Real-Time Estimation of Traffic Self-Similarity Parameter in Simulink with Wavelet Transform

Abstract

The article describes P/M/1/K queuing model and Hurst parameter estimation unit with Wavelet Transform for real-time estimation of the traffic self-similarity parameter in Simulink. It consists of simulation results, which show the possibility to estimate Hurst parameter in real-time by means of Wavelet transform. It is offered to iteratively calculate the averaged Hurst parameter estimation, which improves the accuracy to the accuracy of the estimation over entire traffic series and in some cases even higher, as it has been shown in simulation results analysis. The estimation deviations have been analyzed as well as variance of such deviations. The results also give directions for further research to improve accuracy of traffic parameters estimation.

Spline-approximation-based restoration for self-similar traffic

“…Authors of the works [7][8][9] propose to apply an envelope curve to the values of self-similar traffic, while the approximation determines the use of a definite distribution law. In this case, if the self-similar traffic has "pulsations" and "bursts" at different instants of time, then the error of such estimations can be quite significant.…”

“…Most often, researchers use the Simulink package of Matlab [8,9] as a simulation environment. But the work [8] states that during simulations in Simulink of the Matlab environment, traffic packets are generated only for one set distribution, in this case -the Pareto distribution.…”

“…But the work [8] states that during simulations in Simulink of the Matlab environment, traffic packets are generated only for one set distribution, in this case -the Pareto distribution. The work [9] suggests using the SimEvents package, which allows generating packets for different distributions, but such an approach makes simulation quite complicated due to a large number of additional parameters. At the stage of self-similar traffic model selection, it is necessary to consider that traffic characteristics are quite dynamic and depend on a significant number of parameters and network settings.…”

Using spline-extrapolation in the research of self-similar traffic characteristics

“…Taking into account the above facts, it is possible to note the urgency of solving the problem of predicting self-similar traffic. A number of works by the authors are devoted to the problem of predicting self-similar traffic [5][6][7][8][9][10][11][12]. The proposed models and methods of forecasting are not universal, so autoregression models [5] are used only for processes with poorly expressed selfsimilarity, and models ARIMA and FARIMA [6][7][8] are recommended only for short-term forecasts.…”

“…For demonstration of simulation results, windows are used that record the results of servicing traffic in a QS of the WB/M/1/Ktype in real time: Average waiting time, Average queue length, Count in queue is queue length packets and Count out is number is lost of packets [12].…”