  Schedule-based transit assignment describes congestion in public transport
services by modeling the interactions of passenger behavior in a time-space
network built directly on a transit schedule. This study investigates the
theoretical properties of scheduled-based Markovian transit assignment with
boarding queues. When queues exist at a station, passenger boarding flows are
loaded according to the residual vehicle capacity, which depends on the flows
of passengers already on board with priority. An equilibrium problem is
formulated under this nonseparable link cost structure as well as explicit
capacity constraints. The network generalized extreme value (NGEV) model, a
general class of additive random utility models with closed-form expression, is
used to describe the path choice behavior of passengers. A set of formulations
for the equilibrium problem is presented, including variational inequality and
fixed-point problems, from which the day-to-day dynamics of passenger flows and
costs are derived. It is shown that Lyapunov functions associated with the
dynamics can be obtained and guarantee the desirable solution properties of
existence, uniqueness, and global stability of the equilibria. In terms of
dealing with stochastic equilibrium with explicit capacity constraints and
non-separable link cost functions, the present theoretical analysis is a
generalization of the existing day-to-day dynamics in the context of general
traffic assignment.
