Computational analysis of a Markovian queueing system with geometric mean-reverting arrival process

摘要

In the queueing literature, an arrival process with random arrival rate is usually modeled by a Markov-modulated Poisson process (MMPP). Such a process has discrete states in its intensity and is able to capture the abrupt changes among different regimes of the traffic source. However, it may not be suitable for modeling traffic sources with smoothly (or continuously) changing intensity. Moreover, it is less parsimonious in that many parameters are involved but some are lack of interpretation. To cope with these issues, this paper proposes to model traffic intensity by a geometric mean-reverting (GMR) diffusion process and provides an analysis for the Markovian queueing system fed by this source. In our treatment, the discrete counterpart of the GMR arrival process is used as an approximation such that the matrix geometric method is applicable. A conjecture on the error of this approximation is developed out of a recent theoretical result, and is subsequently validated in our numerical analysis. This enables us to calculate the performance measures with high efficiency and precision. With these numerical techniques, the effects from the GMR parameters on the queueing performance are studied and shown to have significant influences. (C) 2015 Elsevier Ltd. All rights reserved.