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Phase-type representations in random walk and queueing problems. (English) Zbl 0755.60049
A fundamental problem for a random walk is to compute quantities like the ladder height distributions and the distribution of the maximum. The author approaches these problems in a special way. The idea is to restrict the discussion to phase-type distributions [see M. F. Neuts, Matrix-geometric solutions in stochastic models. An algorithmic approach (1981; Zbl 0469.60002)]. Within this setting, he obtains a solution of the random walk problems which is transform-free, avoids complex numbers and has the appealing feature that many of the basic unknown distributions turn out to be again of phase-type.

60G50 Sums of independent random variables; random walks
60J05 Discrete-time Markov processes on general state spaces
60K25 Queueing theory (aspects of probability theory)
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