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MRSPN analysis of Semi-Markovian finite source retrial queues

Author

Listed:
  • Lyes Ikhlef

    (Bejaia University)

  • Ouiza Lekadir

    (Bejaia University)

  • Djamil Aïssani

    (Bejaia University)

Abstract

In this paper, the analysis of Semi-Markovian single server retrial queues by means of Markov Regenerative Stochastic Petri Nets (MRSPN) is considered. We propose MRSPN models for the two retrial queues M/G/1/N/N and M/G/1/N/N with orbital search. By inspecting the reduced reachability graph of both MRSPN models, the qualitative analysis is obtained. The quantitative analysis is carried out after constructing their one step transition probability matrix and computing the steady state probability distribution of each tangible marking. As an example, the queue $$M/Hypo_{2}/1/2/2$$ M / H y p o 2 / 1 / 2 / 2 is treated in order to illustrate the functionality of the MRSPN approach. The exact performance measures (mean number of customers in the system, mean response time, mean waiting time,...) are computed for different parameters of the two systems by an algorithm elaborated in Matlab environment.

Suggested Citation

  • Lyes Ikhlef & Ouiza Lekadir & Djamil Aïssani, 2016. "MRSPN analysis of Semi-Markovian finite source retrial queues," Annals of Operations Research, Springer, vol. 247(1), pages 141-167, December.
    • Handle: RePEc:spr:annopr:v:247:y:2016:i:1:d:10.1007_s10479-015-1883-8
    DOI: 10.1007/s10479-015-1883-8
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    References listed on IDEAS

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    1. Vyacheslav Abramov, 2006. "Analysis of multiserver retrial queueing system: A martingale approach and an algorithm of solution," Annals of Operations Research, Springer, vol. 141(1), pages 19-50, January.
    2. A. G. de Kok, 1984. "Algorithmic Methods For Single Server Systems With Repeated Attempts," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 38(1), pages 23-32, March.
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    4. Li, Hui & Yang, Tao, 1995. "A single-server retrial queue with server vacations and a finite number of input sources," European Journal of Operational Research, Elsevier, vol. 85(1), pages 149-160, August.
    5. Yang, T. & Posner, M. J. M. & Templeton, J. G. C. & Li, H., 1994. "An approximation method for the M/G/1 retrial queue with general retrial times," European Journal of Operational Research, Elsevier, vol. 76(3), pages 552-562, August.
    6. A. Gómez-Corral, 2006. "A bibliographical guide to the analysis of retrial queues through matrix analytic techniques," Annals of Operations Research, Springer, vol. 141(1), pages 163-191, January.
    7. Dudin, A. N. & Krishnamoorthy, A. & Joshua, V. C. & Tsarenkov, G. V., 2004. "Analysis of the BMAP/G/1 retrial system with search of customers from the orbit," European Journal of Operational Research, Elsevier, vol. 157(1), pages 169-179, August.
    8. 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.
    9. M. Lopez-Herrero, 2006. "A maximum entropy approach for the busy period of the M/G /1 retrial queue," Annals of Operations Research, Springer, vol. 141(1), pages 271-281, January.
    10. J.R. Artalejo & M. Pozo, 2002. "Numerical Calculation of the Stationary Distribution of the Main Multiserver Retrial Queue," Annals of Operations Research, Springer, vol. 116(1), pages 41-56, October.
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    Cited by:

    1. 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.
    2. Anatoly Nazarov & János Sztrik & Anna Kvach & Ádám Tóth, 2020. "Asymptotic sojourn time 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. 288(1), pages 417-434, May.
    3. Anatoly Nazarov & János Sztrik & Anna Kvach & Ádám Tóth, 2022. "Asymptotic Analysis of Finite-Source M/GI/1 Retrial Queueing Systems with Collisions and Server Subject to Breakdowns and Repairs," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1503-1518, September.

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