Introduction:A control system for a data processing network interacts with the network by sending commands and receiving responses. Such a control system is responsible for the network viability, and therefore should be analyzed, in particular, in terms of behavior over time, without exhaustive search for possible control options.Purpose:Studying and analyzing the behavior of a control system in a data processing network using mathematical modeling based on finite automata theory, and performing computer simulation of the obtained theoretical positions.Results:A finite state machine is constructed, presented in the form of a transition graph, reflecting the temporal behavior of a part of a specific control system in the data processing network by Plug-and-Play manager. Rules of conduct are specified, and the problem of the manager FSM analysis is defined. As a result, the control vector types have been obtained which lead the PnP manager to the correct temporal behavior. Computer simulation was performed using a script program in MatLab mathematical package. The simulation results are presented as time diagrams of finite state machine transitions. Its behavior varies depending on the incoming signals and the starting state of the machine. On the time diagrams, you can trace the behavior and transitions between states, estimate the frequency of getting into a particular state, or bypass the machine states.Practical relevance:The control vector types found for the PnP manager without an exhaustive search do not lead to incorrect situations in network data processing.

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This paper discusses the dynamical behavior Plug-and-Play manager during time with different initial condition and external influence. A mathematical model based on linear dynamic system theory is described in the paper.