Traffic Congestion Analysis Using Sir Epidemic Model

Abstract

In this work, we propose a mathematical model to represent traffic congestion in the street under some consideration. A congestion problem in a city highway becomes a critical issue since congestion at one point affected congestion propagation on the other points. We focus on the propagation of traffic propagation by adopting the concept of disease spread using the SIR model. We consider that the disease in traffic problems is congestion. Meanwhile, vehicles that enter the highway are susceptible to congestion. In contrast, vehicles free from traffic jams represent individuals free from disease. The SIR model can explain the spread of congestion by looking at the congestion variable as an infected variable. We discuss and analyze the existence and stability of the equilibrium points. The local stability equilibrium point is verified using the Routh-Hurwitz criteria. At the same time, the global stability is analyzed using Lyapunov function. The numerical simulation is provided in the last section to validate the discussion results.