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Figure 4. State transition model of worker W n .
P down (T i ) are given by
utod n
utod n + dtou n )
P up (T i )=(1− utod n − dtou n ) i−1 × (P up (T 1 ) −
utod n
utod n + dtou n
+
(3)
dtou n
utod n + dtou n )
P down (T i )=(1− utod n − dtou n ) i−1 × (P down (T 1 ) −
dtou n
utod n + dtou n
+
(4)
, where P up (T 1 ) and P down (T 1 ) represent the initial state of W n . In the steady-state of
W n (i.e. time step i →∞ ), the probability of getting “up” state is given by following
expression. Note that utod n + dtou n 6=0 .
utod n
utod n + dtou n
P up (T inf )=
(5)
Assume that all workers defect and rejoin to the system similarly ( utod n = p d and
dtou n = p u for n =1, 2,...,W , where probability p d is referred to as the defection rate).
Since workers' activities are independent of the state of VC projects, we assume that the
initial state of the computation is the same as the steady-state of workers. That is, at the start
of the computation, the number of workers in the state “up” is W × P up (steady) , where
p d
p u + p d .
(6)
2.4.
Problems and Motivations
As described in this section, many VC projects have run successfully or is currently run-
ning on the Internet. Those projects are developed using a VC framework, which provides
templates and simplifies the work of creating a VC project. Nowadays it is not so difficult
for any scientist to use VC for high performance computing.                                                             Search WWH ::

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