Method of asymptotic analysis for research of parallel service multiple demands of Markovian renewal flow.
We identify the method of the asymptotic analysis in the queuing theory as a solving of equations defining any characteristics of system while performing under some limiting condition whose type depends on the models and research tasks. We consider queuing system of multiple customers with an input flow of Markovian renewal (MR(2)||M2|) with two blocks of service, each of which contains unlimited number of devices. The input flow is the Markovian renewal of the dual customers, defined by functions of distribution of lengths of intervals and a matrix of transitive probabilities - imbedded on arrival times. Durations of service of various customers are assumed to be stochastically independent, equally distributed in each block and exponentially distributed with parameters 1 and 2, accordingly. The arrived customer occupies any of free devices and after finishing of service the customers leaves system. The problem of investigation of the two-dimensional process which characterizes a number of customers in each block is considered.