The optimal states evaluation of modulated semisyncronous integrated flow of events

There is studied the modulated generalized semisyncronous flow of events, which is one of the mathematical models of informational flows of events functioning in Integrated Services Digital Networks (ISDNs). The flow intensity is a piecewise constant stationary random process A(t) with two states X , X (X > X ). During the time interval, while X(t) = X , there is a Poisson flow of events with intensity X , i = 1,2 . The transition of process A(t) from one state to another state can occur at any time. The duration, while process A(t) stays in a first state, is distributed according to the exponential law with parameter p. At the same time, after the event arrives the process A(t) can change the state to X with probability р or stay in the first state X with probability 1 - р. The duration, while process X(t)stays in a second state, is distributed according to the exponential law with parameter a. At the moment of state changing from second state to first state additional event in a state X is initiated with probability 5. The process X(t) is considered in a steady-state conditions. The explicit formula for a posteriori probability is found and decision is made according to criterion of a posteriory probability maximum. Numerical results obtained by simulation are given.

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