Discomfort in mass transit and its implication for scheduling and pricing

•Formulation of comfort value in public transport.•Impact of crowding on equilibrium train loadings.•Impact of crowding on the choice of departure time.•Comparison of equilibrium and optimum values.•Equilibrium computation in a network with multiple stations.

This paper discusses the formulation of crowding in public transport and its implications for pricing, seating capacity and optimal scheduling. An analytical model is used to describe the user equilibrium and the optimal equilibrium for different stylized conditions. For the one OD pair case with identical desired arrival time, we derive the optimal dynamic pricing and optimal share of seats. For the uniformly distributed desired arrival times case, we derive the optimal time table and the optimal pricing. Next we generalize the results to the case of a small network with several stations, stochastic choice and allocation of seats.