A destination-preserving model for simulating Wardrop equilibria in traffic flow on networks

Emiliano Cristiani; Fabio S. Priuli

doi:10.3934/nhm.2015.10.857

Article Contents

2015, Volume 10, Issue 4: 857-876. Doi: 10.3934/nhm.2015.10.857

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A destination-preserving model for simulating Wardrop equilibria in traffic flow on networks

Emiliano Cristiani^1, and
Fabio S. Priuli^2,

1.
Istituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale delle Ricerche, Via dei Taurini, 19 – 00185 Rome
2.
Istituto per le Applicazioni del Calcolo “M. Picone", Consiglio Nazionale delle Ricerche, Via dei Taurini 19, I-00185 Roma

Received: September 2014

Revised: January 2015

Published: December 2015

Abstract / Introduction Related Papers Cited by

Abstract

In this paper we propose a LWR-like model for traffic flow on networks which allows to track several groups of drivers, each of them being characterized only by their destination in the network. The path actually followed to reach the destination is not assigned a priori, and can be chosen by the drivers during the journey, taking decisions at junctions.
The model is then used to describe three possible behaviors of drivers, associated to three different ways to solve the route choice problem: 1. Drivers ignore the presence of the other vehicles; 2. Drivers react to the current distribution of traffic, but they do not forecast what will happen at later times; 3. Drivers take into account the current and future distribution of vehicles. Notice that, in the latter case, we enter the field of differential games, and, if a solution exists, it likely represents a global equilibrium among drivers.
Numerical simulations highlight the differences between the three behaviors and offer insights into the existence of equilibria.

Keywords:

Mathematics Subject Classification: Primary: 90B20, 49N90; Secondary: 91A40, 35L65.

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