Sensitivity analysis for output performance measures in long-range dependent queueing system

Abstract

Internet traffic has been shown to exhibit characteristics that are very different from traditional telephone network traffic such as long-range dependence (LRD). Therefore, performance analysis of queueing system in LRD traffic is needed to design reliable networks under the tremendous growth of Internet traffic. In this paper, we evaluate the sensitivity of input distribution on the output performance measures. We conduct a Monte Carlo simulation based on a designed experiment in order to relate four performance measures such as the mean and the expected maximum number of requests in queue, and the mean and the expected maximum time in queue to the degree of LRD in arrival, traffic intensities and the types of distributions in G/G/1 queue. Experimental results show that mis-identification of input distributions has a significant effects on the output performances especially when one of the input distributions has LRD property. For such cases, Weibull distribution overestimated the output performances while lognormal distribution underestimated those of the LRD queues. Scope and purpose In the era of information technology, understanding the nature of queueing system associated with a network traffic is crucial for effective network management. The main feature of arrival and service times in information network traffic is LRD property. Many long-tailed distributions have been applied to the fitting of arrival and service time distributions with LRD property. The main purpose of this paper is to see the exchangability of those long-tailed distributions to LRD distributions. We generate both arrival/service time distributions from Pareto, one of the representative distributions with LRD and fit these distributions with long-tailed distributions such as Weibull and lognormal. The result of our sensitivity analysis is expected to provide the case where careful input data analyses are specially needed for the queueing network management.