About the average maximum values of queues in queuing systems

In the classical theory of queuing systems, the assumption of mutual independence of events is fundamental, so we propose to consider the basic principles of the interval method of traffic analysis, which allows us to replace analysis of time intervals between neighboring requests and time intervals for processing requests by analyzing one random variable, i. e. the number of requests received during successive intervals of time for processing each of requests. The concepts of mean maximum values of queues and limiting maximum values are introduced. It is shown that the limit maximum value in a queue will be the largest of the possible maximum values for a given total value of requests in queues during one service cycle. The mean maximum score is the average of the maximum queue values. To determine the characteristics of traffic, we use the well-known «Leaky_bucket» algorithm. The proposed traffic model is based on the total number of requests during their processing cycles. Experimental modeling of the proposed method showed that variance and correlation properties of a specified random variable for a given load completely characterize the average queue size in a queuing system.