Information Technology Reference
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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 .