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Dual processes to solve single server systems. (English) Zbl 1075.60117

Summary: A new approach is used to determine the transient probability functions of the classical queueing systems M/M/1, M/M/1/H, and M/M/1/H with catastrophes. This new solution method uses dual processes, randomization and lattice path combinatorics. The method reveals that the transient probability functions for M/M/1/H and M/M/1/H with catastrophes have the same mathematical form.

MSC:

60K25 Queueing theory (aspects of probability theory)
60J27 Continuous-time Markov processes on discrete state spaces
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