Modeling Allocation of Parallel Flows With General Resource

Abstract: This study considers the problem of optimal allocation of a common resource in systems with parallel structures. We propose a method of solving such problems in models complicated by randomness and possible (but not required) near singularity of the constraint matrix, which commonly arises in systems with parallel processes. The method finds solution of the problem by first solving a simpler problem with an "expanded" constraint set, and then performing a directed transition to the solution of the original problem. In completing these steps the method takes account of the stochastic nature of the problem.