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A Mixed User-Equilibrium and System-Optimal Traffic Flow for Connected Vehicles Stated as a Complementarity Problem

Journal article
Authors S. A. Bagloee
M. Sarvi
Michael Patriksson
A. Rajabifard
Published in Computer-Aided Civil and Infrastructure Engineering
Volume 32
Issue 7
Pages 562-580
ISSN 1093-9687
Publication year 2017
Published at Department of Mathematical Sciences
Pages 562-580
Language en
Keywords freeway incident detection, traveler information-systems, link capacity, constraints, assignment problem, network equilibrium, elastic demand, variational inequality, market penetration, algorithm, model, Computer Science, Construction & Building Technology, Engineering, Transportation
Subject categories Mathematics


Connected vehicles (CVs), be they autonomous vehicles or a fleet of cargo carriers or Uber, are a matter of when they become a reality and not if. It is not unreasonable to think that CV technology may have a far-reaching impact, even to the genesis of a completely new traffic pattern. To this end, the literature has yet to address the routing behavior of the CVs, namely traffic assignment problem (TAP) (perhaps it is assumed, they ought to follow the traditional shortest possible paths, known as user equilibrium [UE]). It is possible that real-time data could be derived from the vehicles' communications that in turn could be used to achieve a better traffic circulation. In this article, we propose a mathematical formulation to ensure the CVs are seeking the system optimal (SO) principles, while the remainder continue to pursue the old-fashioned UE pattern. The model is formulated as a nonlinear complementarity problem (NCP). This article contributes to the literature in three distinct ways: (i) mathematical formulation for the CVs' routing, stated as a mixed UE-SO traffic pattern, is proposed; (ii) a variety of realistic features are explicitly considered in the solution to the TAP including road capacity, elastic demand, multiclass and asymmetric travel time; and (iii) formal proof of the existence and uniqueness of the solutions are also presented. The proposed methodology is applied to the networks of Sioux-Falls and Melbourne.

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