Bayesian inference and prediction in multi-server Markovian queueing system with reverse balking: A simulation-based approach

This article presents an in-depth exploration of classical and Bayesian inference methods to estimate the traffic intensity parameter, providing a comprehensive comparison of these two statistical paradigms in a novel multiserver Markovian queueing model (M/M/s) incorporating the phenomenon of reverse balking. The classical inference relies on maximum likelihood (ML) estimation, while the Bayesian approach leverages prior distributions and posterior analysis to enhance estimates. The results indicate that Bayesian methods offer better flexibility and precision compared to traditional ML estimates. Additionally, the predictive probabilities for the number of customers in the system are calculated for different hyper-parameter values of the prior through extensive simulation techniques. The results provide valuable insights for optimizing queue management and improving service efficiency in systems where reverse balking occurs. Moreover, a real-life example is presented to demonstrate the practical implementation of the proposed methodology. This work not only advances the theoretical understanding of queueing dynamics, but also offers practical implications for industries relying on efficient service mechanisms.