Estimate average queue length and transmission delay in network node

We have considered the problem of non-Poissonian traffic obtained by recording statistical characteristics at given packet arrival rates was considered. To study the statistical characteristics of a multimedia stream, we have studied multicast data transmission where the server generates a data stream and sends it over the network to connected clients. The load intensity of the resulting packet flow at each time point depends on which applications service the sources of requests and on the ratio of their number for different applications. The traffic patterns are also affected by the technological features of the service algorithms applied. Based on measurement histograms and approximate functions for the distribution of time intervals between packet arrival and the packet duration, we have obtained their approximating expressions as the sum of damped exponents satisfying the properties of the distribution function of a random variable. Calculations are performed quickly and efficiently. The approximation method has a simple algorithm. Using the spectral method for solving the Lindley integral equation for the G/G/1 queuing system, we obtained the values ​​for the average packet delay time in the network and the queue length. The accuracy of the solution obtained depends on the accuracy of the approximation of the distributions with a «heavy» tail used.