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2200
0.02
rr1
random
ENR
ECJ(R=inf)
ECJ(R=0)
ε
acc
rr1
random
ENR
ECJ(R=inf)
ECJ(R=0)
0.018
2000
0.016
1800
0.014
1600
1400
0.012
0.01
1200
0.008
1000
0.006
800
600
0.004
0.002
400
0
200
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
pd
pd
(a) Error-rate
(b) Computation time
T
Figure 31. Error rate and Computation time for defection rate
pd
(
acc
=0.01
,
s =0.1
,
f =0.35
,
c =0.0
,
q =0.2
,
P
up
(steady)=0.8
, without blacklisting).
of credibility-based voting stays constant for any
s
even in cases without blacklisting.
Fig.28 (b) and Fig.29 (b) show that the difference between
ENR
method and the round-
robin method is large, different from cases with blacklisting (Fig.24 (b)). In cases without
blacklisting, the saboteurs can rejoin the system and produce incorrect results permanently,
so that more results are invalidated by backtracking and each job's
ENR
becomes widely
disproportionate. This result indicates that consideration of
ENR
becomes an important
reason to select jobs in cases without blacklisting.
Fig.30 and Fig.31 show the error rate and computation time as functions of colluding
rate
c
and defection rate
p
d
, respectively. As shown in these figures, error rates of all job
scheduling methods stay constant for any
c
and
p
d
even in cases without blacklisting. These
figures also show that all job scheduling methods includes
EC
J
method guarantees the
reliability condition for any
c
and
p
d
. This result indicates that
EC
J
method outperforms
round robin method for any
c
and
p
d
even in cases without blacklisting.
4.4.
Conclusion
In this section, we proposed expected-credibility-based job scheduling for credibility-based
voting [23] to improve the performance of the original round-robin job scheduling. The
proposed job scheduling method selects jobs to save unnecessary job allocations based on
two novel metrics: the expected-credibility and the expected number of results.
Through the extensive simulations, we found the following important results;
•
Credibility-based voting can guarantee the reliability condition regardless of used job
scheduling method.
•
The proposed job scheduling method reduces the computation time compared to the
round-robin method, irrespective of the value of unknown parameters
s
,
f
,
c
and
p
d
.
These very important features indicate that the proposed method is applicable to VC sys-
tems of various environments.
