The Markov arrival process (MAP) is a generalization of the Poisson process by having non-exponential distribution sojourn between arrivals. The homogeneous case has rate matrix,
An arrival is seen every time a transition occurs that increases the level (a marked transition), e.g. a transition in the sub-matrix. Sub-matrices and have elements of, the rate of a Poisson process, such that,
and
There are several special cases of the Markov arrival process.
Read more about this topic: Markovian Arrival Processes
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