A Quasi-Sequential Cellular-Automaton Approach to Traffic Modeling

The most popular discrete models to simulate traffic flow are cellular automata, discrete dynamical systems whose behavior is completely specified in terms of its local region. Space is represented as a grid, with each cell containing some data, and these cells act in accordance to some set of rules at each temporal step. Of particular interest to this problem are sequential cellular automata (SCA), where the cells are updated in a sequential manner at each temporal step. We develop a discrete model with a grid to represent the area around a toll plaza and cells to hold cars. The cars are modeled as 5-dimensional vectors, with each dimension representing a different characteristic (e.g., speed). By discretizing the grid into different regimes (transition from highway, tollbooth, etc.), we develop rules for cars to follow in their movement. Finally, we model incoming traffic flow using a negative exponential distribution. We plot the average time for a car to move through the grid vs. incoming traffic flow rate for three different cases: 4 incoming lanes and tollbooths, 4 incoming lanes and 4, 5, and 6 tollbooths. In each plots, we noted at certain values for the flow rate, there is a boundary layer in our solution. As we increase the ratio of tollbooths to incoming lanes, this boundary layer shifts to the right. Hence, the optimum solution is to pick the minimum number of tollbooths for which the maximum flow rate expected is located to the left of the boundary layer.