Switching processes, invented by the author in 1977, is the main tool used in the investigation of traffic problems from automotive to telecommunications. The title provides a new approach to low traffic problems based on the analysis of flows of rare events and 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 networks. The book is devoted to developing the asymptotic theory for the class of switching queuing models which covers models in a Markov or semi-Markov environment, models under the influence of flows of external or internal perturbations, unreliable and hierarchic networks, etc.Content:
Chapter 1 Switching Stochastic Models (pages 19–36):
Chapter 2 Switching Queueing Models (pages 37–55):
Chapter 3 Processes of Sums of Weakly?dependent Variables (pages 57–82):
Chapter 4 Averaging Principle and Diffusion Approximation for Switching Processes (pages 83–116):
Chapter 5 Averaging and Diffusion Approximation in Overloaded Switching Queueing Systems and Networks (pages 117–174):
Chapter 6 Systems in Low Traffic Conditions (pages 175–206):
Chapter 7 Flows of Rare Events in Low and Heavy Traffic Conditions (pages 207–219):
Chapter 8 Asymptotic Aggregation of State Space (pages 221–265):
Chapter 9 Aggregation in Markov Models with Fast Markov Switching (pages 267–290):
Chapter 10 Aggregation in Markov Models with Fast Semi?Markov Switching (pages 291–313):
Chapter 11 Other Applications of Switching Processes (pages 315–327):
Chapter 12 Simulation Examples (pages 329–341):