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.

翻译：基于时刻表的公交分配通过在直接构建于公交时刻表上的时空网络中建模乘客行为的相互作用，来描述公共交通服务中的拥堵。本研究探讨了带排队登车的基于时刻表的马尔可夫式公交分配的理论性质。当车站存在排队时，乘客登车流量根据剩余车辆容量加载，该容量取决于已上车并有优先权的乘客流量。在这种不可分离的路段成本结构以及显式容量约束下，构建了一个均衡问题。网络广义极值（NGEV）模型是一类具有封闭形式表达式的加性随机效用模型，用于描述乘客的路径选择行为。本文提出了均衡问题的一系列公式，包括变分不等式和不动点问题，并由此推导出乘客流量和成本的日均动态。研究表明，与该动态相关的李雅普诺夫函数可被获得，从而确保了均衡的存在性、唯一性和全局稳定性等理想解属性。在处理具有显式容量约束和不可分离路段成本函数的随机均衡方面，本理论分析是对一般交通分配背景下现有日均动态的推广。