Optimal fares and capacity decisions for crowded public transport systems

There is a large operations research literature on public transit system design. An extensive economic literature has also developed on public transit capacity investments, service frequency, and optimal pricing and subsidy policy. These two branches of literature have made significant advances in understanding public transit systems. However, in contrast to the literature on automobile traffic congestion, most of the studies have employed static models that cannot account for travelers' time-of-use decisions and the dynamics of transit congestion and crowding. The time profile of ridership is driven by the trade-off that users face between traveling at peak times and suffering crowding, and avoiding the peak by traveling earlier or later than they would like. A few studies have explored this trade-off using simple microeconomic models that combine trip-scheduling preferences as introduced by Vickrey (1969) with a crowding cost function that describes how utility from travel decreases with passenger loads. In this paper we use this modeling framework to analyze usage of a rail transit line, and assess the potential benefits from internalizing crowding externalities by setting differential train fares. We also present results on optimal train capacity and the number of trains put into service.