Аbоut limit values queue lengths in queuing systems WIT burst flows

The classical queueing theory studies the processing flows of requests under the assumption of sampling independence. However, the traffic of modern multiservice networks is usually strongly correlated and the methods of classical theory do not work. In this paper, we consider generalizations of the Hinchin-Polyachek formula for the mean queue length on stationary flows of requests with arbitrary correlation and the possibility of applying a generalized formula. The burst character of flows is shown on the example of video traffic. The process of formation of queues under burst traffic is considered. The concept of limit values of queues is introduced and ways of their definition are considered. To estimate the specified values of queue sizes for the entire range of traffic analysis, we obtained the appropriate ratios in which, in addition to the load factor, it is necessary to use the numbers of requests received during the active processing periods.