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

  • Authors:

  • E. A. Van Doorn;A. A. Jagers

  • Affiliations:

  • Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands e.a.vandoorn@utwente.nl;Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands a.a.jagers@utwente.nl

  • Venue:
  • Queueing Systems: Theory and Applications
  • Year:
  • 2004

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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.