Asymptotic behavior of the stationary distributions in the GI/PH/c queue with heterogeneous servers

  • Marcel F. Neuts
  • Yukio Takahashi

DOI: 10.1007/BF01025867

Cite this article as:
Neuts, M.F. & Takahashi, Y. Z. Wahrscheinlichkeitstheorie verw Gebiete (1981) 57: 441. doi:10.1007/BF01025867


This paper deals with the stablec-server queue with renewal input. The service time distributions may be different for the various servers. They are however all probability distributions of phase type. It is shown that the stationary distribution of the queue length at arrivals has an exact geometric tail of rate η, 0<η<1. It is further shown that the stationary waiting time distribution at arrivals has an exact exponential tail of decay parameter ξ>0. The quantities η and ξ may be evaluated together by an elementary algorithm. For both distributions, the multiplicative constants which arise in the asymptotic forms may be fully characterized. These constants are however difficult to compute in general.

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Marcel F. Neuts
    • 1
  • Yukio Takahashi
    • 2
  1. 1.Department of Mathematical SciencesUniversity of DelawareNewarkUSA
  2. 2.Department of EconomicsTohoku UniversityKawauchi-SendaiJapan

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