Abstract
In this paper a finite-source M/GI/1 retrial queuing system with collisions of customers is considered. The definition of throughput of the system as average number of customers, which are successfully served per unit time is introduced. It is shown that at some combinations of system parameter values and probability distribution of service time of customers the throughput can be arbitrarily small, and at another values of parameters throughput can be greater than the service intensity. Applying method of asymptotic analysis under the condition of unlimited growing number of sources it is proofed that limiting distribution of the number of retrials/transitions of the customer into the orbit is geometric and the sojourn/waiting time of the customer in the orbit follows a generalized exponential distribution. In addition, the mean sojourn time of the customer under service is obtained.
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References
Sztrik, J., Almási, B., Roszik, J.: Heterogeneous finite-source retrial queues with server subject to breakdowns and repairs. J. Math. Sci. 132, 677–685 (2006)
Dragieva, V.I.: System state distributions in one finite source unreliable retrial queue. http://elib.bsu.by/handle/123456789/35903
Choi, B.D., Shinand, Y.W., Ahn, W.C.: Retrial queues with collision arising from unslotted CSMA/CD protocol. J. Control Comput. Sci. 11(4), 335–356 (1992). Queueing Systems 11 Herald of Tomsk State University
Nazarov, A., Kvach, A., Yampolsky, V.: Asymptotic analysis of closed Markov retrial queuing system with collision. In: Dudin, A., Nazarov, A., Yakupov, R., Gortsev, A. (eds.) ITMM 2014. CCIS, vol. 487, pp. 334–341. Springer, Cham (2014). doi:10.1007/978-3-319-13671-4_38
Kvach, A.S., Nazarov, A.A.: The research of a closed RQ-system M/GI/1//N with collision of the customers in the condition of an unlimited increasing number of sources. In: Probability Theory, Random Processes, Mathematical Statistics and Applications: Materials of the International Scientific Conference Devoted to the 80th Anniversary of Professor Gennady Medvedev, Doctor of Physical and Mathematical Sciences, Minsk, February 23-26, 2015 Minsk, pp. 65–70 (2015). (In Russian) http://vital.lib.tsu.ru/vital/access/manager/Repository/vtls:000535452
Gòmez-Corral, A.: On the applicability of the number of collisions in p-persistent CSMA/CD protocols. Comput. Oper. Res. 37(7), 1199–1211 (2010)
Zhang, F., Wang, J.: Performance analysis of the retrial queues with finite number of sources and service interruptions. J. Korean Stat. Soc. 42(1), 117–131 (2013). doi:10.1016/j.jkss.2012.06.002
Nazarov, A.A., Moiseeva, S.P.: Methods of Asymptotic Analysis in Queueing Theory. NTL Publishing House of Tomsk University, Tomsk (2006). (In Russian)
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The publication was financially supported by the Ministry of Education and Science of the Russian Federation (Agreement number 02.a03.21.0008) and by Peoples Friendship University of Russia (RUDN University).
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Nazarov, A., Sztrik, J., Kvach, A. (2017). Some Features of a Finite-Source M/GI/1 Retrial Queuing System with Collisions of Customers. In: Vishnevskiy, V., Samouylov, K., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2017. Communications in Computer and Information Science, vol 700. Springer, Cham. https://doi.org/10.1007/978-3-319-66836-9_16
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DOI: https://doi.org/10.1007/978-3-319-66836-9_16
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