Queue lengths and workloads in polling systems

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

doi:https://doi.org/10.1016/j.orl.2011.10.006

Queue lengths and workloads in polling systems

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

Department of Statistics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

For a single-server multi-station polling system, we focus on the generating function and LaplaceStieltjes 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.

Original language	English
Pages (from-to)	401-405
Number of pages	5
Journal	Operations Research Letters
Volume	39
Issue number	6
DOIs	https://doi.org/10.1016/j.orl.2011.10.006
State	Published - Nov 2011

Keywords

Polling system
Queue length
Steady-state distribution

All Science Journal Classification (ASJC) codes

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

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https://doi.org/10.1016/j.orl.2011.10.006

Cite this

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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 LaplaceStieltjes 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",

author = "Boxma, {O. J.} and O. Kella and Kosiski, {K. M.}",

note = "Funding Information: The second author is supported by grant No. 434/09 from the Israel Science Foundation and the Vigevani Chair in Statistics . The third author is supported by NWO grant 613.000.701 . The authors would also like to thank Marko Boon for reading the first draft of this paper, which led to the nice simplification of Formula (9) into (10) .",

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TY - JOUR

T1 - Queue lengths and workloads in polling systems

AU - Boxma, O. J.

AU - Kella, O.

AU - Kosiski, K. M.

N1 - Funding Information: The second author is supported by grant No. 434/09 from the Israel Science Foundation and the Vigevani Chair in Statistics . The third author is supported by NWO grant 613.000.701 . The authors would also like to thank Marko Boon for reading the first draft of this paper, which led to the nice simplification of Formula (9) into (10) .

PY - 2011/11

Y1 - 2011/11

N2 - For a single-server multi-station polling system, we focus on the generating function and LaplaceStieltjes 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.

AB - For a single-server multi-station polling system, we focus on the generating function and LaplaceStieltjes 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.

KW - Polling system

KW - Queue length

KW - Steady-state distribution

UR - http://www.scopus.com/inward/record.url?scp=80855131607&partnerID=8YFLogxK

U2 - https://doi.org/10.1016/j.orl.2011.10.006

DO - https://doi.org/10.1016/j.orl.2011.10.006

M3 - مقالة

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

Keywords

All Science Journal Classification (ASJC) codes

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