Performance modelling of generalized processor sharing systems with multiple self-similar traffic flows

Abstract

The Generalized Processor Sharing (GPS) is an important service differentiation scheme in telecommunication systems and has attracted great research interests due to the desirable properties of fairness, traffic isolation, and work conservation. The major limitation of the existing analytical performance models of GPS systems subject to selfsimilar traffic is that these models have been restricted to a simplified scenario with only two traffic flows. To overcome such a limitation, this study proposes a new flowdecomposition approach to modelling GPS systems subject to multiple self-similar traffic flows. We present and prove the existence of a feasible ordering of GPS systems based on the required and guaranteed service rates of traffic flows. With the aid of the feasible ordering, we decompose the GPS system into a group of single-queue systems and then derive the queue length distributions and loss probabilities of individual self-similar traffic flows in the original GPS system. Extensive simulation experiments are conducted to validate the accuracy of the developed analytical model.

Correlation matching method for the weak stationarity test of LRD traffic

“…The threshold γ is set to be 0.70 in the previous analysis. If γ is set to be another value, say 0.80, however, the result with respect to the stationarity test may obviously differ from that with γ = 0.70, referring [16] for details. Therefore, there are two factors that may affect the stationarity test.…”

“…Note that a commonly used model of LRD traffic is fractional Gaussian noise (fGn), see e.g., Tsybakov and Georganas [10], Nogueira et al [11], Li [12], Leland et al [13], Paxson and Floyd [14], Beran [15], Jin and Min [16]. Since there does note exist mean for LRD fGn (Mandelbrot [17]), there does not exist mean for LRD traffic.…”