Ring Algorithms for Scheduling in Grid Systems

We consider the model of task scheduling in Grid systems that can be represented by the first coordinate quadrant. The process of task scheduling is based on the parity of processor resources and time resources. We previously proposed a classification of sets of multiprocessor tasks that are to be processed by a Grid system that consists of three types: circular-type, hyperbolic and parabolic task queues. We describe the polynomial time ring algorithm, apply it to a circular-type task queue, and compare our results with the optimal packing of rectangles in an enclosing rectangle of minimum area. Our comparative analysis demonstrates the applicability of the proposed ring algorithm in task scheduling in Grid systems.