Математична модель одноканальної системи масового обслуговування з двоетапним надходженням вимоги

Abstract

Any queuing system typically includes the following main components: the input stream of requests, the service device, the service queue and the output stream. To analyze the queuing system, we believe that the time of receipt of applications and time of service are random variables, the laws of distribution of which are determined by statistics accumulated in the analysis of such situations. And, of course, this problem is solved by the methods of probability theory, which are used in the theory of queuing. A mathematical model describing the functioning of the queuing system is built and analyzed. The most attractive random processes which describe the functioning of queuing systems are Markov processes. Mathematical model of a one-channel queueing system, for which the time of remand accession consists of two stages, has been presented in this article. We have built a queueing model with a two-step input flow, namely, we have found the basic probabilistic characteristics of the input flow. Particularly, the main probability characteristics of input flow and distribution of probability of number of remands, which comes during t time were found. To find the stationary distribution of the embedded Markov chain, we used the graphoanalytic method. The initial data for the article is the simplest classical queuing system model, complicated by the following: the input flow consists of two stages — the time of preparation of the remand and the time of its transportation. Such models are more approximate to the needs of the practice and allow the opportunity to consider greater number of factors influencing the service process.