A Model of Rush-Hour Traffic Dynamics in an Isotropic Downtown Area

For a quarter century, a top priority in transportation economic theory 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 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 focusing on a special case – the isotropic model with identical commuters and the α − β − γ cost function – for which an analytical solution is possible. A complete, closed-form solution is presented for the no-toll equilibrium in which departures and arrivals occur in masses, and the solution for the social optimum is fully characterized.