Characterizing the BMAP/MAP/1 Departure Process via the ETAQA Truncation

Qi Zhang · Armin Heindl · Evgenia Smirni A

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Advanced Queuing Theory Analysis Network Traffic and Congestion Control Petri Nets in System Modeling

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 interdeparture 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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References

1999Introduction to Matrix Analytic Methods in Stochastic Modeling 1991New results on the single server queue with a batch markovian arrival process 1991Structured Stochastic Matrices of M/G/1 Type and Their Applications.1988A stable recursion for the steady state vector in markov chains of m/g/1 type 2003Modeling IP traffic using the batch Markovian arrival process 2012Queueing Theory: A Linear Algebraic Approach 2001Departure Processes of BMAP/G/1 Queues 2003Approximation models of feed-forward G/G/1/N queueing networks with correlated arrivals

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