Evaluation of Public Transit Systems under Short Random Service Suspensions: A Bulk-Service Queuing Approach

Abstract: This paper proposes a stochastic framework to evaluate the performance of public transit systems under short random service suspensions. We aim to derive closed-form formulations of the mean and variance of the queue length and waiting time. A bulk-service queue model is adopted to formulate the queuing behavior in the system. The random service suspension is modeled as a two-state (disruption and normal) Markov process. We prove that headway is distributed as the difference between two compound Poisson exponential random variables. The distribution is used to specify the mean and variance of queue length and waiting time at each station with analytical formulations. The closed-form stability condition of the system is also derived, implying that the system is more likely to be unstable with high incident rates and long incident duration. The proposed model is implemented on a bus network. Results show that higher incident rates and higher average incident duration will increase both the mean and variance of queue length and waiting time, which are consistent with the theoretical analysis. Crowding stations are more vulnerable to random service suspensions. The theoretical results are validated with a simulation model, showing consistency between the two outcomes.