This paper investigates, using a simulation program, a retrial queuing system with a single server which is subject to random breakdowns. The number of sources of calls is finite, and collisions can take place. We assume that the failure of the server blocks the system’s operation such that newly arriving customers cannot enter the system, contrary to an earlier paper where the failure does not affect the arrivals. All the random variables included in the model construction are assumed to be independent of each other, and all times are exponentially distributed except for the service time, which is gamma distributed. The novelty of this analysis is the inspection of the blocking effect on the performance measures using different distributions. Various figures represent the impact of the squared coefficient of the variation of the service time on the main performance measures such as the mean and variance of the number of customers in the system, the mean and variance of the response time, the mean and variance of the time a customer spends in the service, and the mean and variance of the sojourn time in the orbit.
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References
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.
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).
J. R. Artalejo and A. Gómez-Corral, Retrial Queueing Systems: a Computational Approach, Springer, Berlin (2008).
S. Balsamo, G. L. Dei Rossi, and A. Marin, “Modelling retrial-upon-conflict systems with product-form stochastic Petri nets,” in: International Conference on Analytical and Stochastic Modeling Techniques and Applications, Springer (2013), pp. 52–66.
V. I. Dragieva, “Number of retrials in a finite source retrial queue with unreliable server,” Asia-Pac. J. Oper. Res., 31, No. 2 (2014).
V. I. Dragieva and T. Phung-Duc, “Two-way communication M/M/1//N retrial queue,” in: International Conference on Analytical and Stochastic Modeling Techniques and Applications, Springer (2017), pp. 81–94.
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.
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).
J. Kim and B. Kim, “A survey of retrial queueing systems,” Ann. Oper. Res., 247, No. 1, 3–36 (2016).
J. S. Kim, “Retrial queueing system with collision and impatience,” Commun. Korean Math. Soc., 25, No. 4, 647–653 (2010).
A. Krishnamoorthy, P. K. Pramod, and S. R. Chakravarthy, “Queues with interruptions: a survey,” TOP, 22, No. 1, 290–320 (2014).
A. Kuki, J. Sztrik, Á. Tóth, and T. Bérczes, “A contribution to modeling two-way communication with retrial queueing systems,” Commun. Comput. Inform. Sci., 912, 236–247 (2018).
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).
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).
A. Nazarov, J. Sztrik, A. Kvach, and T. Bérczes, “Asymptotic analysis of finite-source M/M/1 retrial queueing system with collisions and server subject to breakdowns and repairs,” Ann. Oper. Res., 277, No. 2, 213–239 (2018).
A. Nazarov, J. Sztrik, and A. Kvach, “A survey of recent results in finite-source retrial queues with collisions,” Commun. Comput. Inform. Sci., 912, 1–15 (2018).
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).
J. Sztrik, “Tool supported performance modelling of finite-source retrial queues with breakdowns,” Publ. Math., 66, No. 1, 187–213 (2014).
Á. Tóth, T. Bérczes, J. Sztrik, and A. Kuki, “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, No. 6, 846–857 (2019).
J. Wang, L. Zhao, and F. Zhang, “Analysis of the finite source retrial queues with server breakdowns and repairs,” J. Ind. Manag. Optim., 7, No. 3, 655–676 (2011).
F. Zhang and J. Wang, “Performance analysis of the retrial queues with finite number of sources and service interruptions,” J. Korean Stat. Soc., 42, No. 1, 117–131 (2013)
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Proceedings of the XXXV International Seminar on Stability Problems for Stochastic Models, Perm, Russia, September 24–28, 2018. Part I.
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Tóth, A., Bérczes, T., Sztrik, J. et al. The Simulation of Finite-Source Retrial Queueing Systems with Collisions and Blocking. J Math Sci 246, 548–559 (2020). https://doi.org/10.1007/s10958-020-04759-4
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DOI: https://doi.org/10.1007/s10958-020-04759-4