Geodesic
Multi-server queueing system with reserve servers
Journal of the Belarusian State University. Mathematics and Informatics, Tome 3 (2019), pp. 57-70

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In this paper, we investigate a multi-server queueing system with an unlimited buffer, which can be used in the design of energy consumption schemes and as a mathematical model of unreliable real stochastic systems. Customers arrive to the system in a batch Markovian arrival process, the service times are distributed according to the phase law. If the service time of the customer by the server exceeds a certain random value distributed according to the phase law, this server receives assistance from the reserve server from a finite set of reserve servers. In the paper, we calculate the stationary distribution and performance characteristics of the system.
Keywords: queueing system; reserve servers; batch Markovian arrival process; phase type distribution; stationary distribution; performance characteristics. 
@article{BGUMI_2019_3_a4,
     author = {V. I. Klimenok},
     title = {Multi-server queueing system with reserve servers},
     journal = {Journal of the Belarusian State University. Mathematics and Informatics},
     pages = {57--70},
     publisher = {mathdoc},
     volume = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/BGUMI_2019_3_a4/}
}
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V. I. Klimenok. Multi-server queueing system with reserve servers. Journal of the Belarusian State University. Mathematics and Informatics, Tome 3 (2019), pp. 57-70. http://geodesic.mathdoc.fr/item/BGUMI_2019_3_a4/