The waiting time distribution for a correlated queue with exponential interarrival and service times

Bara Kim, Jeongsim Kim

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

We are concerned with the analysis of the waiting time distribution in an M∕M∕1 queue in which the interarrival time between the nth and the (n+1)th customers and the service time of the nth customer are correlated random variables with Downton's bivariate exponential distribution. In this paper we show that the conditional waiting time distribution, given that the waiting time is positive, is exponential.

Original languageEnglish
Pages (from-to)268-271
Number of pages4
JournalOperations Research Letters
Volume46
Issue number2
DOIs
Publication statusPublished - 2018 Mar

Bibliographical note

Funding Information:
We are grateful to the reviewer 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 Elsevier B.V.

Keywords

  • Bivariate exponential distribution
  • Correlated queue
  • Workload

ASJC Scopus subject areas

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

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