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 (ρ̂ADL) 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 (ρ̂EBG), model based regression estimator (ρ̂M) and data based raw estimator (ρ̂R). Results of a simulation study indicate that the performance of ρ̂ADL is reasonable; the overall performance of ρ̂EBG is not significantly different from that of ρ̂ADL and ρ̂M can replace both ρ̂ADL and ρ̂EBG, when the variability of the arrival (service) rate due to random error is relatively small.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Modelling and Simulation
- Statistics, Probability and Uncertainty
- Applied Mathematics