Behaviour of queueing approximations based on sample moments

Abstract

SUMMARYWe investigate moment-based queueing approximations in the presence of sampling error. Let L be the steady-state mean number in the system for a GI/M/I queue. We focus on the estimation of L under the assumption that only sample moments of the interarrival-time distribution are known. A simulation experiment is carried out for several interarrival-time distributions. For each case, sample moments from the interarrival-time disiribution are matched to a n approximating phase-type distribution and the corresponding estimate_ L is obtained. We show that the sampling error in the moments induces bias as well as variability in L. Based on our simulation experiment, we suggest matching only two moments when the sample coefficient of variation is low or when sample size is low; otherwise, matching three moments is preferable.

Algorithms for computing waiting time distributions under different queue disciplines for the D-BMAP/PH/1

“…These difficulties have been alleviated by the introduction of the phase type distribution which is well suited for numerical computations. Phase type distributions are known to approximate most of the general distributions encountered in queueing systems [10,11]. Neuts [17] presented the waiting time distribution for the M/G/1 queue under various queue disciplines.…”