β Scribed by Vladimir V. Kalashnikov (auth.)
No coin nor oath required. For personal study only.
The material of this book is based on several courses which have been delivered for a long time at the Moscow Institute for Physics and Technology. Some parts have formed the subject of lectures given at various universities throughout the world: Freie Universitat of Berlin, Chalmers University of Technology and the University of Goteborg, University of California at Santa Barbara and others. The subject of the book is the theory of queues. This theory, as a mathematical discipline, begins with the work of A. Erlang, who examined a model of a telephone station and obtained the famous formula for the distribution of the number of busy lines which is named after him. Queueing theory has been applied to the study of numerous models: emergency aid, road traffic, computer systems, etc. Besides, it has lead to several related disciplines such as reliability and inventory theories which deal with similar models. Nevertheless, many parts of the theory of queues were developed as a "pure science" with no practical applications. The aim of this book is to give the reader an insight into the mathematical methods which can be used in queueing theory and to present examples of solving problems with the help of these methods. Of course, the choice of the methods is quite subjective. Thus, many prominent results have not even been mentioned.
Front Matter....Pages i-4
Queueing Theory....Pages 5-15
Necessary Facts from Probability Theory and the Theory of Analytic Functions....Pages 16-53
Random Flows....Pages 54-79
Elementary Methods in Queueing Theory....Pages 80-102
Markov Chains....Pages 103-162
Renewal Processes....Pages 163-200
Regenerative Processes....Pages 201-232
Discrete-Time Markov Queueing Models....Pages 233-260
Markov Queueing Models....Pages 261-295
Method of Supplementary Variables....Pages 296-321
First-Occurrence Events....Pages 322-363
Back Matter....Pages 364-381
Probability Theory and Stochastic Processes; Operation Research/Decision Theory; Systems Theory, Control
π SIMILAR VOLUMES
Written by a prominent Russian mathematician, this concise monograph examines aspects of queuing theory as an application of probability. Prerequisites include a familiarity with the theory of probability and mathematical analysis. 1960 edition.
<p><B>From the reviews:</B> "The huge literature in risk theory has been carefully selected and supplemented by personal contributions of the author, many of which appear here for the first time. The result is a systematic and very readable book, which takes into account the most recent developments