Evaluation of service quality parameters in w/γ/1 correlated queue system

Abstract

QoS evaluation (Quality of Service), such as delay, packet jitter variation, packet loss probability is one of the most pressing tasks in designing and predicting the operation of infocommunication networks. At the same time in the furtherance of this goal problems arise concerning features of streams being processed in infocommunication networks: difference from the simplest ones, available self-similarity properties, correlations within and between time sequences of maintained packets. That said, most of analytical works on infocommunication networks and their operation parameters evaluation are based on the assumption of streams’ independence. The article presents a queuing model that enables to consider cross-correlation of time intervals between packets and processing intervals of packets in queue. Analysis of correlated queue in G/G/1 type system is given based on the above model. Weibulla distribution is regarded as an example of randomization of time intervals between packets and gamma distribution as packets’ processing intervals. Values were obtained for delay and queue delay variation estimates if time intervals’ correlations are available between packets and packets’ processing intervals. Copula theory is used for the task in operation. There is analysis given of time intervals’ cross-correlation between packets and packets processing intervals, which results in revealing dependence between Pearson correlation coefficient and Farley — Gumbel — Morgenstern copula parameter. There is also analysis given of behavior for delay and delay variation depending on copula parameter, and, therefore, on degree of correlation in queue. The attained results highlight the need to consider correlations in analyzing traffic-processing systems in infocommunication networks.