E-Bayesian Estimation of Arrival and Service Rates in an M/M/1 Queueing System

This paper develops Bayesian and E-Bayesian estimators for the arrival and service rates in an M/M/1 queueing system using Gamma priors under squared error and precautionary loss functions. To address uncertainty in prior specification, a key emphasis is placed on the E-Bayesian approach, where uniform hyperpriors are introduced to enhance robustness. A Monte Carlo simulation study is conducted to compare the proposed estimators with the classical maximum likelihood estimator in terms of bias and mean squared error. The results indicate that Bayesian estimators improve accuracy, particularly in small samples, while the precautionary loss function yields more conservative estimates. Notably, the E-Bayesian estimators consistently outperform other methods by achieving lower mean squared error and greater stability, highlighting their advantage in effectively handling prior uncertainty and providing a more reliable framework for parameter estimation in queueing systems.