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Rapid advancement of communication technology has changed the landscape of computing. New models of computing, such as business-on-demand, Web services, peer-to-peer networks, and grid computing have emerged to harness distributed computing and network resources to provide powerful services. The non-deterministic characteristic of the resource availability in these new computing platforms raises an outstanding challenge: how to support quality of service (QoS) to meet a user's demand? In this study, we conduct a thorough study of QoS of distributed computing, especially on grid computing where the requirement of distributed sharing and coordination goes to the extreme. We start at QoS policies, and then focus on technical issues of the enforcement of the policies and performance optimization under each policy. This study provides a classification of existing software system based on their underlying policies, a systematic understanding of QoS, and a framework for QoS of grid computing.