Optimal state estimation in MAP event flows with unextendable dead time

We consider the optimal estimation problem for the states of a MAP event flow with two states; it is one of the mathematical models for an incoming stream of claims (events) in digital integral servicing networks. The observation conditions for this flow are such that each event generates a period of dead time during which other events from the flow are inaccessible for observation and do not extend the dead time period (unextendable dead time). 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. We show numerical results obtained with our explicit formulas and imitational modeling.