On the Quality of Dispatching of Mondrian-Type Arrays in Grid Systems

Abstract

Grid systems of centralized architecture, with multisite dispatching, characterized by the ability to execute a multiprocessor application on several parallel systems simultaneously, are modeled by a resource quadrant. The user's request for maintenance by the Grid system dispatcher is modeled by a resource rectangle with horizontal and vertical dimensions, respectively, equal to the number of time and processor resource units required to fulfill the request. Due to the exponential complexity of the optimal distribution of computational and time resources, heuristic algorithms of polynomial complexity based on the operations of dynamic integration of resource rectangles in the environment of resource rectangles are of practical value. The quality of dispatching is evaluated by a non-Euclidean heuristic measure that takes into account the area and shape of the occupied resource area. The quality of dispatching arrays of exact form with applications requiring approximately the same work, understood as the product of the number of required processors at runtime, is analyzed. In this paper, the quality of six polynomial-level algorithms is evaluated when dispatching arrays with applications of approximately the same area equal to the product of the number of required processors at the time of execution of the application. The adaptability of the analyzed algorithms is demonstrated on seven test arrays induced by Mondrian squares. Such arrays contain circular, hyperbolic and parabolic type applications. It is shown that the smallest value of the heuristic measure of H-level algorithms in length is 0.76, whereas in V-level algorithms in height, the smallest value of the heuristic measure is 0.83. At the same time, the H-level algorithm in length with a minimum deviation has the lowest value of the maximum of the heuristic measure of 0.5 + 0.59 on the test arrays of resource rectangles under consideration. When servicing arrays of exact forms with applications of approximately the same measure in Grid systems, it is recommended to use the considered polynomial H-level algorithm in length with minimal deviation.