Calculable Congestion: Modeling Effects of Traffic Light on Traffic Flow Using ODEs and PDEs

Abstract

The study analyzes the effect of traffic lights on traffic flow using ordinary differential equation (ODE) and partial differential equations (PDE) models. I consider several different cases. First, I assume constant inflow and outflow of traffic on a single link with a traffic light at one end. This model allows the traffic volume to increase without limit. Then, I consider cases where the link volume is limited on a single link without traffic light, a one-link system with a traffic light, and a two-link system with a traffic light. I compare these ODE models to a PDE model. Both ODE and PDE models are found to be able to adequately predict whether the link(s) would jam, given information on inflow and red/green light length. The ODE models provide overall information such as link volume at any time and time of jamming, while the PDE model is better at showing detailed situations at specific locations of the link(s), such as the jam length, when and where the waiting queue will be cleared and cars released can catch up with the previous line of cars. The study demonstrates that both ODE and PDE formulations can be very powerful tools in describing effects of traffic light on traffic flow, with each of them having its own distinctive merits. When both are used conjunctively, they provide even more insight.