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AnM/M/1 retrial queue with control policy and general retrial times

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Abstract

We consider anM/M/1 retrial queueing system in which the retrial time has a general distribution and only the customer at the head of the queue is allowed to retry for service. We find a necessary and sufficient condition for ergodicity and, when this is satisfied, the generating function of the distribution of the number of customers in the queue and the Laplace transform of the waiting time distribution under steady-state conditions. The results agree with known results for special cases.

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References

  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. E. Çinlar,Introduction to Stochastic Processes (Prentice-Hall, Englewood Cliffs, 1975).

    Google Scholar 

  3. J.W. Cohen, Basic problems of telephone traffic theory and the influence of repeated calls, Philips Telecomm. Rev. 18 (1957) 49–100.

    Google Scholar 

  4. A. Erdélyi, W. Magnus, F. Oberhettinger and F.G. Tricomi,Table of Integral Transforms, Vol. 1 (McGraw-Hill, New York, 1954).

    Google Scholar 

  5. G.I. Falin, A survey of retrial queues, Queueing Systems 7 (1990) 127–167.

    Google Scholar 

  6. K. Farahmand, Single line queue with repeated demands, Queueing Systems 6 (1990) 223–228.

    Google Scholar 

  7. G. Fayolle, A simple telephone exchange with delayed feedbacks, Traffic Anal. and Comput. Performance Evaluation (1986) 245.

  8. T. Hanschke, Bestimmung von Grenzwahrscheinlichkeiten bei Wartesschlangenmodellen mit Hilfe des Jacobi-Perron-Algorithmus, Berichte der math-stat Sektion im Forschungszentrum Graz 126 (1979).

  9. P. Hokstad, A supplementary variable technique applied to theM/G/1 queue, Scand. J. Stat. 2 (1975) 95–98.

    Google Scholar 

  10. C.E.M. Pearce, Extended continued fractions, recurrence relations and two-dimensional Markov processes, Adv. Appl. Prob. 21 (1989) 357–375.

    Google Scholar 

  11. B. Pourbabai, Analysis of aG/M/K/0 queueing system with heterogeneous servers and retrials, Int. J. Syst. Sci. 18 (1987) 985–992.

    Google Scholar 

  12. T. Yang and J.G.C. Templeton, A survey on retrial queues, Queueing Systems 2 (1987) 203–233.

    Google Scholar 

  13. T. Yang, A broad class of retrial queues and the associated generalized recursive technique, Ph.D. thesis, Univ. of Toronto (1990).

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Authors and Affiliations

  1. Department of Mathematics, Korea Advanced Institute of Science and Technology, 373-1 Kusong-dong, Yusong-gu, Taejon, Korea

    Bong Dae Choi

  2. Electronics and Telecommunications Research Institute, P. O. Box 8, Daejon, Korea

    Kwang Kyu Park

  3. Applied Mathematics Department, Adelaide University, G.P.O. Box 498, 5001, Adelaide, SA, Australia

    C. E. M. Pearce

Authors
  1. Bong Dae Choi
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  2. Kwang Kyu Park
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  3. C. E. M. Pearce
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Supported by KOSEF 90-08-00-02.

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Choi, B.D., Park, K.K. & Pearce, C.E.M. AnM/M/1 retrial queue with control policy and general retrial times. Queueing Syst 14, 275–292 (1993). https://doi.org/10.1007/BF01158869

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  • DOI: https://doi.org/10.1007/BF01158869

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