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Grid computing is a newly emerging technology aimed at large-scale resource sharing and global-area collaboration. It is the next step in the evolution of parallel and distributed computing. Due to the largeness and complexity of the grid system, its performance and reliability are difficult to model, analyze, and evaluate. This paper presents a model that relaxes some assumptions made in prior research on distributed systems that were inappropriate for grid computing. The paper proposes a virtual tree-structured model of the grid service. This model simplifies the physical structure of a grid service, allows service performance (execution time) to be efficiently evaluated, and takes into account data dependence and failure correlation. Based on the model, an algorithm for evaluating the grid service time distribution and the service reliability indices is suggested. The algorithm is based on Graph theory and probability theory. Illustrative examples and a real case study of the BioGrid are presented.