A bathtub model of transit congestion

Lewis J. Lehe, Ayush Pandey

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number102892
JournalTransportation Research Part B: Methodological
StatePublished - Mar 2024


  • Bathtub model
  • Congestion
  • Economics
  • Equilibrium
  • MFD
  • Stability
  • Transit

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation


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