Queueing Systems

, Volume 17, Issue 3–4, pp 347–382

Approximations for multi-server queues: System interpolations

  • Toshikazu Kimura
Invited Paper


This paper provides a unifying method of generating and/or evaluating approximations for the principal congestion measures in aGI/G/s queueing system. The main focus is on the mean waiting time, but approximations are also developed for the queue-length distribution, the waiting-time distribution and the delay probability for the Poisson arrival case. The approximations have closed forms that combine analytical solutions of simpler systems, and hence they are referred to as system-interpolation approximations or, simply, system interpolations. The method in this paper is consistent with and generalizes system interpolations previously presented for the mean waiting time in theGI/G/s queue.


Queues multi-server approximations system interpolations asymptotic analysis mean waiting time queue-length distribution delay probability 


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Copyright information

© J.C. Baltzer AG, Science Publishers 1994

Authors and Affiliations

  • Toshikazu Kimura
    • 1
  1. 1.Department of Business AdministrationHokkaido UniversitySapporoJapan

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