Analytical model for calculating the performance plan of distributing multiprocessor system resources in solving the problems of special class

A model of multiprocessor system designed to solve the tasks that are parallelized on weakly dependent calculations is considered. As a model, multiservice queuing system with apparent losses, Poisson incoming flow, and general service time distribution functions of tasks is used. Recursion formulas for calculating the stationary probability distribution of states and the explicit expressions for the probability of system failure for different types of tasks are obtained. In this model, a method for assessing the capacity of a multiprocessor system for a given resource allocation static plan is suggested.