ESTIMATION OF THE UNIFORM DISTRIBUTION PARAMETER OF UNEXTENDABLE DEAD TIME DURATION IN A GENERALIZED ASYNCHRONOUS FLOW OF EVENTS IN SPECIAL CASE.

We consider a generalized asynchronous flow of events (a generalized MMPP flow), which is a common mathematical model of a flow of elementary particles, information flows of applications operating in telecommunication and information-computer communication networks, and belongs to the class of doubly stochastic flows of events. The functioning of the flow is considered under the conditions of a random unextendable dead time distributed according to the uniform law on the interval [0, 71. A special case is considered when restrictions are imposed on the flow parameters: 2i + ai = + az, p = 1. The dead time parameter r is estimated using the moment method. The results of statistical experiments are presented. The mathematical expectation of the duration r of the interval between adjacent events of the observed flow is given by the formula The estimate 1* is found numerically from the equation of moments M(r T*) = C1, Ci = (1 / n)E;',1_1(tk+i tk); the value CI is found by simulating the observed flow. An analysis of the numerical results shows that, in the sense of the introduced criterion, an increase in the parameter T* negatively affects the quality of the estimates, which is quite natural: an increase in the parameter T* leads to an increase in the number of lost events in the initial stream. Based on the results of the study, the following conclusions can be drawn: 1) it is analytically shown that the equation of moments has a unique solution; 2) the results of simulation modeling show that the quality of the estimates in the sense of the introduced criterion (sampling variance of the estimate T*) is quite satisfactory; in this case, the bias of the estimates relative to the true value of the parameter r does not exceed hundredth values.