Investigation of input flow for the GRID-system withadaptive providing of computing resources

We consider mathematical model of the GRID-system with adaptive providing of computingresources. The model is represented as queuing system with input MMPP-flow and server blockswhich service intervals depend on input modulating process state.We obtained an expression for characteristic function of multidimensional distribution fornumber of arrivals at each modulating process state. Input flow projection on single modulatingprocess state was particularly considered. It was shown that probability distribution of eventsnumber ns arriving in the flow at modulating process state s during period t is defined as( , ) 1 ( , )2jusnsP ns t e h ust dusƒ−−ƒ=ƒ  ,where h(us,t) = R exp{Bs(us)t}E, R is row vector of stationary distribution of modulating processstate, E is unit column vector, Bs(us) is a matrix with elements which are equal to elements of infinitesimalmatrix Q for modulating process except the single element bss which is equal to(jus 1)e − ƒs + qss ; ƒs is input flow intensity at state s, qss is element of the matrix Q.First moment and general form of differential equations system for second and mixed momentsof the considered distribution are obtained in the paper also. Results of the paper can be appliedto GRID-system construction practice.

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