Abstract
In this paper, we investigate a queueing system consisting of an infinite buffer and two unreliable heterogeneous servers which fail alternately. If both servers are able to provide the service, they serve a customer in parallel, independently of each other. The service of a customer is completed when his/her service by any of two servers ends. The service times at the servers have PH-type (Phase-type) distributions. The input flow and the flow of breakdowns are described by the MAP (Markovian Arrival Process). An arriving breakdown is directed to the first server with some probability and to the second server with complementary probability. After a breakdown occurrence a server fails and the repair period starts immediately. A customer, whose service is interrupted by the breakdown, goes to another server if it is idle, or enters the queue otherwise We derive a condition for the stable operation of the system, calculate its stationary distribution and base performance measures. Illustrative numerical examples are presented.
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References
Vishnevsky, V., Kozyrev, D., Semenova, O.V.: Redundant queueing system with unreliable servers. In: Proceedings of the 6th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops, Moscow, pp. 383–386 (2014)
Arnon, S., Barry, J., Karagiannidis, G., Schober, R., Uysal, M. (eds.): Advanced Optical Wireless Communication Systems. Cambridge University Press, New York (2012)
Nadeem, F., Leitgeb, E., Kvicera, V., Grabner, M., Awan, M.S., Kandus, G.: Simulation and analysis of FSO/RF switch over for different armospheric effects. In: Proceedings of the 10th International Conference on Telecommunications, Zagreb, Croatia, pp. 39–43 (2009)
Letzepis, N., Nguyen, K.D., Guillen, I., Fabregas, A., Cowley, W.G.: Outage analysis of the hybrid free-space optical and radio-frequency channel. IEEE J. Sel. Areas Commun. 27, 1709–1719 (2009)
Vishnevsky, V.M., Semenova, O.V., Sharov, S.Y.: Modeling and analysis of a hybrid communication channel based on free-space optical and radio-frequency technologies. Autom. Remote Control 72, 345–352 (2013)
Dudin, A., Klimenok, V., Vishnevsky, V.: Analysis of unreliable single server queueing system with hot back-up server. Commun. Comput. Inf. Sci. 499, 149–161 (2015)
Sharov, S.Y., Semenova, O.V.: Simulation model of wireless channel based on FSO and RF technologies. In: Distributed Computer and Communication Networks. Theory and Applications, pp. 368–374. Moscow (2010)
Klimenok, V., Vishnevsky, V.M.: Unreliable queueing system with cold redundancy. In: Gaj, P., Kwiecień, A., Stera, P. (eds.) CN 2015. Communications in Computer and Information, vol. 522, pp. 336–346. Springer, Cham (2015). doi:10.1007/978-3-319-19419-6_32
Lucantoni, D.M.: New results on the single server queue with a batch Markovian arrival process. Commun. Stat. Stoch. Models 7, 1–46 (1991)
Neuts, M.: Matrix-geometric Solutions in Stochastic Models - An Algorithmic Approach. Johns Hopkins University Press, Baltimore (1981)
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Klimenok, V. (2017). Two-Server Queueing System with Unreliable Servers and Markovian Arrival Process. In: Dudin, A., Nazarov, A., Kirpichnikov, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2017. Communications in Computer and Information Science, vol 800. Springer, Cham. https://doi.org/10.1007/978-3-319-68069-9_4
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DOI: https://doi.org/10.1007/978-3-319-68069-9_4
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