated road to make them saturated. This approach is basically a subgradient method in which the penalty terms bear some resemblances to the marginal cost of the concept of system optimal traffic flow. We then circumvented the complexity of multiclass facet by adopting a bias term for each user class in the Beckmann's formulation. Hence, we arrived at an uncapacitated single-class TAP in which the penalty terms are updated iteratively. The proposed algorithm obviates any additional parameter, which is not a trivial task as shown in the past studies.

Keywords: multiclass traffic assignment; side constraint; capacity constraint.

DOI: 10.1504/IJOR.2019.099547

International Journal of Operational Research, 2019 Vol.35 No.1, pp.108 - 131

Received: 13 Feb 2016
Accepted: 10 Jun 2016
Published online: 09 May 2019 *

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