Analysis of the correlated queue in the G/G/1 system

This article discusses correlated queues in which the packet service time is strongly correlated with the time between packets due to the finite throughput of the input and output channels. Approaches to assessing the parameters of the functioning of networks with correlated queues are considered. An analytical method for obtaining an estimate of the packet waiting time in the network based on the copula approach is presented. The correlation properties of real video traffic are investigated, the distribution laws for the time intervals between packets and the packet processing times are determined. The Weibull distribution gave the most accurate approximation. It has been determined that the time intervals between packets and the processing times of the packets have significant cross-correlation. Estimates are obtained for the average latency of a packet in the network and for the variation of the packet delay during transmission in the G/G/1 network.