The queue M|G|1 with Markov modulated arrivals and services

G.J.K. Regterschot; J.H.A. de Smit

doi:10.1287/moor.11.3.465

The queue M|G|1 with Markov modulated arrivals and services

G.J.K. Regterschot, J.H.A. de Smit

Discrete Mathematics and Mathematical Programming

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Abstract

We study an M|G|1 queue in which both the arrival rate and the service time distribution depend on the state of an underlying finite-state Markov chain. The solution is obtained by a matrix factorization method. This leads to results for waiting times and queue lengths both at arrival epochs and in continuous time. A numerical algorithm for the calculation of several quantities of interest is described and some numerical examples are given.

Original language	Undefined
Pages (from-to)	465-483
Journal	Mathematics of operations research
Volume	11
Issue number	3
DOIs	https://doi.org/10.1287/moor.11.3.465
Publication status	Published - 1986

Keywords

IR-98505

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10.1287/moor.11.3.465

Regterschot86queue

Cite this

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abstract = "We study an M|G|1 queue in which both the arrival rate and the service time distribution depend on the state of an underlying finite-state Markov chain. The solution is obtained by a matrix factorization method. This leads to results for waiting times and queue lengths both at arrival epochs and in continuous time. A numerical algorithm for the calculation of several quantities of interest is described and some numerical examples are given.",

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AU - de Smit, J.H.A.

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AB - We study an M|G|1 queue in which both the arrival rate and the service time distribution depend on the state of an underlying finite-state Markov chain. The solution is obtained by a matrix factorization method. This leads to results for waiting times and queue lengths both at arrival epochs and in continuous time. A numerical algorithm for the calculation of several quantities of interest is described and some numerical examples are given.

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