Estimation comparison on busy period for a controllable M/G/1 system with bicriterion policy

We propose an estimator for the expected busy period (denoted by β) of a controllable M/G/1 queueing system in which the server applies a bicriterion 〈p, N〉 policy during his idle period. Using this estimator, we construct new confidence intervals for β, which are based on five bootstrap methods; standard bootstrap (SB), percentile bootstrap (PB), bootstrap pivotal (BP), bias-corrected percentile bootstrap (BCPB), bias-corrected and accelerated bootstrap (BCa). A numerical simulation study is conducted in order to demonstrate performance of the proposed estimator $\hat{\beta }$ and bootstrap confidence intervals for β. From the simulation results, we show that $\hat{\beta }$ is a consistent estimator for β, which agrees with the theoretical results. In addition, we also investigate the accuracy of the five bootstrap confidence intervals by calculating the coverage percentage and the relative coverage (defined as the ratio of coverage percentage to average length of confidence interval). Detailed discussions of simulation results for three queueing models are presented.