Optimization of the Structure of a Real-Time Multiprocessor System

The problem of optimizing the structure of a real-time multiprocessor computing system is considered, where the structure is understood as a set of connections between processors, which can change in time under certain conditions. These conditions, firstly, are related to the physical possibility or impossibility of establishing communication between each pair of processors at certain points in time and, secondly, they must guarantee the existence of an admissible schedule for the given set of jobs with the known characteristics (directive intervals, work volumes, binding to certain processors, and the amount of memory required). Establishing such links makes it possible to switch the execution of work from one processor to another and requires some costs. The task is to determine the structure with minimal costs. It is reduced to a multicommodity flow problem in a network of a special type, for which necessary and sufficient conditions for the existence of a solution in the form of a system of linear Boolean relations for the initial parameters are obtained.