Mathematical review of the macroscopic and microscopic models of traffic flow.

Abstract

Traffic flow phenomenon can be described through mathematical model such as continuous dynamic model with an ordinary differential equation so that it can be solved with integral factors. In this paper three simple models of traffic flow are discussed, i.e, two macroscopic and one microscopic models. Macroscopic model formulates dynamics of the traffic flow that occurs on a large number of vehicles on a road. While the microscopic model explains drivers’ behavior in their interaction with other vehicles ahead, i.e, car-following model. This paper shows the existence of ordinary differential equation found in the traffic flow model and indicates some different representations in the context of the same model. It also reviews a simple model of traffic flow along a single link, which leads to some unexpected results, i.e, it can express the solution model in term of link outflows as well as trip time. In the microscopic model, simulation is done to illustrate the behavior of the drivers with a sensitivity coefficient as a benchmark parameter.