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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.6 P.927-936

http://doi.org/10.1631/jzus.2006.A0927


Fork-Join program response time on multiprocessors with exchangeable join


Author(s):  WANG Yong-cai, ZHAO Qian-chuan, ZHENG Da-zhong

Affiliation(s):  Center for Intelligent and Networked Systems, Department of Automation, Tsinghua University, Beijing 100084, China

Corresponding email(s):   wangyongcai@mails.tsinghua.edu.cn

Key Words:  Exchangeable join, First come first served (FCFS), Fork-Join, Multiprocessor, Response time


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WANG Yong-cai, ZHAO Qian-chuan, ZHENG Da-zhong. Fork-Join program response time on multiprocessors with exchangeable join[J]. Journal of Zhejiang University Science A, 2006, 7(6): 927-936.

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Abstract: 
The fork-Join program consisting of K parallel tasks is a useful model for a large number of computing applications. When the parallel processor has multi-channels, later tasks may finish execution earlier than their earlier tasks and may join with tasks from other programs. This phenomenon is called exchangeable join (EJ), which introduces correlation to the task’s service time. In this work, we investigate the response time of multiprocessor systems with EJ with a new approach. We analyze two aspects of this kind of systems: exchangeable join (EJ) and the capacity constraint (CC). We prove that the system response time can be effectively reduced by EJ, while the reduced amount is constrained by the capacity of the multiprocessor. An upper bound model is constructed based on this analysis and a quick estimation algorithm is proposed. The approximation formula is verified by extensive simulation results, which show that the relative error of approximation is less than 5%.

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Reference

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[7] Medhi, J., 1990. Stochastic Models in Queueing Theory. Academic Press Inc.

[8] Nelson, R., Tantawi, A.N., 1988. Approximate analysis of Fork/Join synchronization in parallel queues. IEEE Transactions on Computers, 37(6):739-743.

[9] Taha, M.E., Stidham, S., 1999. Sample-Path Analysis of Queueing Systems. Kluwer Academic Publishers.

[10] Towsley, D., Rommel, C.G., Stankovic, J.A., 1990. Analysis of Fork-Join program response times on multiprocessors. IEEE Transctions on Parallel and Distributed Systems, 1(3):286-303.

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