Stochastic Queues

The book is devoted to developing of the asymptotic theory for the class of switching queuing models which covers state-dependent models in a Markov or semi-Markov environment, models under the influence of flows of external or internal perturbations, unreliable and hierarchic networks, etc. Switching processes, invented by the author in 1977, is the main tool used in the investigation. Asymptotic results for processes with rare switching provide a new approach to low traffic problems, to the analysis of flows of rare events and asymptotic aggregation of state space in queuing models. In the case of fast switching, averaging principle and diffusion approximation results are proved and applied to the investigation of transient phenomena for wide classes of overloading queuing Markov and semi-Markov networks and hierarchic models in different time scales. The book contains many practical examples and is aimed at researchers, postgraduate students and engineers specializing in mathematics, stochastic modeling and other related applications.