In order to develop a toy model for car's traffic in cities, in this paper we analyze, by means of numerical simulations, the transition among fluid regimes and a congested jammed phase of the flow of kinetically constrained hard spheres in planar random networks similar to urban roads. In order to explore as timescales as possible, at a microscopic level we implement an event driven dynamics as the infinite time limit of a class of already existing model (Follow the Leader) on an Erdos-Renyi two-dimensional graph, the crossroads being accounted by standard Kirchoff density conservations. We define a dynamical order parameter as the ratio among the moving spheres versus the total number and by varying two control parameters (density of the spheres and coordination number of the network) we study the phase transition. At a mesoscopic level it respects an, again suitable, adapted version of the Lighthill-Whitham model, which belongs to the fluid-dynamical approach to the problem. At a macroscopic level, the model seems to display a continuous transition from a fluid phase to a jammed phase when varying the density of the spheres (the amount of cars in a city-like scenario) and a discontinuous jump when varying the connectivity of the underlying network.

A NUMERICAL INVESTIGATION OF THE JAMMING TRANSITION IN TRAFFIC FLOW ON DILUTED PLANAR NETWORKS / Gabriele, Achler; Barra, Adriano. - In: INTERNATIONAL JOURNAL OF MODERN PHYSICS B. - ISSN 0217-9792. - 24:32(2010), pp. 6351-6363. [10.1142/s0217979210057687]

A NUMERICAL INVESTIGATION OF THE JAMMING TRANSITION IN TRAFFIC FLOW ON DILUTED PLANAR NETWORKS

BARRA, ADRIANO
2010

Abstract

In order to develop a toy model for car's traffic in cities, in this paper we analyze, by means of numerical simulations, the transition among fluid regimes and a congested jammed phase of the flow of kinetically constrained hard spheres in planar random networks similar to urban roads. In order to explore as timescales as possible, at a microscopic level we implement an event driven dynamics as the infinite time limit of a class of already existing model (Follow the Leader) on an Erdos-Renyi two-dimensional graph, the crossroads being accounted by standard Kirchoff density conservations. We define a dynamical order parameter as the ratio among the moving spheres versus the total number and by varying two control parameters (density of the spheres and coordination number of the network) we study the phase transition. At a mesoscopic level it respects an, again suitable, adapted version of the Lighthill-Whitham model, which belongs to the fluid-dynamical approach to the problem. At a macroscopic level, the model seems to display a continuous transition from a fluid phase to a jammed phase when varying the density of the spheres (the amount of cars in a city-like scenario) and a discontinuous jump when varying the connectivity of the underlying network.
traffic flow; phase transition and critical phenomena; glassy behavior
01 Pubblicazione su rivista::01a Articolo in rivista
A NUMERICAL INVESTIGATION OF THE JAMMING TRANSITION IN TRAFFIC FLOW ON DILUTED PLANAR NETWORKS / Gabriele, Achler; Barra, Adriano. - In: INTERNATIONAL JOURNAL OF MODERN PHYSICS B. - ISSN 0217-9792. - 24:32(2010), pp. 6351-6363. [10.1142/s0217979210057687]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/442861
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