Switching Queueing Networks

• Published in: Network Performance Engineering pp. 258 - 283
• Main Author: Anisimov, Vladimir V.
• Format: Book Chapter
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2011
• Series: Lecture Notes in Computer Science
• Subjects: asymptotic aggregation; averaging principle; diffusion approximation; heavy-traffic; networks; Queueing models; switching process
• ISBN: 3642027415; 9783642027413
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-642-02742-0_12

The paper is devoted to the asymptotic investigation of switching queueing systems and networks. The method of analysis uses the limit theorems of averaging principle and diffusion approximation types for the class of ”Switching Processes” developed by the author. This class can be used to describe hierarchic stochastic systems with random switching due to internal and external factors. Different classes of overloaded switching queueing models (heavy traffic conditions) operating under the influence of internal and external random environment, e.g. state-dependent models with Markov and semi-Markov switching, are investigated. The approximation of models with fast switching by simpler models with aggregated state space and averaged transition rates are also considered. These results form a new methodology for the investigation of transient phenomena for queueing models in heavy-traffic conditions and provide an analytic approach to performance evaluation of queueing networks of a complex structure. Different examples are considered.