Dispatching Arrays with Tasks of Equal Resource Measure in GRID Systems

The role of computing and time resource management of parallel systems when dispatching multiprocessor tasks increases significantly in Grid systems consisting of multiple sites with multiprocessor computing systems, with multisite execution of a parallel task on several sites simultaneously. Such Grid systems of centralized architecture are modeled by the resource quadrant. 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. Examples of the exponential complexity of dispatching resource rectangles are the stacking of consecutive resource squares and consecutive resource rectangles of equal perimeter into an enclosing rectangle of the minimum area. Heuristic algorithms of polynomial labor intensity 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 assessed by a non-Euclidean heuristic measure that takes into account the area and shape of the occupied resource area. The quality of dispatching arrays with requests of the same resource measure equal to the product of the number of required processors and runtime is analyzed. In this paper, the quality of three polynomial level algorithms in height and three polynomial level algorithms in length (with the nearest approach to the level, with exceeding of the level and with minimum deviation) is evaluated when dispatching arrays with requests of equal resource measure. Such arrays belong to the parabolic quadratic type and contain user's tasks of circular, hyperbolic and parabolic type. On five test arrays, it is shown that H-finite-level algorithms with a with the nearest approach to the level and with minimum deviation have the smallest value of the maximum of the heuristic measure of 8.45. When servicing arrays with user's tasks of the same resource measure in Grid systems, it is recommended to use the polynomial Н- finite-level algorithm in length with the nearest approach to the level which is introduced in this paper.