An M/G/1 queue with cyclic service times

S. M R Iravani*, M. J M Posner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this paper we consider a single server queue with Poisson arrivals and general service distributions in which the service distributions are changed cyclically according to customer sequence number. This model extends a previous study that used cyclic exponential service times to the treatment of general service distributions. First, the stationary probability generating function and the average number of customers in the system are found. Then, a single vacation queueing system with a N-limited service policy, in which the server goes on vacation after serving N consecutive customers is analyzed as a particular case of our model. Also, to increase the flexibility of using the M/G/1 model with cyclic service times in optimization problems, an approximation approach is introduced in order to obtain the average number of customers in the system. Finally, using this approximation, the optimal N-limited service policy for a single vacation queueing system is obtained.

Original languageEnglish (US)
Pages (from-to)145-169
Number of pages25
JournalQueueing Systems
Volume22
Issue number1-2
DOIs
StatePublished - May 1996

Keywords

  • Cyclic service
  • General service times
  • Queue-cart problem
  • Queues with vacations

ASJC Scopus subject areas

  • Statistics and Probability
  • Computer Science Applications
  • Management Science and Operations Research
  • Computational Theory and Mathematics

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