Advances in Mobile Cloud Computing Systems

Toward Energy-Efficient Task Execution in Mobile Cloud Computing 85

time by simulating the data transmission for a large number of times

for Equations 2.33 and 2.35.

Similarly, we can have the backward value iteration for the mini-

mum expected energy cost,

f

k

(x

k

)=min

π

k+1



x

k+1

P(x

k+1

|x

k

,π

k+1

)[e

k+1

(x

k

,π

k+1

)+f

k+1

(x

k+1

)],

f

n+1

(x

n+1

) = 0, (2.43)

where

f

k

(x

k

) is the minimum expected energy cost from state x

k

at stage k

to state x

n+2

at stage n +2

f

0

(x

0

) is the minimum expected energy consumption to complete

the entire application

We can also have the backward value iteration for the minimum

expected aggregated cost,

J

k

(x

k

)=min

π

k+1



x

k+1

P(x

k+1

|x

k

,π

k+1

)[e

k+1

(x

k

,π

k+1

)

+ λd

k+1

(x

k

,π

k+1

)+J

k+1

(x

k+1

)], (2.44)

J

n+1

(x

n+1

)=0,

where

J

k

(x

k

) is the minimum expected aggregated cost ...