Joint discovery and estimation of intensity of unstationary stream of calls

S.N. Teplitskaya, К.А. Ovchinnikov, V.P. Skibin

Kharkiv National University of Radio Electronics

The problem of joint detection and rating intensity of а stream applications in telecommunication system is examined. A mathematical model, which includes a flow model, procedure of estimation of parameters and threshold device, which finds that or other critical level which determines the level  of traffic intensity, is offered in the article. In algorithms which describe functioning of this mathematical model, key moments is an exposure of critical level of loading, which consists in the evaluation of trend of unstationarity and determination of achievement of critical level. During the decision of solving problem of critical loading level two possible states of loading are determined, which are described by possibility hypotheses:    – intensity of entry calls on the interval supervision    keeps a value which does not exceed some known value intensity of input stream  ,   – intensity of entry calls on the interval of supervision   exceeds a level  .
A method which determines the rules of exposure is based on the criterion of a minimum of probability error of admission at the set level of probability false detection. For the estimation of parameters the method of maximal plausibility is used. Call distribution corresponds to the Poisson model.
For estimation of traffic unstationary trend the smoothed recursive algorithm based on Robins-Monro procedure is suggested. With the use of simulation techniques, influence of different algorithm parameters on quality of critical level of intensity stream detection is analyzed. It is shown that smoothing results in decrease of fluctuation level of estimated components; the level of estimated components goes down and a shift of maximum of unstationary estimation appears. Recommendations on the use of procedure in different mechanisms of overload prevention like RED, SPD, ECN and other are given. The optimum rule of detection of threshold excesses was obtained.