Investigation of the parallel service system with multiple claims of the Poisson process

One of the main principles in designing the present-day computer networks is the parallelismin the information processing. The aim of this article is to analyze the mathematical model withthe k-service blocks functioning in parallel.The queuing system with the parallel service of the multiple claims is consided and eachblock contains an unlimited number of facility. The Poisson process of k-claims with the ƒ parameterenters the system, k clams come into the system simultaneously at the moment of eventoccurrence.The service discipline is as follows: one of these claims comes into the first service block, thesecond one - into the second service block and so on. Every claim comes into any of the vacantfacility where it is served during a stochastic time distributed according to the exponential lawwith the parameters μ1, μ2,…, μk respectively.The state of the system is defined by the number of the occupied facilities in each serviceblock. In this paper the method of generating functions is applied, it allows to define not only thekind of the generating function, but also to write down the main probabilistic characteristics of kdimensionalMarkov chains characterizing.

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