Acyclic fork-join queuing networks
Journal of the ACM (JACM)
On the execution of parallel programs on multiprocessor systems—a queuing theory approach
Journal of the ACM (JACM)
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
A performance evaluation of several priority policies for parallel processing systems
Journal of the ACM (JACM)
IEEE Transactions on Computers
Analysis of Fork-Join Program Response Times on Multiprocessors
IEEE Transactions on Parallel and Distributed Systems
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WE CONSIDER A TWO SERVER SYSTEM THAT PROCESSES A MIXTURE OF REGULAR CUSTOMERS AND FORK/JOIN CUSTOMERS. A REGULAR CUSTOMER IS ONE THAT REQUIRES SERVICE AT ONE SERVER WHEREAS A FORK/JOIN CUSTOMER REQUIRES SERVICE AT BOTH SERVERS. WE STUDY THE BEHAVIOR OF THIS SYSTEM OPERATING UNDER TWO DIFFERENT SCHEDULING POLICIES FOR REGULAR CUSTOMERS. THE ''DISTRIBUTED SCHEDULING POLICY (DSP)'' ROUTES REGULAR CUSTOMERS PROBABLISTICALLY TO EITHER SERVER. CUSTOMERS ARE SERVED IN A FIRST-COME FIRST-SERVE (FCFS) MANNER AT EACH SERVER. THE ''CENTRALIZED SCHEDULING POLICY (CSP)'' PLACES ALL REGULAR AND FORK/JOIN CUSTOMERS INTO A SINGLE QUEUE. CUSTOMERS ARE SCHEDULED FROM THIS QUEUE IN A FCFS MANNER. WE USE A MATRIX-GEOMETRIC FORMULATION TO MODEL THE SYSTEM OPERATING UNDER EACH POLICY. FOR THE FIRST POLICY, WE OBTAIN THE EXACT DISTRIBUTION OF THE SOJOURN TIME OF A REGULAR CUSTOMER AND TIGHT BOUNDS ON THE SOJOURN TIME DISTRIBUTION OF A FORK/JOIN CUSTOMER. FOR THE SECOND POLICY, WE OBTAIN TIGHT BOUNDS FOR THE AVERAGE SOJOURN TIME OF EITHER CLASS OF CUSTOMER. LAST, WE COMPARE THE PERFORMANCE OF BOTH POLICIES TO EACH OTHER.