Algorithmic analysis of the BMAP/D/k system in discrete time

Abstract

We exploit the structural properties of the BMAP/D/k system to carry out its algorithmic analysis. Specifically, we use these properties to develop algorithms for studying the distributions of waiting times in discrete time and the busy period. One of the structural properties used results from considering the system as having customers assigned in a cyclic order—which does not change the waiting-time distribution—and then studying only one arbitrary server. The busy period is defined as the busy period of an arbitrary single server based on this cyclic assignment of customers to servers. Finally, we study the marginal distribution of the joint queue length and phase of customer arrival. The structural property used for studying the queue length is based on the observation of the system every interval that is the length of one customer service time.

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