Optimal state estimation of a generalized MAP event flow with an arbitrary number of states

We consider the optimal state estimation problem for a generalized MAP-flow (Markovian Arrival Process) with $n$ states, which is one of the mathematical models of real information flows of messages. An explicit form of the a posteriori probabilities of the states of the flow under study is found. The decision on the state of the flow is made according to the maximum a posteriori probability criterion. The results of numerical calculation of state estimates based on the constructed simulation model of a generalized MAP event flow are presented.