Large distributed information systems (LDIS) are the basis for digitization of production processes in industry, transport and public administration. Organization of their engineering servicing (ES) for timely restoration in case of failure is a topical issue of scientific research. LDIS consists of computer complexes which include both major and additional elements. The literature provides no solution which allows us to define the engineering servicing resources (ESR), considering the variable significance of elements of computer complexes. The task was first set and solved in this publication.
      For solution of this task, we applied the mean dynamic method. This method was chosen because it makes it possible to obtain a system of differential equations for describing the change over time of the mean number of elements in different states.
      Analysis of the differential equations system solution allowed us to find analytical expressions for determining ESR – the number of staff and the number of spare elements- at which the mean number of computer complexes in perfect state reaches its maximum. The results are applicable when calculating the ESR of real LDIS. They can also serve in simulation modeling as initial approximations of the optimal volume of ESR if it necessary to take into account the specific features of the system. In addition, the solution of differential equations makes it possible to solve the problem of optimizing the resources for servicing the LDIS according to economic criteria, when the costs of staff and spare elements are comparable with the income from operating the computer complexes.