Distributions in Stochastic Network Models

✍ Scribed by G. Sh. Tsitsiashvili, M. A. Osipova

• Publisher: Nova Science Publishers
• Year: 2008
• Tongue: English
• Leaves: 85
• Edition: illustrated edition
• Category: Library

✦ Synopsis

This monograph presents important research results in the areas of queuing theory, risk theory, graph theory and reliability theory. The analysed stochastic network models are aggregated systems of elements in random environments. To construct and to analyse a large number of different stochastic network models it is possible by a proof of new analytical results and a construction of calculation algorithms besides of the application of cumbersome traditional techniques Such a constructive approach is in a prior detailed investigation of an algebraic model component and leads to an appearance of new original stochastic network models, algorithms and application to computer science and information technologies.Accuracy and asymptotic formulas, additional calculation algorithms have been constructed due to an introduction of control parameters into analysed models, a reduction of multi-dimensional problems to one dimensional problems, a comparative analysis, a graphic interpretation of network models, an investigation of new models characteristics, a choice of special distributions classes or principles of subsystems aggregation, proves of new statements.

✦ Table of Contents

DISTRIBUTIONS IN STOCHASTICNETWORK MODELS......Page 3
NOTICE TO THE READER......Page 6
Contents......Page 7
Preface......Page 9
1.1. Preliminaries......Page 11
1.2. Networks with completely variable structure......Page 15
1.4. Networks with variable sets of transitions between nodes......Page 16
1.5. Interaction of networks with variable sets of nodes......Page 17
1.6. Networks with variable state sets......Page 18
1.7. Networks with variable types: opened and closed......Page 19
1.8. Additional algorithms......Page 20
2.1. Unreliable servers and common queue to renewal......Page 23
2.2. Unreliable servers and their independent renewal......Page 24
2.3. Unreliable servers and their renewal in closed network......Page 26
2.4. Unreliable transitions between nodes and theirindependent renewal......Page 29
3.1. Customers group transition between different sets of networknodes......Page 31
3.2. Appearance and disappearance of customersin network nodes......Page 33
3.3. Decrease and increase in some times numbers of customersin network nodes and group exchange between nodes by customers......Page 34
3.4. Unreliable customers......Page 35
3.5. Network with few types of customers......Page 36
3.6. Network with “negative” customers flow......Page 37
4.1. Problem formulation......Page 39
4.2. Calculation of ability to handle customers......Page 40
4.3. Minimization of vector components maximum......Page 42
4.4. Maximization of ability to handle customers by route matrix......Page 43
5.1. Product theorem......Page 45
5.2. Abilities to handle customers of opened networks......Page 48
6.1. Preliminaries......Page 49
6.2. Systems with a competition of servers......Page 50
6.3. Systems with a competition of customers......Page 53
6.4. A generalized Lindley model......Page 54
6.5. Proves of theorems......Page 57
7.1. Preliminaries......Page 63
7.2. Stationary characteristics of an aggregated system......Page 64
7.3. An aggregated system with a competition of servers......Page 66
8.2. Graphs with unreliable arcs......Page 67
8.4. Calculation of graph characteristics......Page 68
8.5. Proves of main statements......Page 71
9.1. Preliminaries......Page 73
9.2. Cooperative effects......Page 74
9.3. Individual and group risks......Page 75
9.5. Insurance of forward contracts......Page 76
Bibliography......Page 79
INDEX......Page 83