Queueing Systems

, Volume 19, Issue 1–2, pp 215–229 | Cite as

M/G/1 retrial queueing systems with two types of calls and finite capacity

  • Bong Dae Choi
  • Ki Bong Choi
  • Yong Wan Lee
Article

Abstract

We consider anM/G/1 priority retrial queueing system with two types of calls which models a telephone switching system and a cellular mobile communication system. In the case that arriving calls are blocked due to the server being busy, type I calls are queued in a priority queue of finite capacityK whereas type II calls enter the retrial group in order to try service again after a random amount of time. In this paper we find the joint generating function of the numbers of calls in the priority queue and the retrial group in closed form. When λ1=0, it is shown that our results are consistent with the known results for a classical retrial queueing system.

Keywords

Retrial queue finite capacity non-preemptive priority 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    B.D. Choi and K.K. Park, TheM/G/1 retrial queue with Bernoulli schedule, Queueing Systems 7 (1990) 219–228.Google Scholar
  2. [2]
    C.H. Yoon and C.K. Un, Performance of personal portable radio telephone system with and without guard channels, IEEE J. Select. Areas Commun. 11 (1993) 911–917.Google Scholar
  3. [3]
    J.W. Cohen,Single Server Queue (Wiley, New York, 1969).Google Scholar
  4. [4]
    Z. Khalil, G. Falin and T. Yang, Some analytical results for congestion in subscriber line modules, Queueing Systems 10 (1992) 381–402.Google Scholar
  5. [5]
    G.I. Falin, A survey of retrial queues, Queueing Systems 7 (1990) 127–168.Google Scholar
  6. [6]
    G.I. Falin, J.R. Artalejo and M. Martin, On the single server retrial queue with priority customers, Queueing Systems 14 (1993) 439–455.Google Scholar
  7. [7]
    G.I. Falin, On sufficient conditions for ergodicity of multichannel queueing systems with repeated calls, Adv. Appl. Prob. 16 (1984) 447.Google Scholar
  8. [8]
    P. Hokstad, A supplementary variable technique applied toM/G/1 queue, Scan. J. Stat. 2 (1973) 95–98.Google Scholar
  9. [9]
    T. Yang and J.G.C. Templeton, A survey of retrial queues, Queueing Systems 2 (1987) 203–233.Google Scholar

Copyright information

© J.C. Baltzer AG, Science Publishers 1995

Authors and Affiliations

  • Bong Dae Choi
    • 1
  • Ki Bong Choi
    • 1
  • Yong Wan Lee
    • 1
  1. 1.Department of MathematicsKorea Advanced Institute of Science and TechnologyTaejonKorea

Personalised recommendations