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550
0.002
M-first(M=2)
M-first(M=3)
M-first with sp o t-checking(M=2)
M-first with spot-checking(M=3)
Credibility-based voting(random)
Credibility - based voting(rr1)
ε acc
M-first(M=2)
M-first ( M = 3 )
M-first with spot-c heck i n g ( M=2)
M-first wit h s p o t-checking(M=3)
Credibil i t y -based voting(random)
C r e d ibility-based voting(rr1)
500
0.0015
450
400
0.001
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300
0.0005
250
0
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0
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0.4
0.6
0.8
1
0
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1
s
s
(a) Error-rate
(b) Computation time T
Figure 14. M -first voting with spot-checking vs. Credibility-based voting for sabotage
rate s ( acc =0.001 , f =0.35 , c =1.0 , q =0.1 , p d =0 , random scheduling without
blacklisting).
figure shows that, even if M =3 , M -FVSC can not guarantee the reliability condition,
while credibility-based voting achieves it for any s . It requires larger redundancy ( M ≥ 4 )
for M -FVSC, which results in increased computation time. Also, the computation time of
credibility-based voting is smaller than that of 3 -FVSC. This result indicates that credibility-
based voting is the most promising approach of spot-checking-based sabotage-tolerance
methods for high-performance and reliable VC systems.
0.002
550
M-first(M=2)
M-first(M=3)
M-first with spot-checking(M=2)
M-first with spot-checking(M=3)
Credibility-based voting(random)
Credibility-based voting(rr1)
ε acc
M-first(M=2)
M-first(M=3)
M-first with spot-checking(M=2)
M-first with spot-checking(M=3)
Credibility-based voting(ra n dom)
Credibility-based voting(rr1)
500
0.0015
450
400
0.001
350
300
0.0005
250
0
200
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
0
0.05 0.1 0.15 0.2 0.25 0.3 0.35
f
f
(a) Error-rate
(b) Computation time T
Figure 15. M -first voting with spot-checking vs. Credibility-based voting for fraction f
( acc =0.001 , s =0.1 , c =1.0 , q =0.1 , p d =0 , random scheduling with blacklisting).
Fraction f Fig.15 (a) shows the error rates of each method for fraction f in cases with
blacklisting. This figure shows that both spot-checking-based methods guarantee the relia-
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