Empirical Bayesian analysis for traffic intensity: M/M/1 queues with covariates

In this paper, we consider a set of individual M/M/1 queues in which variations in both arrival rates and service rates are partly explained by some covariates representing associated characteristics of individual queues. The random error that takes into account the remaining variation is assumed to follow a gamma distribution. Bayes and empirical Bayes procedures are suggested to make inferences concerning individual traffic intensity parameters that can be applied to several industrial queueing problems.