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Cluster computing has come to prominence as a cost-effective parallel processing tool for solving many complex computational problems. The key to making cluster computing work well is the middleware technologies that can manage the policies, protocols, networks, and job scheduling across the interconnected set of computing resources. The research question addressed in this paper is the on-line job scheduling problem for multi-cluster systems. To this end, we propose an on-line dynamic scheduling policy that manages multiple job streams across both single and multiple cluster computing systems with the objectives of improving the mean response time and system utilization. The performance of the proposed scheduling policy is compared against a space-sharing policy and a time-sharing policy. The results of the experiments show that the proposed policy produces significantly better response times than the other two policies.