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Finite Markov chain models skip-free in one direction. (English) Zbl 0551.90097

Finite Markov processes are considered, with bidimensional state space, such that transitions from state (n,i) to state (m,j) are possible only if \(m\leq n+1\). The analysis leads to efficient computational algorithms, to determine the stationary probability distribution, and moments of first passage times.

MSC:

90C40 Markov and semi-Markov decision processes
60K15 Markov renewal processes, semi-Markov processes
90B22 Queues and service in operations research
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