Skip to main content
Log in

Comparison of Two Operation Modes of Finite-Source Retrial Queueing Systems with Collisions and a Non-Reliable Server by Using Simulation

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

In this paper a finite-source retrial queuing system with collision of the customers is investigated by means of computer simulation. The server is not reliable; it is subjected to breakdowns, and the repairs depend on whether the state of the server is idle. The random variables used in the model are jointly independent and are exponential and gamma distributed. Two operation modes are considered in the case of busy breakdown. The novelty of the investigation is a comparison of the performance measures of these modes, and estimations obtained by the simulation are graphically illustrated showing the influence of the difference of the working modes on the performance measures such as mean and variance of the response time, mean and variance of the number of customers in the system, mean and variance of the sojourn time in the orbit, mean and variance of time time a customer spent in service.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A.A. Ali and S. Wei, “Modeling of coupled collision and congestion in finite source wireless access systems,” in: Wireless Communications and Networking Conference (WCNC) (2015), pp. 1113–1118.

  2. B. Almási, J. Roszik, and J. Sztrik, “Homogeneous finite-source retrial queues with server subject to breakdowns and repairs,” Math. Comput. Model., 42, No. 5–6, 673–682 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  3. J.R. Artalejo and A. Gómez-Corral, Retrial Queueing Systems: A computational Approach, Springer, Berlin (2008).

    Book  MATH  Google Scholar 

  4. S. Balsamo, G.L. Dei Rossi, and A. Marin, “Modelling retrial-upon-conflict systems with productform stochastic petri nets,” in: International Conference on Analytical and Stochastic Modeling Techniques and Applications, Springer (2013), pp. 52–66.

  5. V.I. Dragieva, “Number of retrials in a finite source retrial queue with unreliable server,” Asia-Pac. J. Oper. Res., 31, No. 2 (2014).

  6. P. A. Fishwick, “Simpack: Getting started with simulation programming in C and C++,” in: WSC 92 Proceedings of the 24th Conference on Winter Simulation, ACM, New York (1992), pp. 154–162.

    Book  Google Scholar 

  7. N. Gharbi and C. Dutheillet, “An algorithmic approach for analysis of finite-source retrial systems with unreliable servers,” Comput. Math. Appl., 62, No. 6, 2535–2546 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  8. J. Kim and B. Kim, “A survey of retrial queueing systems,” Ann. Oper. Res., 247, No. 1, 3–36 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  9. J.S. Kim, “Retrial queueing system with collision and impatience,” Commun. Kor. Math. Soc., 25, No. 4, 647–653 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  10. A. Kvach and A. Nazarov, “Sojourn time analysis of finite source Markov retrial queuing system with collision,” Commun. Comput. Inform. Sci., 564, 64–72 (2015).

    Article  Google Scholar 

  11. A. Nazarov, A. Kvach, and V. Yampolsky, “Asymptotic analysis of closed Markov retrial queuing system with collision,” Commun. Comput. Inform. Sci., 487, 334–341 (2014).

    Article  MATH  Google Scholar 

  12. Y. Peng, Z. Liu, and J. Wu, “An M/G/1 retrial G-queue with preemptive resume priority and collisions subject to the server breakdowns and delayed repairs,” J. Appl. Math. Comput., 44, No. 1–2, 187–213 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Wang, L. Zhao, and F.Zhang, “Analysis of the finite source retrial queues with server breakdowns and repairs,” J. Ind. Man. Opt., 7, No. 3, 655–676 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  14. F. Zhang and J. Wang, “Performance analysis of the retrial queues with finite number of sources and service interruptions,” J. Kor. Stat. Soc., 42, No. 1, 117–131 (2013).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Á. Tóth.

Additional information

Proceedings of the XXXIV International Seminar on Stability Problems for Stochastic Models, Debrecen, Hungary.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tóth, Á., Bérczes, T., Sztrik, J. et al. Comparison of Two Operation Modes of Finite-Source Retrial Queueing Systems with Collisions and a Non-Reliable Server by Using Simulation. J Math Sci 237, 846–857 (2019). https://doi.org/10.1007/s10958-019-04211-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-019-04211-2

Navigation