Busy Periods for Queues Alternating Between Two Modes

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Abstract

We study the busy period of a single server queueing system operating in two alternating modes - working and vacation. In the two modes the systems run as an MX/ G/ 1 queue with disasters, but with different parameters. The vacation mode starts once the number of customers drops to zero. It is terminated randomly (when it is not empty) with a transition to the working mode. At such a transition moment all the customers are transferred to the working mode; the service of the customer being served is lost and it starts from scratch in the working mode. Every busy period starts with a batch arrival into an empty system and terminates at the first time that the number of customers drops to zero. The working and the vacation periods are analyzed too. Finally, we apply the results to obtain the probability generating functions of the number of customers in the working, as well as in the vacation periods.

Original languageEnglish
Article number60
JournalMethodology and Computing in Applied Probability
Volume25
Issue number2
DOIs
StatePublished - Jun 2023

Bibliographical note

Funding Information:
The research of Esther Frostig is partially funded by ISF (Israel Science Foundation), Grant Grant 1999/18). The research of David Perry is partially funded by ISF (Israel Science Foundation), Grant 3274/19.

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

  • Busy period
  • Disasters
  • M/G/1
  • Taboo states
  • Vacations

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (all)

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