Models of the departure process of a BMAP/MAP/1 queue

Abstract

We propose a family of finite approximations for the departure process of a BMAP/MAP/1 queue. The departure process approximations are derived via an exact aggregate solution technique (called ETAQA) applied to M/G/1-type Markov processes. The proposed approximations are indexed by a parameter n ( n < 1), which determines the size of the output model as n + 1 block levels of the M/G/1-type process. This output approximation preserves exactly the marginal distribution of the true departure process and the lag correlations of the inter-departure times up to lag n -2. Experimental results support the applicability of the proposed approximation in traffic-based decomposition of queueing networks.

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