Traffic equilibrium between transit lines serviced by capacitated vehicles: a route choice model with passenger waiting on platform

A theory is provided for the problem of passenger waiting and route choice at a transit station where a set of lines serviced by vehicles of limited capacity are available to reach a given destination. It is assumed that the platform layout involves one boarding zone only. The theory addresses waiting discipline – either priority queuing or mingled waiting – and choice behaviour – either selfish or social. The problem of passenger traffic assignment to capacitated transit lines is modelled in a stationary framework, basically assuming memoryless services and passenger arrivals. The size of the passenger stock on the platform is the main state variable as it determines the attractivity condition of a line with respect to alternative routes. Traffic equilibrium is based on the attractivity of a line bundle; it is characterized as the solution to a recursive program. Its existence and uniqueness are demonstrated. When the stock size increases the attractive bundle is enlarged and its average cost is increased. An efficient solution algorithm is provided. The transition from traffic theory to network assignment is discussed. Lastly, a Markovian model of the traffic problem is developed; an analytical solution is given for the case of two lines of unit or infinite vehicle capacity.