Optimum estimation of conditions of generalized semisynchronousstream of events in the conditions of non-extended dead time.

Generalized semi-synchronous flow of events which intensity is piecewise constant stochastic process λ(t) with two states λ₁ and λ₂ (λ1 > λ2) is considered. On the interval when λ(t) = λ_i , Poisson flow of events takes place with the intensity λ , i = 1,2. Transition from the first state of the process λ(t) into the second is possible only at the moment of event arrival, thus, the transition is carried out with probability p (0 < p< 1); with probability 1 - p process λ(t) remains in the first state. In this case the time of being λ( t) in the first state is a random variable with exponential distribution function F1(τ) = 1 - e- . Transition from the second state of process into the first one can occur at any moment of time. Thus, the time of being λ(t) in the second state is distributed according the exponential law: F₂(τ) = 1-e . By transition λ(t) from the second state into thefirst an additional event is initiated with probability 5 (0 < 5 < 1). Each registered event follows by the interval of fixed length T (dead time) during which other events of initial generalized semisynchronous flow of events are unobservable. Those events which appeared during the dead time do not cause prolongation of the period (not lasting dead time). Upon termination of dead time the first event creates the period of dead time of duration Т, etc. The problem of optimum estimation of the states of generalized semi-synchronous flow of events under condition of not lasting dead time is considered. The explicit formula for posterior probability of the first state of flow is obtained. The algorithm for posterior probability calculation w(λ₁ | t) is formulated. The decision on process state λ(t) is made taking into account the criterion of maximum of a posteriori probabilities: if w(λj | t) > w(λ_i | t), i = 1,2, i ≠ j then the estimation of process state is λ(t) = λj. Numerical results obtained by making use of the explicit formula and by simulation are given.

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