Vehicular motion on a selected path in a 2d traffic network controlled by signals

We study the dynamic behavior of vehicular traffic through a series of traffic lights on selected paths in a two-dimensional (2d) traffic network. The city traffic network is made of one-way perpendicular streets arranged in a square lattice with traffic signals where vertical streets are oriented upwards and horizontal streets are oriented rightwards. A vehicle moves through the series of signals on a path selected by the driver. The selected path is one of the straight, zigzag, and random paths in a 2d traffic network. The vehicular motion on a selected path is presented by the nonlinear-map model. Vehicular traffic exhibits very complex behavior with varying selected paths, cycle times, and vehicular density. The dependence of the arrival time on cycle time, selected path, and density is clarified for 2d city traffic.