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Semi-Markov models of two-phase asynchronous lines with storage

A significant portion of modern production and telecommunication systems include asynchronous lines for the transmission of material and information flows. In this case, to increase the system reliability storage units are installed between the equipment units, performing various functions. Thus, in information systems, storage units are used to store information, in energy systems – to accumulate energy, in production systems – to create an interpretational stock of blanks, etc. Mathematical modeling of asynchronous lines allows us to evaluate the predicted characteristics of their reliability and operational efficiency at the design stage, which helps to minimize subsequent operating costs. In this connection, the urgent task of developing mathematical models of asynchronous lines, taking into account their application features and structure, as well as the parameters of the interpretational storage device, arises. To solve this problem, it is advisable to use the methods of semi-Markov processes theory with general state space. This allows to soften the known restrictions on the distribution laws of random variables characterizing the system stay in certain states and transitions from one state to another. The article presents the developed semi-Markov models with discrete-continuous phase space states for the analysis of the functioning of a two-phase asynchronous line. We consider two modes of its operation: only via storage device and only by direct transmission. Based on the use of the semi-Markov model and the asymptotic phase merging algorithm, we obtain approximate expressions for finding the reliability stationary characteristics of the functioning of the systems under consideration. The indicated dependencies are described in mathematical expectation terms and are applicable to arbitrary distribution laws of random variables characterizing the system. Someone can quite easily implement proposed models using common mathematical packages. It is shown that semi-Markov models of two-phase asynchronous lines make it possible to determine the main reliability indicators with acceptable accuracy, taking into account the dependence of these indicators on the capacity of the interpretational storage device and its operating mode. This makes it possible to conduct a comparative analysis of the operating modes under consideration, to solve optimization problems when determining the structure and control parameters of the modeled system both during its design and during operation. Read more...