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The term Grid computing refers to multiple clusters of resource linked together in order to achieve a common objective. The power of grid computing lies in its capacity to aggregate widely distributed heterogeneous resources, and provide non-trivial services to users. Task management or workload management is a key issue that must be solved in grid computing, and a better scheduling scheme can greatly improve the efficiency of grid. In this paper we propose a multiple queuing scheme that employs a sorting mechanism and a trust based scheduling scheme that ensures the shortest makespan possible. In order for users to gain simultaneous access for their applications to be executed in parallel, advance reservation of resource is necessary.