amdahl's law and gustafson's law
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Parallel processing speedup Parallel processing speedup performance laws and their performance laws and their
characteristicscharacteristics
Sukhnandan Kaur Sukhnandan Kaur M-tech(CSE)M-tech(CSE)
1717
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AbstractAbstract Use Amdahl's Law and Gustafson's law
to measure the speedup factor Characteristics
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What is Amdahl's law What is Amdahl's law Amdahl’s law states that the speedup
achieved through parallelization of a program is limited by the percentage of its workload that is inherently serial
We can get no more than a maximum speedup equal to 1 / (s + p / N )
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What is Gustafson’s law Gustafson’s law states that, with
increasing data size, the speedup obtained through parallelization increases, because the parallel work increases with data size
The speedup factor is S + N ( 1 – S )
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In detailsIn details Amdahl's Law Gustafson's law
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Amdahl’ law: quantify parallelizability
Amdahl's law is named after computer achitect Gene Amdahl, and was made in 1967 when Amdahl was working in IBM
Amdahl's Law quantifies the theoretical speedup that can be obtained by parallelizing a computational load among a set number of processors
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Classic Model of Parallel Classic Model of Parallel ProcessingProcessing
Multiple Processors available (4)
A Process can be divided into serial and parallel portions
The parallel parts are executed concurrently
Serial Time: 10 time units
Parallel Time: 4 time units
S - Serial or non-parallel portion
A - All A parts can be executed concurrently
B - All B parts can be executed concurrently
All A parts must be completed prior to executing the B parts
An example parallel process of time 10:
Executed on a single processor:
Executed in parallel on 4 processors:
S A A A A B B B B S
SA
A
A
A
B
B
B
B
S
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Amdahl’s Law (Analytical Amdahl’s Law (Analytical Model)Model)
Analytical model of parallel speedup from 1960s
Parallel fraction () is run over n processors taking /n time
The part that must be executed in serial (1- ) gets no speedup
Overall performance is limited by the fraction of the work that cannot be done in parallel (1- )
diminishing returns with increasing processors (n)
processors ofnumber parallelin done
becan work thatoffraction
,)1(
1
n
where
n
meParallelTiSerialTimeSpeedup
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Shortcomings of Amdahl’s lawShortcomings of Amdahl’s law Using Amdahl's Law as an argument
against massively parallel processing is not valid
The serial percentage is not practically obtainable
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We have Gustafson’s lawWe have Gustafson’s law In 1988, John Gustafson refined Amdahl's
model Adding due consideration for large-scale
resources and tasks View an example to prove that why we
need Gustafson’s law
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Equations of Gustafson’s lawEquations of Gustafson’s law
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Compare the two lawsCompare the two laws Amdahl’s law: Suppose two cities are 60 km apart, a car
has spent one hour travelling the first 30 km. No matter how fast it drives the last 30 km, it is impossible to achieve 90 km/h before arriving the destination
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Compare the two laws (Cont’d)Compare the two laws (Cont’d) Gustafson’s law: Suppose a car has already been travelling for
some time at speed of less than 90km/h, and when given enough time and distance to travel, the car’s average speed can reach 90km/h as long as it drives faster than 90 km/h for some time. And also the average speed can reach 120km/h and even 150km/h as long as it drives fast enough in the following part
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CharacteristicsCharacteristicsHigh PerformanceExpandability and ScalabilityHigh ThroughputHigh Availability
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ConclusionConclusion Amdahl’s presumption of fixed data size
is obviously a restriction which does not map into reality for many problems
Both laws are in fact different perspective over the same truth – one sees data size as fixed and the other sees the relation as a function of data size
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Thank you