Queue lengths and workloads in polling systems

O.J. Boxma; O. Kella; K.M. Kosinski

doi:10.1016/j.orl.2011.10.006

Queue lengths and workloads in polling systems

O.J. Boxma, O. Kella, K.M. Kosinski

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Abstract

For a single-server multi-station polling system, we focus on the generating function and Laplace–Stieltjes transform of the time-stationary joint queue length and workload distributions, respectively, under no further assumptions on the service discipline. We express these quantities as expressions involving the generating functions of the joint queue length distribution at visit beginnings and visit completions at the various stations. The latter is known for a broad variety of cases. Finally, we identify a workload decomposition result. Keywords: Polling system; Queue length; Steady-state distribution

Original language	English
Pages (from-to)	401-405
Journal	Operations Research Letters
Volume	39
Issue number	6
DOIs	https://doi.org/10.1016/j.orl.2011.10.006
Publication status	Published - 2011

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title = "Queue lengths and workloads in polling systems",

abstract = "For a single-server multi-station polling system, we focus on the generating function and Laplace–Stieltjes transform of the time-stationary joint queue length and workload distributions, respectively, under no further assumptions on the service discipline. We express these quantities as expressions involving the generating functions of the joint queue length distribution at visit beginnings and visit completions at the various stations. The latter is known for a broad variety of cases. Finally, we identify a workload decomposition result. Keywords: Polling system; Queue length; Steady-state distribution",

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AU - Boxma, O.J.

AU - Kella, O.

AU - Kosinski, K.M.

PY - 2011

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N2 - For a single-server multi-station polling system, we focus on the generating function and Laplace–Stieltjes transform of the time-stationary joint queue length and workload distributions, respectively, under no further assumptions on the service discipline. We express these quantities as expressions involving the generating functions of the joint queue length distribution at visit beginnings and visit completions at the various stations. The latter is known for a broad variety of cases. Finally, we identify a workload decomposition result. Keywords: Polling system; Queue length; Steady-state distribution

AB - For a single-server multi-station polling system, we focus on the generating function and Laplace–Stieltjes transform of the time-stationary joint queue length and workload distributions, respectively, under no further assumptions on the service discipline. We express these quantities as expressions involving the generating functions of the joint queue length distribution at visit beginnings and visit completions at the various stations. The latter is known for a broad variety of cases. Finally, we identify a workload decomposition result. Keywords: Polling system; Queue length; Steady-state distribution

U2 - 10.1016/j.orl.2011.10.006

DO - 10.1016/j.orl.2011.10.006

M3 - Article

SN - 0167-6377

VL - 39

SP - 401

EP - 405

JO - Operations Research Letters

JF - Operations Research Letters

IS - 6

ER -

Queue lengths and workloads in polling systems

Abstract

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