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scheduling cost for the proposed method, i.e.
Cost
prop
(t)
, is calculated as

Cost
prop
(t)=(1− q)(t
c
+2(t
c
+ t
e
)) + qt(t
c
+(t
c
+ t
e
))

= Cost
orig
(t)+(t
c
+ t
e
)(2(1 − q)+qt).
(21)

By definition, the time to calculate
EC
J
is almost identical as
t
c
(the time to calculate
C
J
).

The average of
Cost
prop
(t)
, i.e.
E(Cost
prop
)
, is given as the following.

T
X

E(Cost
prop
)=
1

T

Cost
prop
(t)

t=1

=2× t
c
((1 − q)+
q(T +1)

2

)+t
c
(1 − q)

+t
e
(2(1 − q)+
q(T +1)

2

).

(22)

The value of
q
is between 0 and 1 and
T>>1
(several orders of magnitude). Therefore,

the second term in eq.(22) is negligibly small compared to the first. The third term in

eq.(22) is also negligibly small compared to the first because calculation of
ENR
involves

the simple addition shown in eq.(17), then
t
e
is negligibly small. Therefore,
E(Cost
prop
)

can be represented as follows.

E(Cost
prop
) ≈ 2 × E(Cost
orig
).

(23)

From eqs. (20) and (23), it is apparent that the scheduling costs of both methods are negligi-

bly small compared to the execution time of a job in general VC systems (e.g. several hours

in [11]), because
t
c
, the calculation cost of one credibility, is a very small value (on the order

of microseconds). Furthermore, both scheduling costs (for a single worker) are independent

of the system scale, such as the number of jobs and the number of workers. Consequently,

both methods will work well in large-scale VC systems, without a considerable increase in

the workers' waiting time.

4.3.

Performance Evaluation

4.3.1.

Simulation Conditions

We evaluate the effectiveness of the proposed job scheduling method through the simula-

tion of VCs. Computation times
T
and error rates of VCs are evaluated as the average

of 100 simulation results for different job scheduling methods: random (denoted by “ran-

dom”), round robin (denoted by “rr1”) [23], and several variants of the proposed method.

The variants of the proposed method select jobs using
ENR
and
EC
J
. They are called,

respectively, “
ENR
method” and “
EC
J
method”.

• ENR
method:

This method selects a job that has a minimum
ENR
in all unfinished jobs. A round-

robin selection is used if some jobs have the same
ENR
.

• EC
J
method

This method selects a job that has a minimum
EC
J
in the candidate jobs
CS
. De-

pending on the value of
R
, i.e. how to create
CS
, there are several variants of
EC
J

method.