Multi-server tandem queue with Markovian arrival process, phase-type service times, and finite buffers

Hendrik Baumann and Werner Sandmann

European Journal of Operational Research, 2017, vol. 256, issue 1, 187-195

Abstract: We consider multi-server tandem queues where both stations have a finite buffer and all services times are phase-type distributed. Arriving customers enter the first queueing station if buffer space is available or get lost otherwise. After completing service in the first station customers proceed to the second station if buffer space is available, otherwise a server at the first station is blocked until buffer space becomes available at the second station. We provide an exact computational analysis of various steady-state performance measures such as loss and blocking probabilities, expectations and higher moments of numbers of customers in the queues and in the whole system by modeling the tandem queue as a level-dependent quasi-birth-and-death process and applying suitable matrix-analytic methods. Numerical results are presented for selected representative examples.

Keywords: Queueing; Multi-server tandem queue; Markovian arrival process; Phase-type service time distributions; Matrix-analytic method (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:256:y:2017:i:1:p:187-195

DOI: 10.1016/j.ejor.2016.07.035

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