An easy-to-use algorithm for simulating traffic flow on networks: Numerical experiments

Gabriella Bretti; Maya Briani; Emiliano Cristiani

doi:10.3934/dcdss.2014.7.379

Article Contents

2014, Volume 7, Issue 3: 379-394. Doi: 10.3934/dcdss.2014.7.379

This issue Previous Article Interaction of road networks and pedestrian motion at crosswalks Next Article Pattern formation in 2D traffic flows

An easy-to-use algorithm for simulating traffic flow on networks: Numerical experiments

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

Received: April 30, 2013

Revised: June 30, 2013

Published: May 2014

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Abstract

In this paper we propose a Godunov-based discretization of a hyperbolic system of conservation laws with discontinuous flux, modeling vehicular flow on a network. Each equation describes the density evolution of vehicles having a common path along the network. We show that the algorithm selects automatically an admissible solution at junctions, hence ad hoc external procedures (e.g., maximization of the flux via a linear programming method) usually employed in classical approaches are no needed. Since users have not to deal explicitly with vehicle dynamics at junction, the numerical code can be implemented in minutes. We perform a detailed numerical comparison with a Godunov-based scheme coming from the classical theory of traffic flow on networks which maximizes the flux at junctions.

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Mathematics Subject Classification: Primary: 65M08; Secondary: 90B20.

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