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4 standard deviation σ are evaluated .The sample mean of all
System progresses are to be evaluated by using formula: SP
mean
= ∑ SP
i
n The variance σ
2
can be estimated as : σ
2 est
= 1 n-1 ∑SP
k
– SP
mean 2
The general relationship between the parameters is given as Pr { – t ≤ SP
mean
≤ + t} = 1 – α where t is the tolerance on either side of mean within which
the estimated to fall within probability 1 – α. The normal
density function is Φy = y
1- α2,
the upper confidence limit UL and lower confidence limit LL of System progress can be
obtained respectively. y
Φy =
∫
1√2Π e
–z
2
2
dz
–α
Where z = √n
SP
mean
– σ
est
UL = SP
mean
+ y
1- α2
σ
est
√n LL = SP
mean
– y
1- α2
σ
est
√n y
1- α2
= 2.58 99 confidence level The interval UL - LL will contain the true mean with a
specific certain experimental confidence value [12].
3.2 Simulation results
Simulation result shows that the System Performance is affected by the various factors such as number of checkpoint
intervals, Clock drift rate of processors, Fault rate of processors, Time of saving checkpoints .In our simulation
experiment such variations of factors against System Progress are shown in tabular as well as graphical form.
3.2.1 Checkpoint interval vs. system progress
The following table expresses the parametric values used in proposed model. The first column shows when varying values
of Fault rate Table 4, Drift rate Table 5, Checkpoint intervals Table 2 and second and third column shows the
corresponding other variable names and their particular values.
Table 1: Parametric values of System model
According to these values the system progress is evaluated and respective graphs are drawn. First according to increasing
values of checkpoint intervals L corresponding decreasing values of system progress is evaluated i.e. obviously as
number of checkpoint intervals are increased corresponding system progress get decreased Fig 4 i.e. The system progress
is affected by number of checkpoints
Table 2. Checkpoint intervals vs. System Progress
Checkpoint Intervals L
System Progress SP
100 0.9925
10100 0.950282
20100 0.902832
30100 0.857017
40100 0.81285
50100 0.770316
Fig 4: Checkpoint intervals vs. System Progress
3.2.2 Saved Checkpoint time vs. system progress
Table 3. describes as time to save checkpoints get increased the system progress get decreased.
This is illustrated in Fig.5 which is obviously true as the time to save checkpoint get increased the system progress will
decrease.
Table 3. Saved Checkpoint time vs. System Progress
Saved checkpoint Time ts
System Progress SP
1 0.98183
2 0.981554
3 0.981278
4 0.980999
5 0.980723
6 0.980441
7 0.980166
8 0.979887
9 0.979609
10 0.979331
11 0.979053
12 0.978775
13 0.978498
14 0.978221
15 0.977942
SYSTEM PROGRESS EVALUATION Used System parameters
Variable tr
0.1 State
Tdiff 0.01
t
min
0.001 fr
L 3600
Fault rate ts
0.7 ρ
0.000001 ρ
fr 0.00001
Drift rate L
3600 ts
0.7 L
fr 0.00001
Ckeckpoint Interval
ρ 0.000001
ts 0.7
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Fig 5: Checkpoint intervals vs. System Progress
3.2.3 Fault Rate vs. system progress
This subsection describes how fault rate affects the system progress.
Table 4. describes as fault rate get increased The system progress get decreased.This is illustrated in Fig.6
Table 4. Fault Rate vs. system progress
Fault Rate fr
System Progress SP
1.00E-16 0.999803
1.00E-15 0.999741
1.00E-14 0.999767
1.00E-13 0.999783
1.00E-12 0.999802
1.00E-11 0.999761
1.00E-10 0.999726
1.00E-09 0.999765
1.00E-08 0.999658
1.00E-07 0.999625
Fig 6 Fault Rate vs. System Progress
3.2.4 Drift Rate vs. system progress
This subsection describes how drift rate affects the system progress. For low value of drift rate the system progress is
high little bit .The System Progress of non blocking protocol is not much affected for different values of drift rate the
System .Table 5. and Fig.6 illustrates this.
Table 5. Drift Rate vs. System progress
Drift Rate ρ
System Progress SP
0.1 0.994184
0.01 0.993871
1.00E-03 0.993605
1.00E-04 0.983866
1.00E-05 0.993416
1.00E-06 0.994208
1.00E-07 0.993747
1.00E-08 0.994071
1.00E-09 0.993928
1.00E-10 0.994053
Fig 7 Drift Rate vs. System Progress
3.2.5 System progress validation
In Table 6. the first column, first entry illustrates that 10 samples of checkpoint interval of length 100 are taken and
corresponding System progress of 100,200,…..1000
checkpoint intervals gets evaluated, their average is shown in second column i.e. 0.99520.The third and fourth column
shows their standard deviation, upper and lower confidence limit respectively. Similarly System Progress of other samples
having checkpoint intervals 2000, 3000 …10000 are validated Similar validation can be applied to other system parameters.
The difference between upper and lower confidence limit should be less than 2
Tolerance value. Here tolerance value is 0.001 for 99 confidence
Table 6. System progress validation
Sample No.
System Progress
average σ
est
Upper Confidence.
Limit Lower
Confidence Limit
1000 0.99520
0.00114 0.9961
0.99427 2000
0.99180 0.00141
0.9929 0.99065
3000 0.98702
0.00146 0.9882
0.98583 4000
0.98215 0.00014
0.9833 0.98095
5000 0.97727
0.00014 0.9784
0.97606 6000
0.97238 0.00147
0.9735 0.97117
7000 0.96750
0.00147 0.9687
0.96629 8000
0.96263 0.00147
0.9638 0.96143
9000 0.95777
0.00146 0.9589
0.95658 10000
0.95293 0.00146
0.9541 0.95174
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4. CONCLUSION
