Effect of obstacles on formation of traffic jam in a two-dimensional traffic network

We investigate the effect of obstacles on formation of a traffic jam for a traffic flow in a network of city roads. We consider a square lattice of two bonds between two nearest crossings as a network of city roads; we assume that there are three lattice sites in a crossing. We put five decorated sites on each bond between two nearest crossings. A car or an obstacle is assumed to be located on one of these decorated sites or one of the lattice sites. We assume only two types of cars; namely one type of cars move mainly in the positive x direction and change their direction to the positive y direction with a probability and the other type of cars move mainly in the positive y direction and change their direction to the positive x direction with the same probability. One of two lanes is assumed to be used mainly for passing the obstacles or jamming other cars. We set rules for car moving in order to make our traffic-flow model by taking into account all the possible situations. By using numerical simulations, we find that a phase transition from a free-moving phase to a traffic-jam phase is formed more easily for obstacles placed very close to traffic signals in the traffic direction than for those in the other cases.