Hybrid Metaheuristic Approach for Scheduling of Aperiodic OS Tasks - Complex System Modelling and Control Through Intelligent Soft Computations - page 830

Solution 3: minimize the c ðw h Þ
i

(9)

￿

By applying Eq. ( 3 ) that notices:

R ðw h Þ
i

d ðw h Þ
i

f ðw h Þ
i

¼ ; we have :

R ðw h Þ
i

d ðw h Þ
i

C ðw h Þ
i

:

¼ t

Or, to obtain a feasible system after a recon guration scenario ðw h Þ , the fol-

lowing formula must be enforced:

R ðw h Þ
i

0 :

By this result we can write:

d ðw h Þ
i

C ðw h Þ t

inew

0 ; ð where C inew is the new worst case execution time value Þ

Or C ðw h Þ

inew ¼ C ðw h Þ

þ b ðw h Þ
i

:

i

So ; d ðw h Þ
i

t C ðw h Þ
i

b ðw h Þ
i

0

d ðw h Þ
i

C ðw h Þ
i

ðw h Þ
i

) t b

ðw h Þ
i

d ðw h Þ
i

C ðw h Þ
i

) b

t

Solution 4: Enforcing the release time to come back:

￿

a ðw h Þ
i

a ðw h Þ
inew

! ð where a inew is the new activation time value Þ

a ðw h Þ
inew

a ðw h Þ
i

!ð þ D Þ ð Þ

¼ t 10

By applying Eq. ( 1 ) that notices:

d ðw h Þ
i

a ðw h Þ
i

D ðw h Þ
i

¼ þ ;

we have:

R ðw h Þ
i

a ðw h Þ
i

D ðw h Þ
i

C ðw h Þ
i

¼ þ t :

Or, to obtain a feasible system after a recon guration scenario ðw h Þ , the fol-

lowing formula must be enforced:

R ðw h Þ
i

0

a ðw h Þ
i

D ðw h Þ
i

C ðw h Þ
i

) þ t 0 :