The generalized problem of software system resources distribution

The paper presents the statement and the solution of the optimization problem for a dynamic system with a linear output and the quadratic performance criterion. System uncertainty is described by the observed second-order stochastic process. The need to optimize resource distribution of software systems gives practical justification to the problem. In such interpretation, the uncertainty of a system describes user activity and the output describes running queries or the volume of the requested memory. The goals of optimization are formalized by the quadratic performance criterion of the general form. The criterion, in particular, summarizes two problems of resource distribution of software systems discussed earlier. The objective functional makes it possible, in particular, to state the problem of adequate program resources allocation (of threads, memory, etc.), penalizing for unlimited spending. To solve the problem, the method of dynamic programming is used. The optimal strategy is a linear combination of the output and state predictions up to the control horizon. In the context of computational complexity of the optimal strategy, the possibility of its simplicity and of using the locally-optimal strategy is discussed.