Geodesic
Multichannel queueing systems with regenerative input flow
Teoriâ veroâtnostej i ee primeneniâ, Tome 58 (2013) no. 2, pp. 210-234

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We consider the multichannel queueing system with nonidentical servers and regenerative input flow. The necessary and sufficient condition for ergodicity is established, and functional limit theorems for high and ultra-high load are proved. As a corollary, the ergodicity condition for queues with unreliable servers is obtained. Suggested approaches are used to prove the ergodic theorem for systems with limitations. We also consider the hierarchical networks of queueing systems.
Keywords: multichannel queueing system; regenerative flow; ergodicity; stochastic boundedness. 
@article{TVP_2013_58_2_a1,
     author = {L. G. Afanasyeva and A. V. Tkachenko},
     title = {Multichannel queueing systems with regenerative input flow},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {210--234},
     publisher = {mathdoc},
     volume = {58},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2013_58_2_a1/}
}
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L. G. Afanasyeva; A. V. Tkachenko. Multichannel queueing systems with regenerative input flow. Teoriâ veroâtnostej i ee primeneniâ, Tome 58 (2013) no. 2, pp. 210-234. http://geodesic.mathdoc.fr/item/TVP_2013_58_2_a1/