Performance Metrices

8/3/2019 Performance Metrices

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Performance Metrics


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Outline:-

Performance Metrics Introduction

Running Time

Speedups

Efficiency

Communication Overheads

Scalability


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What are Performance Metrics ?

Performance metrics are a tool to help programmers reduce

the running time of their applications.

To determine best parallel algorithm

Evaluate hardware platforms

Examine the benefits from parallelism

These metrics have been developed to help in the

performance debugging of parallel programs


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Metric 1:- Running Time(Run-time is the dominant metric)

Running time is the Execution Time of a program.

It is the measure of how long the parallel program needs to

run to solve our problem, we can directly measure itseffectiveness.

The running time is the amount of time consumed in

execution of an algorithm for a given input on the N-

processor based parallel computer.

It is denoted by T(n) where n signifies the number of

processors employed.

If n=1, it is sequential computer.


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The relation between Execution time vs.

Number of processors

It can be easily seen from the graph that as the number of processors increases,

initially the execution time reduces but after a certain optimum level the execution

time increases as number of processors increases. This discrepancy is because of the

overheads involved in increasing the number of processes.


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Metric 2:-Speedup

To find out how much better our program does on the parallel machine,

compared to a program running on only one processor, taking the ratio of

the two is a natural solution. This measure is called the speedup.

Speed up is the ratio of the time required to execute a given program using

a specific algorithm on a machine with single processor (i.e. T (1) (wheren=1)) to the time required to execute the same program using a specific

algorithm on a machine with multiple processors (i.e. T(n)).

S(n) = T(1) or

T(n)

It may be noted that the term T(1) signifies the amount of time taken to

execute a program using the best sequential algorithm i.e., the algorithm

with least time complexity.

Measures performance gain and relative benefit achieved by parallelizing

a given application over sequential implementation.


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Example:-


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Example (Contd..)


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Graph showing Speedup

No of processors required

Sublinear

Linear

Assumptions :-

The p PEs used are assumed to be identical to the one used by the sequential

algorithm

Superlinear


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Resultant Speedups

Linearspeedup:

Super-linearspeedup

Sub-linearspeedup:

pS p

pS p

pS p


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Defination of Speedups

Linear speedup:- Implicitly means 1 to 1 speedup perprocessor.

Sub-linear Speedup:- It means Speedup(n) less thann, reflecting the fact that not all parts of a program benefitfrom parallel execution. More normal due to overhead of

startup, synchronization and communication etc.

Super-linear speedup:- In rare situations, forSpeedup(n) to be larger than n. This is called a super-linear speedup meansthe program has been speed up by

more than the increase of CPUs.


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Causes of Superlinear Speedup

A super-linear speedup comes about because each CPU is

now working on a smaller set of memory. The problem

data handled by any one CPU fits better in cache, so each

CPU executes faster than the single CPU could do.Other reasons are:-

Overhead reduced

Latency hidden

Mathematical inefficiency of the serial algorithm

Higher memory access cost in sequential processing


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Metric 3:- Efficiency (Throughput)

Measures fraction of time for which a PE is usefully

employed

Defined as ratio of the speedup to the number of PEs

In ideal parallel systems

Speedup is equal to p, and

Efficiency is equal to one

In practice

Speedup is less than p, and

Efficiency is between zero and one


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Metric 4:- Communication Overhead

Total time spent by all the PEs over and above that

required by the fastest known sequential algorithm on a

single PE for solving the same problem

Represented by an overhead function

Total time spent in solving a problem using p PEs is

Time spent for performing useful work is

The remainder is overhead given by


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Factor Causing Parallel Overheads

Uneven Load Distribution

In the parallel computer, the problem is split into sub-problems and is

assigned for computation to various processors. But sometimes the

sub-problems are not distributed in a fair manner to various sets of

processors which causes imbalance of load between various

processors. This event causes degradation of overall performance of

parallel computers.

Cost involved in inter-processor communication

As the data is assigned to multiple processors in a parallel computerwhile executing a parallel algorithm, the processors might be required

to interact with other processes thus requiring inter-processor

communication. Therefore, there is a cost involved in transferring data

between processors which incurs an overhead.


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Contd..

Synchronization

In order to execute a parallel algorithm on a parallel computer, K

number of processors are required. As we know, execution time

decreases with increase in number of processors. However, when input

size is fixed and we keep on increasing the number of processors, in

such a situation after some point the execution time starts increasing.

This is because of overheads encountered in the parallel system.

Parallel Balance Point

Multiple processors require synchronization with each other whileexecuting a parallel algorithm. That is, the task running on processor X

might have to wait for the result of a task executing on processor Y.

Therefore, a delay is involved in completing the whole task distributed

among K number of processors.


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Metric 5:-Scalability of parallel systems

The ability to maintain performance gain when system and

problem size increase

Total overhead function is a function of both problem

size and the number of processing elements p

In many cases, grows sub-linearly with respect to Ts

In such cases, efficiency increases if problem size is

increased keeping number of PEs constant

One can simultaneously increase the problem size and

number of processors to keep efficiency constant

Such systems are called scalable parallel systems


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Performance Metrices

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