Ladder heights and the Markov-modulated M/G/1 queue
The waiting time distribution is studied for the Markov-modulated M/G/1 queue with both the arrival rate [beta]i and the distribution Bi of the service time of the arriving customer depending on the state i of the environmental process. The analysis is based on ladder heights and occupation measure identities, and the fundamental step is to compute the intensity matrix Q of a certain Markov jump process as the solution of a non-linear matrix equation. The results come out as close matrix parallels of the Pollaczek-Khinchine formula without using transforms or complex variables. Further it is shown that if the Bi are all phase-type, then the waiting time distribution is so as well.
Year of publication: |
1991
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Authors: | Asmussen, Søren |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 37.1991, 2, p. 313-326
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Publisher: |
Elsevier |
Keywords: | M/G/1 queue Markov-modulation waiting time Pollaczek-Khinchine formula ladder heights Wiener-Hopf factorization time reversal occupation measure phase-type distributions non-linear matrix iteration |
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