An Algorithmic Approach for Sensitivity Analysis of Perturbed Quasi-Birth-and-Death Processes
Queueing Systems: Theory and Applications
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For a queueing system with a low traffic intensity, the expected number of customers in the queue is small. However, with a bursty input process, long queues may build up in a short time. In this paper, we study light traffic queueing systems with bursty input processes. We study the distributions of queue lengths, waiting times, busy and active periods, and their corresponding expansions when the traffic intensity is small. Special attention goes to some conditional distributions of queue lengths, waiting times, and system-active periods. The expansions given in this paper provide a potential asymptotic approach to the computation of various descriptors of queueing systems. The coefficients of those expansions reflect some important features of episodic queues. We also report numerical results which give a graphic view of our approximations and of the effect of the burstiness of the input and service processes on the queues.