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Article:

# Consecutive detection of the disorder moment of hidden markov chain supervisions at unknown parametres in a problem of separation of group traffic of a network with package switching

Keywords:

A.M. Andreev – Associate Professor, Department «Computer systems and networks»,
Bauman Moscow State Technical University
S.V. Usovik – Post-graduate Student, Bauman Moscow State Technical University
S.M. Jammoul – Post-graduate Student, Bauman Moscow State Technical University

While doing research work of telecommunication networks with packet switching, it’s interesting to try to find a solution for the following problem – to search for a moment of statistics change (disorder problem) of the observed accidental process created by the hidden Mar-kov chain. The reason for this is mainly that the traffic model of telecommunication networks with packet switching is described using a mathematical tool of the hidden Markov chain. It’s required to find traffic properties disorders and the moments when they appear while analyzing data flows of different network devices in telecommunication networks multicast channels when the exact source of these data is not known beforehand. The article defines and solves the general problem of the consecutive search of the disorder moment of the observed accidental process of traffic arrival described using a mathematical tool of the hidden Markov chain and an algorithm of cumulative sums (ACS) at the pre-set type I error. While solving this problem, we have solved two specific tasks:
1. The task to find a value of minimal observation scope required to obtain the assessment of traffic model parameters closest to the true value. 2. The task to detect asap the model parameters disorder given prior uncertainty of the model parameters after the disorder and the moment the disorder arose.
The first specific task is solved using EM method for tests implementations with the set parameters. In order to solve the second specific test, we have revealed a threshold rule to make a decision if the observed model parameters jump. Threshold value is chosen given the risks to make an erroneous decision. Solution of the specific tasks defined in the article determines the possibility and peculiarities of use of the consecutive disorder moment detection method while observing the hidden Markov chain with unknown parameters. The general problem solution is achieved by using ACS to the assessment of maximum likelihood of the observations created by the hidden Markov chain. The maximum likelihood of the observations is assessed by using the algorithm of forward trace evaluating the probability of observations appearance for the specific (current) traffic model. Use of the obtained in the article results allows to define the moment of disorder appearance at the pre-set type I error value more accurately than when packets recurrences intensities and packet intervals are considered. We have checked how the algorithm works using the example of parameters observation of a real networks traffic with packet switching. Applying the stated in the article results, we can solve the problem of multicast traffic separation, thus allowing to solve the problem of identification of separate sources traffic in the grouped arrivals.

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May 29, 2020

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