The Inhomogeneous BMAP/G/? Queue

TL;DRAbstract

In queueing theory, most models are based on time-homogeneous arrival processes and service time distributions. However, in communication networks arrival rates and/or the service capacity usually vary periodically in time. In order to reflect this property accurately, it is most natural to consider inhomogeneous arrival processes in queueing models. In the present paper, the inhomogeneous BMAP/G/∞ queue with time–dependent service time distributions is examined. Exact transient distributions as well as approximation formulae are derived. For the special case of homogeneous BMAP/G/∞ queues, stability conditions and asymptotic distributions are given. Finally, it is shown how to derive bounds for the (inhomogeneous) BMAP/G/c/c loss system by means of analyzing the BMAP/G/∞ (inhomogeneous) queue.

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