Static Processor Allocation in a Soft Real-Time Multiprocessor Environment
IEEE Transactions on Parallel and Distributed Systems
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WE CONSIDER PARALLEL EXECUTION OF STRUCTURED JOBS WITH REAL TIME CON- STRAINTS IN (POSSIBLY HETEROGENEOUS) MULTIPROCESSOR SYSTEMS. A JOB IS COM- POSED OF A SET OF TASKS AND A PARTIAL ORDER SPECIFYING THE PRECEDENCE CON- STRAINTS BETWEEN THE TASKS. THE TASK PROCESSING TIMES ARE RANDOM VARIABLES WITH KNOWN PROBABILITY DISTRIBUTION FUNCTIONS. THE INTERARRIVAL TIME OF THE JOBS ARE ALSO RANDOM VARIABLES WITH ARBITRARY DISTRIBUTIONS. THE REAL TIME CONSTRAINTS ARE SPECIFIED BY REFERENCE TIMES, ALSO CALLED SOFT REAL-TIME DEADLINES. IN THE DISCUSSION WE ASSUME FIRST THAT ALL THE JOBS HAVE THE SAME TASK GRAPH, I.E, THE SAME TASK SET AND THE SAME PARTIAL ORDER. WE ASSUME THAT THERE IS A PREDEFINED MAPPING FROM THE SET OF TASKS ONTO THE SET OF TASKS ONTO THE SET OF MACHINES, IDENTICAL FOR ALL JOBS, THAT ALLO- CATES TASKS TO MACHINES. WE FOCUS ON DYNAMIC SCHEDULING POLICIES WHICH DO NOT USE INFORMATION ON THE PROCESSING TIMES OF THE TASKS TO BE SCHEDULED. THE POLICIES CAN BE NON-PREEMPTIVE OR PREEMPTIVE-RESUME. FOR NON-PREEMPTIVE POLICIES, WE ASSUME THAT TASKS PROCESSING TIMES ARE INDEPENDENTLY AND IDEN- TICALLY DISTRIBUTED, WHEREAS FOR THE PREEMPTIVE ONES, WE ASSUME THAT THEY ARE INDEPENDENTLY AND IDENTICALLY DISTRIBUTED AND COME FROM SOME SPECIFIC DISTRIBUTIONS. SOME OF THE RESULTS THAT ARE OBTAINED GENERALIZE TO THE CASE WHERE JOBS HAVE A RANDOM STRUCTURE. THIS MORE DIFFICULT CASE IS TREATED AT THE END OF THE PAPER.