ЗАДЕРЖКИ В ОЧЕРЕДЯХ СМО СО СТАЦИОНАРНЫМИ ПОТОКАМИ ЗАЯВОК

Abstract

During all periods of the study of telecommunications systems traffic, the analysis was based on mass service theory. The subjects of the study here are request flows to be processed by some limited performance resources. Resource constraints and the random nature of requests’ receipt lead to refusals in processing or queues. The first works devoted to the analysis of teletraffic belong to A. K. Erlang. Request flows represented flows of requests for connections in networks with channel switching. Since requests were received from a large number of independent users, the flows of such requests could be defined as stationary, ordinary with no effect, or as recurring requests, with an exponential distribution of time intervals between neighboring requests. Connection request flows to a telephone exchange node are a superposition of a large number of low-intensity flows from independent users. Therefore, the fixed Poisson flow model describes the real flows in telephone exchanges with channel switching quite well. Therefore, the stationary Poisson flow model describes real flows in telephone exchanges with channel switching rather well. The emergence of telecommunications networks with packet switching, especially multiservice networks, showed the impossibility of using Poisson flow models for their analysis. The article is devoted to the analysis of delays in queues of queuing systems with correlated stationary flows of general type requests. The traffic of packets in multiservice networks is typically characterized by a high degree of correlation. On the basis of interval methods of analysis, the relations generalizing the Khinchin-Pollaczek formula for the average value of waiting time in queuing systems with flows of the general kind of requests are obtained. The main parameters to be analyzed when outputting the above formulas are time intervals between neighboring requests. It is shown that the values of time delays in queues depend on the dispersion and dispersion index of a random value characterizing the degree of additional maintenance of processed requests.