Waiting time analysis for G/G/1 queue

The paper presents two methods for determining the average waiting time for G/G/1 queue: he method of scale averaging and approximation and the approximation of the sum of the elements to find a solution to Lindley’s integral equation. The practical significance of studying queues with dependent arrival processes is obvious, since exact analytical or numerical solutions are usually not available for G/G/1 system; the operations to investigate network traffic on IP networks where each type of traffic is mapped to a distribution law. The distribution functions (Weibull and Pareto) of time parameters were obtained in Easy Fit data analysis program. The traffic was captured using Wireshark traffic analyzer program. The approximation of PMRQ in the average waiting time in TES+/G/1, MMRR was compared with the analytical solution for the same value in case of the solution of the spectral method of Lindley’s integral equation and the error was about 4-14% which is acceptable. The comparison of methods of approximating network traffic allows to estimate the average waiting time of the packet using statistical data analysis, which makes it possible to improve the quality of service and predict the traffic behavior.