Influence of a prior distribution on traffic intensity estimation with covariates

In this paper, several methods are suggested to estimate the expected traffic intensity (ρ) in M/M/1 queues with covariates. A Monte-Carlo simulation is used to generate M/M/1 queues where the arrival (service) rates are governed by both their covariate effects and the random error which follows a lognormal distribution. An ad hoc estimator (ρ̂^ADL) is derived for traffic intensity based on a lognormal prior. Its performance is compared to those of the following procedures, when the true prior is a lognormal distribution: empirical Bayes estimator obtained based on a gamma prior distribution (ρ̂^EBG), model based regression estimator (ρ̂^M) and data based raw estimator (ρ̂^R). Results of a simulation study indicate that the performance of ρ̂^ADL is reasonable; the overall performance of ρ̂^EBG is not significantly different from that of ρ̂^ADL and ρ̂^M can replace both ρ̂^ADL and ρ̂^EBG, when the variability of the arrival (service) rate due to random error is relatively small.