Equilibrium traffic dynamics in a bathtub model: A special case

- In the bottleneck model, traffic flow cannot decrease in traffic density.
- In contrast, the bathtub model we present does admit hypercongestion.
- Closed form solution of no-toll equilibrium and analytical solution of social optimum.
- Equilibrium and optimum characterized by contiguous travel masses of commuters.
- In equilibrium, efficiency gains from optimal tolling may exceed revenue raised.

For a quarter century, a top priority in transportation economics has been to develop models of rush-hour traffic dynamics that incorporate hypercongestion - situations of heavy congestion where throughput decreases as traffic density increases. Unfortunately, even the simplest models along these lines appear in general to be analytically intractable, and none of the models that have made approximations in order to achieve tractability has gained widespread acceptance. This paper takes a different tack, developing an analytical solution for a special case - a no-toll equilibrium in an isotropic downtown area with identical commuters, Greenshields' congestion technology, and the α−β cost function (no late arrivals permitted). This is followed by a discussion of directions for future research.