Abstract
In recent years, there has been an increased interest in the application of probabilistic methods, in particular. the theory of queuing, to the evaluation of the effectiveness of the activities of management companies in the organization of the operation of technical systems of residential buildings.
 The article considers the M|G|1 service system with the possibility of breaks in the work of repair teams for basic requirements, when, for example, repair teams work on third-party orders. The optimization problem is solved from the point of view of the cost criterion. As controlled factors, the probability of a break α and its duration are proposed. Under fairly general assumptions about the behavior of the system at breaks, it is established that the optimal value of the probability α is either zero or one. Necessary and sufficient conditions are given under which a break should be implemented, i.e. α=1. With a constant duration of breaks, the conditions are determined under which α=1, and the duration of the break is optimal.
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