The Optimal Control of Heterogeneous Queueing Systems: A Paradigm for Load-Sharing and Routing
IEEE Transactions on Computers
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CONSIDER A SET OF PROCESSORS `P(SUBSCRIPT)1,P(SUBSC)2,...,P(SUBSC)N'' DIFFERING ONLY IN SPEED, A SET OF `M'' JOBS WITH EXPONENTIALLY DISTRIBUTED EXECUTION TIMES, AND AN EXPONENTIALLY DISTRIBUTED DEADLINE. THE PROBLEM WE CONSIDER IS TO SCHEDULE THE JOBS NON-PREEMPTIVELY SO AS TO MAXIMIZE THE EXPECTED NUMBER OF JOB COMPLETIONS BEFORE THE DEADLINE. WE PROVE THAT A THRESHOLD POLICY ACHIEVES THIS OBJECTIVE AND PROVIDE AN ALGORITHM TO CALCULATE THE VALUES OF THE THRESHOLDS.