DocumentCode :
977518
Title :
Amdahl´s law: a generalization under processor failures
Author :
Önyüksel, Ibrahim ; Hosseini, Seyed Hossein
Author_Institution :
Dept. of Comput. Sci., Northern Illinois Univ., DeKalb, IL, USA
Volume :
44
Issue :
3
fYear :
1995
fDate :
9/1/1995 12:00:00 AM
Firstpage :
455
Lastpage :
462
Abstract :
Recent advances in VLSI technology make it possible to manufacture computer systems with thousands of processors that can work concurrently on the same problem and improve the running time of programs. Amdahl´s law measures the speedup (the ratio of the running time of a program on a 1-processor system to the running time of the same program on a multi-processor system) under the assumptions that processors are fault free and do not fail. This paper generalizes Amdahl´s law under the assumption that processors are subject to failures. If the failure of processors is modeled as random, the actual number of processors available to a program becomes a random variable as well. This stochastic process is represented by a closed queuing network, and it is completely analyzed under certain assumptions. Numerical results show that value of the degradation factor (the ratio of failure rate of processors to their repair rate) is crucial to the system performance. Amdahl´s law implicitly uses the fact that all of the processors are used by the parallel portion of a program. However, for a real system, processors are subject to failure, and consequently, the number of available processors becomes random. This paper assumes that processors may fail and re-evaluates the expression for the speedup factor in Amdahl´s law. It obtains closed-form expressions for the speedup factor and the PLF (performance loss factor)
Keywords :
fault tolerant computing; parallel architectures; parallel programming; performance evaluation; queueing theory; reliability; stochastic processes; Amdahl´s law; VLSI; closed queuing network; closed-form expressions; computer systems manufacture; degradation factor; fault free; multiprocessor system; numerical results; performance loss factor; processor failure; repair rate; speedup; stochastic process; system performance; Computer aided manufacturing; Concurrent computing; Degradation; Manufacturing processes; Queueing analysis; Random variables; Stochastic processes; Time measurement; Velocity measurement; Very large scale integration;
fLanguage :
English
Journal_Title :
Reliability, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9529
Type :
jour
DOI :
10.1109/24.406581
Filename :
406581
Link To Document :
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