Job scheduling is a fundamental issue in achieving high performance on the Grids. In this paper, a hierarchical job scheduling architecture has been proposed for the Grids. The stochastic high-level Petri net (SHLPN) model of the proposed architecture and the refined model are presented. The job scheduling algorithms for an incoming job to be distributed to a waiting queue of any processor in any node of the Grid architecture is integrated by the node-selection algorithm at the global scheduler, the job-dispatching algorithm at the local scheduler, and job-scheduling algorithm at the processor scheduler. The integrated job scheduling policy is investigated using SHLPN performance analysis methods. The performance metrics concerned include the delay time of jobs in the Grid node and the response time perceived by the users. The numerical example shows the efficiency of the performance evaluation technique.