This paper is focused on the problem of optimal estimation of the states (or the problem of filtering the intensity process) of the modulated semi-synchronous integrated flow of events, which is one of the mathematical models for an incoming streams of events (claims) in computer communication networks and which is related to the class of Markovian arrival processes (MAPs). The flow is considered in presence of a constant dead time. The algorithm for optimal estimation of the flow states is proposed. The decision about the flow state is made according to criterion of a posteriori probability maximum. This criterion allows to find the most complete characteristic of the flow state, which could be received from observations of the flow. The criterion minimizes the total probability of making a wrong decision. Also simulation experiments and numerical results are presented.