Book Description

The monograph is devoted to an investigation of co-operative effects in stochastic models. It includes original results of the authors in the last decade. The main object of the monograph is an analysis of an influence of a stochastic model structure on its characteristics. Problems of a co-operation and a decomposition are actual in a solution of a lot of concrete problems. These problems are: a parallelisation of algorithms and programs, a modelling of supercomputers, computer networks, systems of mobile telephones catastrophes in complex systems, a design and an improvement of technological and economical processes etc. The co-operative effects create a source of significant dependencies between complex system characteristics under large random disturbances. To analyse these effects is necessary to create special methods based on structural analysis of multi-element stochastic models together with majoral asymptotic bounds of these models characteristics. At the same time it demands to develop new approaches to a processing of statistical data and a skill in an usage of the probability theory limit theorems and related asymptotic series and bounds. A choice of the monograph material is defined as by initial applied problems so by probability methods of their solution. Conditionally the monograph may be divided into two parts. First of them contains four sections devoted to a finding of the co-operative effects and to a development of new related analytical and numerical methods. This part has presumably methodological character and creates a theoretical base of an investigation of applied stochastic systems. Second part contains three sections devoted to a solution of different applied problems. It has some interesting substantial results.