Calculating robustness indices of distributedcomputer systems

It is most claimed when efficiency indices of functioning distributed computer systems (CS)are expressed by means of mathematical expectations of serviceable resources and of other randomvariables.Method for functioning analysis of large-scale CS in transient and stationary modes is presented.It allows to deduce analytical formulae for a set of CS robustness indices from uniformmethodological positions.The method essence is mentioned below. System of differential equations for probabilities ofCS states (describing homogeneous Markovian process) is derived. It is reduced to one linearequation in partial derivatives by using technique of generating function. Consecutive differentiationon a system variable allows to obtain ordinary differential equation for a row of moments ofarbitrary order (for example moment of the first order is mean of number of CS serviceable elementarymachines).Calculation models of robustness indices of CS were constructed on the presented method basis.The differential equations for calculating probabilities of CS states and also initial and centralmoments of arbitrary order for number of system serviceable machines were deduced. Solutionsof equations for transient and stationary modes of functioning CS were obtained.

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