Estimating the change point in M/E k / 1 queueing model: Classical and Bayesian approaches

This study investigates a single server phase-type Service with Markovian arrival (i.e., M/Ek/1) queueing system with structural changes occurring in the interarrival and service time distributions. Such change points can arise due to operational changes, policy modifications, or technological advancements, and if ignored these changes, may lead to inaccurate system analysis and suboptimal decision-making. To address such variability, this article considers a change-point model and employs both Maximum Likelihood (ML) and Bayesian estimation methods to infer the model parameters. Furthermore, to evaluate the significance of the change point, we employed classical hypothesis testing using the Likelihood Ratio (LR) test, along with Bayesian model comparison through the Bayes Factor. Simulation studies demonstrate that Bayesian estimates yield lower mean squared errors (MSEs) compared to ML estimates, indicating more robustness and estimation accuracy. An application to a simulated workshop queueing system further illustrates the practical utility of the proposed approach. The findings highlight the importance of accounting for structural changes in queueing systems to enhance performance monitoring and decision-making.