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Bause, F.:

Doubly Stochastic and Circulant Structured Markovian Arrival Processes.

Technical Reports in Computer Science, No. 824, TU Dortmund (Germany), 2009.

 

Abstract:

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This paper defines Structured Markovian Arrival Processes (SMAPs).  An SMAP consists of several blocks each being represented by a random variable specifying the duration of staying in that block. Leaving a block indicates an arrival event of the SMAP. The routing between blocks is governed by a stochastic matrix Q. It is shown that the joint moments of the SMAP can be directly determined from the moments of the block random variables and routing matrix Q, if Q is doubly stochastic. The characteristics of the SMAP can be computed very efficiently if Q is in addition circulant.  Furthermore we show that for given block random variables the determination of a routing matrix Q and thus the fitting of the SMAP essentially results in solving a set of linear equations.