Redundancy and Renewal of Servers in Opened Queuing Networks

G. Sh. Tsitsiashvili; M. A. Osipova

doi:10.66721/z1kr4z31

Authors

G. Sh. Tsitsiashvili Institute of Applied Mathematics, Far Eastern Branch of RAS Author
M. A. Osipova Institute of Applied Mathematics, Far Eastern Branch of RAS Author

DOI:

https://doi.org/10.66721/z1kr4z31

Abstract

An opened queuing network with a redundancy and a renewal of servers is considered. To calculate a stationary regime in this network directly it is necessary to consider sufficiently complicated and large system of linear algebraic equations. A special control of the network route matrix allows to use product theorems and so to simplify these calculations significantly. At first the network with a variable set of servers is analyzed. Then we suppose that an each server of the network may fail and be restored independently. At last we consider different variants of servers redundancy in the opened network. Considered network models are on a joint of queuing and reliability theories.

References

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[2] Tsitsiashvili G.Sh., Osipova M.A. New Product Theorems for Queuing Networks // Problems of Information Transmission. Vol. 41, № 2, 2005. Pp. 171-181. DOI: https://doi.org/10.1007/s11122-005-0021-7

[3] Gnedenko B.V., Beliaev Yu.K., Soloviev A.D. Mathematical methods in reliability theory. Moscow: Science, 1965, 524 p. (in Russian).