Queue lengths and workloads in polling systems

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

doi:10.1016/j.orl.2011.10.006

Queue lengths and workloads in polling systems

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

^*Corresponding author for this work

Department of Statistics

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

28 Scopus citations

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

Bibliographical 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) .

Keywords

Polling system
Queue length
Steady-state distribution

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10.1016/j.orl.2011.10.006

Cite this

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AU - Kosiski, K. M.

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KW - Polling system

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KW - Steady-state distribution

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Queue lengths and workloads in polling systems

Abstract

Bibliographical note

Keywords

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