Grid computing provides a powerful, virtual parallel system known as a computational Grid on which users can run parallel applications to solve problems quickly. However, users must be careful to allocate tasks to nodes properly because improper allocation of only one task could result in lengthy executions of applications, or even worse, applications could crash. This allocation problem is called the mapping problem, and an entity that tackles this problem is called a mapper. In this thesis, we aim to develop an efficient, practical, portable mapper. To study the mapping problem, researchers often make unrealistic assumptions such as that nodes of Grids are always reliable, that execution times of tasks assigned to nodes are known a priori, or that detailed information of parallel applications is always known. As a result, the practicality and portability of mappers developed in such conditions are uncertain. Our review of related work suggested that a more efficient tool is required to study this problem; therefore, we developed GMap, a simulator researchers/developers can use to develop practical, portable mappers. The fact that nodes are not always reliable leads to the development of an algorithm for predicting the reliability of nodes and a predictor for identifying reliable nodes of Grids. Experimental results showed that the predictor reduced the chance of failures in executions of applications by half. The facts that execution times of tasks assigned to nodes are not known a priori and that detailed information of parallel applications is not alw ays known, lead to the evaluation of five nearest-neighbour (nn) execution time estimators: k-nn smoothing, k-nn, adaptive k-nn, one-nn, and adaptive one-nn. Experimental results showed that adaptive k-nn was the most efficient one. We also implemented the predictor and the estimator in GMap. Using GMap, we could reliably compare the efficiency of six mapping algorithms: Min-min, Max-min, Genetic Algorithms, Simulated Annealing, Tabu Search, and Quick-quality Map, with none of the preceding unrealistic assumptions. Experimental results showed that Quick-quality Map was the most efficient one. As a result of these findings, we achieved our goal in developing an efficient, practical, portable mapper
