Numerical Simulations for Traffic Flow in Two-Dimensional Network with Obstacles

Abstract

We investigate effect of obstacles on formation of a traffic jam for a traffic flow in a network of city roads, by numerical simulations. The network of city roads is implemented in a double-bond square lattice, instead of a usual single-bond square lattice; we assume that each bondhas five d ecoratedsites. A car or an obstacle is assumedto be locatedat one of those decorated sites or lattice sites. Two types (µ and ν types) of cars are assumed; cars of µ type (ν type) move mainly to the positive x (y) direction and change their direction to the positive y (x) direction with a probability. What we found is that a traffic jam is formed more easily for obstacles placedclose to traffic signals in the traffic flow d irection than for those in the other cases. Control of traffic flow is an important subject in our modern society. Traffic jams appear in highways, in networks of city roads or in computer networks and should be avoided if possible. The nature of a transition between a free-movingphase and a traffic-jam phase has to be clarified in order to control the traffic flow. Biham, Middleton and Levin (BML) proposed a two-dimensional traffic flow model on a network of city roads with one lane; 1) there is a crossingat each lattice site and cars are located only at crossings. There are two types of cars in the BML model, each of which moves only to the positive x (y) direction or the positive y direction. They found that there is a phase transition of the first-order type between the free-movingphase and the traffic-jam phase. The BML model has been modified by Cuesta et al. 2) so that cars can change their direction by a probability. In those models, cars move directly from a crossingto its nearest crossingif that movingis allowed. This direct movingfrom a crossingto its nearest crossinghas been lifted by puttingdecorated sites. 3), 4) In the present paper, we investigate effect of obstacles, such as illegally parking cars on roads, on the formation of a traffic jam, by using a network of city roads with two lanes, which is obtained by extendingthe model given by Horiguchi and Sakakibara. 4)