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Performance analysis of a multiprogramming–multiprocessor retrial queueing system with orderly reattempts

Author

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  • B. Krishna Kumar

    (Anna University)

  • A. Thanikachalam

    (Anna University)

  • V. Kanakasabapathi

    (Anna University)

  • R. Rukmani

    (Pachaiyappa’s College)

Abstract

This paper deals with retrial queueing models having an unlimited/a finite orbit capacity with control retrial policy of a multiprogramming–multiprocessor computer network system. Under the Markovian assumptions and light-traffic condition, the steady-state probabilities of the number of programs in the system and the mean number of programs in the orbit are studied using matrix geometric/analytic methods. The expressions for the Laplace-Stieglitz transforms of the busy period and the waiting time are obtained. The probability generating function for the number of retrials made by a tagged program is also derived. Some interesting performance measures of the system and the various moments of quantities of interest are discussed. Finally, extensive numerical results are illustrated to reveal the impact of the system parameters on the performance measures.

Suggested Citation

  • B. Krishna Kumar & A. Thanikachalam & V. Kanakasabapathi & R. Rukmani, 2016. "Performance analysis of a multiprogramming–multiprocessor retrial queueing system with orderly reattempts," Annals of Operations Research, Springer, vol. 247(1), pages 319-364, December.
    • Handle: RePEc:spr:annopr:v:247:y:2016:i:1:d:10.1007_s10479-015-2005-3
    DOI: 10.1007/s10479-015-2005-3
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    References listed on IDEAS

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    1. B. Kumar & J Raja, 2006. "On multiserver feedback retrial queues with balking and control retrial rate," Annals of Operations Research, Springer, vol. 141(1), pages 211-232, January.
    2. Artalejo, J. R. & Gomez-Corral, A. & Neuts, M. F., 2001. "Analysis of multiserver queues with constant retrial rate," European Journal of Operational Research, Elsevier, vol. 135(3), pages 569-581, December.
    3. Donald P. Gaver & Gerald S. Shedler, 1973. "Processor Utilization in Multiprogramming Systems via Diffusion Approximations," Operations Research, INFORMS, vol. 21(2), pages 569-576, April.
    4. B. Avi-Itzhak & D. P. Heyman, 1973. "Approximate Queuing Models for Multiprogramming Computer Systems," Operations Research, INFORMS, vol. 21(6), pages 1212-1230, December.
    5. Hans Daduna, 1986. "Cycle Times in Two-Stage Closed Queueing Networks: Applications to Multiprogrammed Computer Systems with Virtual Memory," Operations Research, INFORMS, vol. 34(2), pages 281-288, April.
    6. Falin, G. I. & Artalejo, J. R., 1998. "A finite source retrial queue," European Journal of Operational Research, Elsevier, vol. 108(2), pages 409-424, July.
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    Cited by:

    1. B. Krishna Kumar & R. Sankar & R. Navaneetha Krishnan & R. Rukmani, 2023. "Multiserver call center retrial queue under Bernoulli vacation schedule with two-way communication and orbital search," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 84(1), pages 23-51, September.
    2. Anatoly Nazarov & János Sztrik & Anna Kvach & Tamás Bérczes, 2019. "Asymptotic analysis of finite-source M/M/1 retrial queueing system with collisions and server subject to breakdowns and repairs," Annals of Operations Research, Springer, vol. 277(2), pages 213-229, June.

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