Scheduling Calculations for a Multiprocessor System in Real Time

The problem of scheduling computations in a multiprocessor system is considered for the case when, at some time instants, requests for the execution of job packages with known characteristics are received. Interrupts and switching from one processor to another are allowed. In the first formulation, the composition of all complexes and the characteristics of tasks are known in advance. In the second setting, this information becomes known only at the time of each request. It is required to determine whether there is an admissible schedule for the total set of jobs and build it in the case of a positive answer. A setting is studied in which, in addition to processors, there is a nonrenewable resource. A polynomial algorithm for solving the problem is developed, based on the construction of a network flow model and the search for the maximum flow.