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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.




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.