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Studies of transit dwell times suggest that the delay caused by passengers boarding and alighting rises with the number of passengers on each vehicle. This paper incorporates such a "friction effect" into an isotropic model of a transit route with elastic demand. We derive a strongly unimodal "Network Alighting Function" giving the steady-state rate of passenger flows in terms of the accumulation of passengers on vehicles. Like the Network Exit Function developed for isotropic models of vehicle traffic, the system may exhibit hypercongestion. Since ridership depends on travel times, wait times and the level of crowding, the physical model is used to solve for (possibly multiple) equilibria as well as the social optimum. Using replicator dynamics to describe the evolution of demand, we also investigate the asymptotic local stability of different kinds of equilibria. • Incorporates "friction effects" into an isotropic model of a transit route. • Derives a strongly unimodal Network Alighting Function with hypercongested states. • The route exhibits multiple equilibria for a given fare and fleet size. • Derives optimal fares and fleet size. • Investigates the local asymptotic stability of equilibria. [ABSTRACT FROM AUTHOR]

For a static economic model of auto traffic in an isotropic zone, this paper classifies possible equilibria into three types, by whether traffic is hypercongested and by the relative slopes of "supply" and "demand" curves. We then conduct a local stability analysis of each type when density, demand and the unit travel time (inverse speed) evolve gradually and simultaneously according to dynamical systems of differential equations. Some hypercongested equilibria may be stable when demand adjusts quickly enough to congestion. Other hypercongested equilibria, which have counterintuitive comparative statics, are never stable. Non-hypercongested equilibria can be unstable under special circumstances. A discrete event simulation with a dynamic Poisson arrival process supports the results of the formal analysis. • Examines equilibrium stability for a static model of traffic in an isotropic zone with elastic demand. • Builds autonomous systems governing how density, demand and speed adjust. • Some hypercongested equilibria can be stable if demand adjusts quickly enough. • Non-hypercongested equilibria can be unstable under special circumstances. • Validates results using a trip-based simulation with a dynamic Poisson arrival process. [ABSTRACT FROM AUTHOR]