A performance evaluation of a general parallel processing model
SIGMETRICS '90 Proceedings of the 1990 ACM SIGMETRICS conference on Measurement and modeling of computer systems
Analysis of Fork-Join Program Response Times on Multiprocessors
IEEE Transactions on Parallel and Distributed Systems
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
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IN THIS PAPER WE DERIVE AN EXPRESSION FOR THE MEAN RESPONSE TIME OF A FORK-JOIN JOB IN A SINGLE SERVER PROCESSOR-SHARING QUEUEING SYSTEM. WE ALSO DERIVE AN EXPRESSION FOR THE MEAN RESPONSE TIME OF A FORK-JOIN JOB CONDITIONED ON THE REQUIRED SERVICE TIME OF THE LARGEST TASK. IN OUR APPROACH A FORK-JOIN JOB IS COMPOSED OF A NUMBER OF INDEPENDENT TASKS WHICH CAN BE SCHEDULED INDEPENDENTLY OF EACH OTHER. THE JOB IS CONSIDERED COMPLETE ONCE THE LAST TASK COMPLETES. EACH TASK SERVICE TIME IS ASSUMED TO BE AN EXPONENTIALLY DISTRIBUTED RANDOM VARIABLE. WE PROVIDE BOTH LOWER AND UPPER BOUNDS ON MEAN RESPONSE TIME OF FORK-JOIN JOBS. THE LOWER BOUND TO THE MEAN RESPONSE TIME OF THE FORK-JOIN PROBLEM IS VERY TIGHT WHEN THE NUMBER OF TASKS IN THE JOB IS LARGE (