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