Bulk Service Queueing for Transit Resilience under Short Random Service Suspensions
For transit operators, this provides a tractable method to assess the impact of short service suspensions on passenger queues and waiting times, though it is an incremental extension of queueing theory to a specific transit problem.
This paper develops an analytical framework to quantify the resilience of a transit line under short random service suspensions, deriving stability conditions and closed-form expressions for queue length and waiting time. Numerical experiments show that short suspensions disproportionately affect congested stations and that incident duration and scheduled headway dominate vehicle capacity changes.
Short service suspensions are common in public transit systems, but their operational impacts remain difficult to quantify. We develop an analytical framework for measuring the resilience of a transit line under short random service suspensions. Vehicle movement is represented by a two state process in which vehicles either travel normally or stop during a suspension, and the induced stochastic headways enter a bulk service queueing model with finite vehicle capacity and passenger carryover. The model yields two classes of resilience indicators. Stability conditions determine whether station queues remain bounded, while closed form expressions characterize the mean and variance of station level queue length and waiting time. We construct an independent renewal approximation for headways whose common marginal distribution is obtained by taking the positive part of a raw headway formed from the incident adjusted scheduled headway and the difference between two independent compound Poisson exponential variables. The renewal approximation preserves the marginal effects of short suspensions while omitting serial dependence and delay propagation across multiple vehicles. Combining the resulting passenger arrival distribution with a Markov representation of passenger loads across stations allows the resilience indicators to be computed sequentially along the route. Numerical experiments show that short suspensions disproportionately affect congested stations and that changes in incident duration and scheduled headway can dominate comparable changes in vehicle capacity. A recursive first in, first out simulation assesses the analytical approximations and clarifies the role of headway variability.