Anisimov, V. V.2016-02-082016-02-0820020257-0130http://hdl.handle.net/11693/24584The asymptotic behavior of a queueing process in overloaded state-dependent queueing models (systems and networks) of a switching structure is investigated. A new approach to study fluid and diffusion approximation type theorems (without reflection) in transient and quasi-stationary regimes is suggested. The approach is based on functional limit theorems of averaging principle and diffusion approximation types for so-called Switching processes. Some classes of state-dependent Markov and non-Markov overloaded queueing systems and networks with different types of calls, batch arrival and service, unreliable servers, networks (MSM,Q/MSM,Q/1/∞)r switched by a semi-Markov environment and state-dependent polling systems are considered.EnglishAveraging principleDiffusion approximationFluid limitMarkov processNetworksQueueing systemsSemi-Markov processSwitching processArticle10.1023/A:1014371517599