Algorithm of estimationfor number of states and state rates of MC-flow.

The MC-flow is widely applied as model of an input process of events in queuing theory. The MC-flow is a doubly stochastic Poisson process in which the current rate is determined or modulatedby a continuous-time Markov chain. And the model of MC-flow contains following parameters: state rates, parameters of exponential distribution of sojourn times, matrix of transitionprobabilities. It is necessary to estimate parameters of the MC-flow using only a observations of a real flow of events (real traffic trace).For definition of number of states of the MC-flow using real traffic trace it is necessary to findstationary state intervals in the real trace [1]. Then it is necessary to estimate state rates on theseintervals. After that state rates estimations {Ґлˆ1i) ,Ґлˆ (2) ,Ў¦,Ґлˆ (k )} need to be grouped on closeness oftheir values. The following criterion of closeness of values of estimations in group is offered: the value for the group {ˆ (i) , ˆ (i 1) , , ˆ ( j)}Lij = Ґл Ґл - Ў¦ Ґл , calculate by the following formula( ) ( )( )ˆ ˆ( )1 ˆ1j i ij j l l i c L j i Ґл −ҐлҐл− - ҐТ is less than reassigned value с0. The recursive algorithm for a finding of compact groups of the estimations is offered. The number of compact groups is an estimation of number of states of the MC-flow. The estimation of intensity of a state is calculated by formula: ˆ ˆ ( ) ˆ ( )jl l ij j l i s s i L n = n Ґл = Ґл =ҐТ Ґл ҐТ .The numerical results of functioning of algorithm of estimation for number of states and staterates of MC-flow are presented.

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