The basic idea of Microscopic approach (A1) (2)is that the behavior of each vehicle is affected by neighboring vehicles, and the entire traffic flow is represented as statistical occurrences. The Cellular Automaton (CA) based model (3) (4) and (11) is widely known idea to represent the behavior of each vehicle. In the CA model, the road is discretized into many small cells. Each cell can be either empty or occupied by only one vehicle. The behavior of each vehicle in each cell is specified by the geometrical relationship with other vehicles together with some stochastic parameters. Although many simulation results based on these microscopic models showed high similarity to the measured real data, these approaches are not suitable for the large-scale traffic network modeling and its traffic light controller design. This is because they require enormous computational efforts to find all vehicles’ behavior. Furthermore, the precise information on initial positions and speeds of all vehicles are usually not available in advance. On the other hand, it has been a common strategy in the macroscopic approach (A2) (9) that the designer uses a fluid approximation model where the behavior of traffic flow is regarded as a continuous fluid with density k(x, t) and volume q(x, t) at location x and time t. In this case, k(x, t) and q(x, t) must satisfy the following law of mass conservation;
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