Ladder heights and the Markov-modulated M/G/1 queue

Søren Asmussen

Stochastic Processes and their Applications, 1991, vol. 37, issue 2, 313-326

Abstract: 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.

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 (search for similar items in EconPapers)
Date: 1991
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Citations: View citations in EconPapers (3)

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