The book is devoted to developing the asymptotic theory for the class of switching queueing 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, are the main tools used in the investigation. Asymptotic results for processes with rare switching provide a new approach to low traffic problems, the analysis of flows of rare events and asymptotic aggregation of state space in queueing 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 queueing Markov and semi-Markov systems and networks and hierarchic models in different time scales.
1. Switching Stochastic Models.
2. Switching Queueing Models.
3. Processes of Sums of Weakly-dependent Variables.
4. Averaging Principle and Diffusion Approximation for Switching Processes.
5. Averaging and Diffusion Approximation in Overloaded Switching Queueing Systems and Networks.
6. Systems in Low Traffic Conditions.
7. Flows of Rare Events in Low and Heavy Traffic Conditions.
8. Asymptotic Aggregation of State Space.
9. Aggregation in Markov Models with Fast Markov Switching.
10. Aggregation in Markov Models with Fast Semi-Markov Switching.
11. Other Applications of Switching Processes.
12. Simulation Examples.
Prof. Vladimir V. Anisimov is Director of the Research Statistics Unit at GlaxoSmithKline, UK. He has written about 200 papers, nine books and manuals in this area.