Analysis of the waiting time distribution for polling systems with retrials and glue periods

Bara Kim, Jeongsim Kim

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

We consider a single-server multi-station polling system with retrials and glue periods. Just before the server arrives at a station, there is a deterministic glue period. During a glue period, arriving customers (either newly arriving customers or retrying customers) at the station stick in the queue of that station and will be served during the following service period of that station. Whereas during any other period, arriving customers at the station join the orbit of that station and will retry after an exponentially distributed time. In this paper, we derive the Laplace–Stieltjes transform of the waiting time distribution of an arbitrary customer. This transform allows us to obtain the mean and variance of the waiting time.

Original languageEnglish
Pages (from-to)197-212
Number of pages16
JournalAnnals of Operations Research
Volume277
Issue number2
DOIs
Publication statusPublished - 2019 Jun 30

Bibliographical note

Funding Information:
Acknowledgements We are grateful to the reviewers for valuable comments and suggestions, which greatly improved this paper. B. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2017R1A2B4012676). J. Kim’s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A1B03029542).

Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

  • Glue periods
  • Polling system
  • Retrials

ASJC Scopus subject areas

  • General Decision Sciences
  • Management Science and Operations Research

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