Estimation of the probability density parameters of the interval duration between events in correlated semi-synchronous event flow of the second order by the method of moments

We consider a correlated semi-synchronous event flow of the second order with two states; it is one of the mathematical models for an incoming stream of claims (events) in modern digital integral servicing networks, telecommunication systems and satellite communication networks. We solve the problem of estimating the probability density parameters of the values of the interval duration between the moments of the events occurrence by the method of moments for general and special cases of setting the flow parameters. The results of statistical experiments performed on a flow simulation model are given

Estimation of the Probability Density Parameters of the Interval Duration Between Events in Correlated Synchronous Generalized Flow of the Second Order

We consider the problem of estimating the probability density parameters of the interval duration values between adjacent moments of occurrence of events in correlated synchronous generalized doubly stochastic event flow of the second order under conditions of its complete observability. The explicit form of parameter estimates is found by the method of moments and the quality of estimates within the selected criteria is established through the work of the flow simulation model. Finally, numerical results of statistical experiments obtained using computational analytical formulas and simulation modeling are given

Distribution Parameters Estimation in Recurrent Synchronous Generalized Doubly Stochastic Flow of the Second Order

We solve the estimation problem of the probability density parameters of the inter-event interval duration in a synchronous generalized flow of the second order, which can be used as a powerful mathematical model for the arrival processes in queuing systems and networks. The explicit form of the parameter estimates is determined by the method of moments on the basis of observations of the doubly stochastic flow under the recurrence conditions that are formulated in terms of the joint probability density of the durations of two adjacent inter-event intervals. The quality of the estimates is established by using the model, reproducing the flow behavior under conditions of complete observability