A Note on the GI/GI/∞ System with Identical Service and Interarrival-Time Distributions

E.A. van Doorn, A.A. Jagers

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)

Abstract

We study the stationary distribution of the number of busy servers in a GI/GI/∞ system in which the service-time distribution is identical to the interarrival-time distribution, and obtain several representations for the variance. As a result we can verify an expression for the variance, conjectured by Rajaratnam and Takawira (IEEE Trans. Vehicular Technol. 50 (2001) 954–970), when the common distribution of interarrival and service times is a gamma distribution.
Original languageEnglish
Pages (from-to)45-52
Number of pages7
JournalQueueing systems
Volume47
Issue number1-2
DOIs
Publication statusPublished - 2004

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Keywords

  • METIS-218294
  • busy-server distribution
  • EWI-12826
  • Gamma distribution
  • IR-62330
  • Mellin transform
  • Infinite-server system

Cite this

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title = "A Note on the GI/GI/∞ System with Identical Service and Interarrival-Time Distributions",
abstract = "We study the stationary distribution of the number of busy servers in a GI/GI/∞ system in which the service-time distribution is identical to the interarrival-time distribution, and obtain several representations for the variance. As a result we can verify an expression for the variance, conjectured by Rajaratnam and Takawira (IEEE Trans. Vehicular Technol. 50 (2001) 954–970), when the common distribution of interarrival and service times is a gamma distribution.",
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A Note on the GI/GI/∞ System with Identical Service and Interarrival-Time Distributions. / van Doorn, E.A.; Jagers, A.A.

In: Queueing systems, Vol. 47, No. 1-2, 2004, p. 45-52.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - A Note on the GI/GI/∞ System with Identical Service and Interarrival-Time Distributions

AU - van Doorn, E.A.

AU - Jagers, A.A.

PY - 2004

Y1 - 2004

N2 - We study the stationary distribution of the number of busy servers in a GI/GI/∞ system in which the service-time distribution is identical to the interarrival-time distribution, and obtain several representations for the variance. As a result we can verify an expression for the variance, conjectured by Rajaratnam and Takawira (IEEE Trans. Vehicular Technol. 50 (2001) 954–970), when the common distribution of interarrival and service times is a gamma distribution.

AB - We study the stationary distribution of the number of busy servers in a GI/GI/∞ system in which the service-time distribution is identical to the interarrival-time distribution, and obtain several representations for the variance. As a result we can verify an expression for the variance, conjectured by Rajaratnam and Takawira (IEEE Trans. Vehicular Technol. 50 (2001) 954–970), when the common distribution of interarrival and service times is a gamma distribution.

KW - METIS-218294

KW - busy-server distribution

KW - EWI-12826

KW - Gamma distribution

KW - IR-62330

KW - Mellin transform

KW - Infinite-server system

U2 - 10.1023/B:QUES.0000032799.30173.b7

DO - 10.1023/B:QUES.0000032799.30173.b7

M3 - Article

VL - 47

SP - 45

EP - 52

JO - Queueing systems

JF - Queueing systems

SN - 0257-0130

IS - 1-2

ER -