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Grid computing has emerged as an important new field, distinguished from conventional distributed computing by its focus on large-scale resource sharing, innovative applications, and high-performance orientation. A Grid integrates and coordinates resources and users that live within different control domains with the goal of delivering nontrivial quality of service (QoS). Consequently, task management and scheduling is of central importance for the Grid-based systems. In this paper, we model the task dispatching and selecting on the distributed Grid computing system by a multiserver multiqueue (MSMQ) model, and propose a modeling and analysis technique based on Stochastic Petri Net (SPN) methods. An approximate analysis technique is also proposed to reduce the complexity of the model.