Abstract
We consider a multi-server queuing system that can be useful for solving the problem of reaching a trade-off between energy saving considerations and quality of customer’s service by the use of so-called backup servers. A backup server joins to the service of a customer in case the timer installed at the service beginning moment on the main server expires. Such service organization allows to avoid too much delays in the system in conditions of reasonable energy savings. The system under consideration can also be considered as a model of an unreliable system where in the case of a failure of a main server a customer is serviced by a back-up server. In this case, the time set on the timer is interpreted as the time before the breaking-down of a main server. The behavior of the system is described by two-dimensional continuous time Markov chain which is successfully analysed in this paper.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Klimenok, V., Savko, R.: Tandem system with retrials and impatient customers. Autom. Remote Control 76, 1387–1399 (2015)
Kim, C.S., Klimenok, V., Taramin, O.: A tandem retrial queueing system with two Markovian flows and reservation of channels. Comput. Oper. Res. 37, 1238–1246 (2010)
Kim, C.S., Klimenok, V., Dudin, A.: Priority tandem queueing system with retrials and reservation of channels as a model of call center. Comput. Ind. Eng. 96, 61–71 (2016)
Arnon, S., Barry, J., Karagiannidis, G., Schober, R., Uysal, M.: Advanced Optical Wireless Communication Systems. Cambridge University Press, Cambridge (2012)
Vishnevsky, V., Kozyrev, D., Semenova, O.: Redundant queueing system with unreliable servers. In: Proceedings of the 6th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), Moscow, pp. 383–386 (2014)
Vishnevsky, V., Semenova, O., Sharov, S.: Modeling and analysis of a hybrid communication channel based on free-space optical and radio-frequency technologies. Autom. Remote Control 72, 345–352 (2013)
Sharov, S., Semenova, O.: Simulation model of wireless channel based on FSO and RF technologies. In: Proceedings of the International Conference on Distributed Computer and Communication Networks, Theory and Applications (DCCN-2010), Moscow, pp. 368–374 (2010)
Mitrani, I.: Trading power consumption against performance by reserving blocks of servers. In: Tribastone, M., Gilmore, S. (eds.) EPEW 2012. LNCS, vol. 7587, pp. 1–15. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36781-6_1
Mitrani, I.: Managing performance and power consumption in a server farm. Ann. Oper. Res. 202, 121–134 (2013)
Mitrani, I.: Service center trade-offs between customers impatience and power consumption. Perform. Eval. 68, 1222–1231 (2011)
Shwartz, C., Pries, R., Tran-Gia, P.: A queueing analysis of an energy-saving mechanism in data centers. In: Proceedings of the International Conference on Information Networking, pp. 70–75 (2012)
Kim, C.S., Dudin, A., Dudin, S., Dudina, O.: Hysteresis control by the number of active servers in queueing system with priority service. Perform. Eval. 101, 20–33 (2016)
Klimenok, V., Dudin, A., Samouylov, K.: Analysis of the BMAP/PH/\(N\) queueing system with backup servers. Appl. Math. Model. 57, 64–84 (2018)
Neuts, M.: Matrix-Geometric Solutions in Stochastic Models. The Johns Hopkins University Press, Baltimore (1981)
Acknowledgments
This work has been financially supported by the Russian Science Foundation and the Department of Science and Technology (India) via grant No 16-49-02021 (INT/RUS/RSF/16) for the joint research project by the V.A. Trapeznikov Institute of Control Problems of the Russian Academy Sciences and the CMS College Kottayam.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Klimenok, V., Dudin, A., Shumchenia, U. (2018). A Multi-server Queueing System with Backup Servers. In: Dudin, A., Nazarov, A., Moiseev, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM WRQ 2018 2018. Communications in Computer and Information Science, vol 912. Springer, Cham. https://doi.org/10.1007/978-3-319-97595-5_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-97595-5_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-97594-8
Online ISBN: 978-3-319-97595-5
eBook Packages: Computer ScienceComputer Science (R0)