Afanasyeva, L. G.; Tkachenko, A. V. Multichannel queueing systems with regenerative input flow. (English) Zbl 1306.60130 Theory Probab. Appl. 58, No. 2, 174-192 (2014); translation from Teor. Veroyatn. Primen. 58, No. 2, 210-234 (2013). Summary: We consider a multichannel queueing system with nonidentical servers and regenerative input flow. A necessary and sufficient condition for ergodicity is established, and functional limit theorems for high and ultra-high load are proved. As a corollary, an ergodicity condition for queues with unreliable servers is obtained. The suggested approaches are used to prove the ergodic theorem for systems with limitations. We also consider hierarchical networks of queueing systems. Cited in 8 Documents MSC: 60K25 Queueing theory (aspects of probability theory) 90B22 Queues and service in operations research Keywords:multichannel queueing system; regenerative flow; ergodicity; stochastic boundedness PDFBibTeX XMLCite \textit{L. G. Afanasyeva} and \textit{A. V. Tkachenko}, Theory Probab. Appl. 58, No. 2, 174--192 (2014; Zbl 1306.60130); translation from Teor. Veroyatn. Primen. 58, No. 2, 210--234 (2013) Full Text: DOI