A hierarchical multiprocessor system designed to control complex production facilities is investigated. It is shown that distributed computing in such systems is performed at the strategic, tactical and functional-logical levels. Since the control process unfolds in real physical time, in which both digital controllers and a control computer operate, when developing software for such systems, the problem of estimating the time complexity of control algorithms arises. A matrix equation is obtained that describes a closed multi-loop control system, in which data asymmetry and pure delays are taken into account. It is shown that time delays worsen the characteristics of transient processes during the transition of an object to a steady state of operation. A method for soft estimation of time complexity is developed, based on the sequential simplification of the semi-Markov process, represented by the algorithm, with recalculation of its time characteristics at each step. It is shown that the method allows one to estimate both data distortions and delays in the feedback loops.