A Bathtub Model of Traffic Congestion

In the standard economic models of traffic congestion, traffic flow does not fall under heavily congested conditions. But this is counter to experience, especially in the downtown areas of most major cities during rush hour. This paper presents a bathtub model of traffic congestion. The height of water in the bathtub corresponds to traffic density, velocity is negatively related to density, and outflow is the product of density and velocity. Above a critical density, outflow falls as density increases. The model indicates that, when demand is high relative to capacity, applying an optimal time-varying congestion tolls generates benefits that are considerably larger than those obtained from the standard models and exceed the toll revenue collected.