Optimal state estimation of semi-synchronous event flow of the second order under its complete observability

We consider the optimal estimation problem for the states of a semi-synchronous event flow of the second order with two states; it is one of the adequate mathematical models for an incoming stream of claims (events) in modern digital integral servicing networks, telecommunication systems, satellite communication networks. We find an explicit form for posterior probabilities of the flow states. The decision about the flow state is made with the maximal a posteriori criterion

Optimal estimation of the states of synchronous generalized flow of events of the second order under its complete observability

We consider the optimal estimation problem of the states of synchronous generalized flow of events of the second order with two states; it is one of the mathematical models for an incoming stream of claims (events) in digital integral servicing networks and which is related to the class of Markov chains. The observation conditions for this flow are such that each event is accessible to observation. We offer the optimal estimation algorithm for the flow states, where the decision about the flow state is made by criterion of a posteriori probability maximum. The results of the analytical calculations of a posteriori probability and the simulation experiments with numerical results are presented

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

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