Hybrid Metaheuristic Approach for Scheduling of Aperiodic OS Tasks - Complex System Modelling and Control Through Intelligent Soft Computations - page 829

and the activation time of some tasks or to remove some soft tasks as the following
steps:

Step 1: the agent automatically merges VP ðw h 1 Þ
1

and VP ðw h 1 Þ
2

into VP ðw h Þ
1

and

￿

calculates VP ðw h Þ
1

and R ðw h Þ ,

￿ Step 2: it calculates new deadlines for old and new sporadic tasks in order to

obtain the feasibility of the system and to reduce the response time,

￿ Step 3: it calculates new WCETs,

Step 4: it calculates new activation times a ðw h Þ
i

,

￿

￿ Step 5:itde nes the tasks can miss their deadlines (k among (n + m)),

n ðw h Þ in order to ￿ Step 6:itde nes which tasks can be removed from the system

obtain the system ' s feasibility.

￿ Solution 1: Moving some arrival tasks to be scheduled in idle times. (idle times

are caused when some tasks complete before its worst case execution
time)

(7)

Solution 2: maximize the d ðw h Þ
i

(8)

￿

By applying Eq. ( 3 ) that notices:

R ðw h Þ
i

d ðw h Þ
i

f ðw h Þ
i

¼ ; we have :

and by applying Eq. ( 4 ) that notices:

f w h
1

c w h
1

, we can deduce that f ðw h Þ
i

c w h
i

¼ t þ ¼ t þ and 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
inew

C ðw h Þ
i

t 0 ; ð where d inew is the new deadline value Þ or

d ðw h Þ
inew

d ðw h Þ
i

þ h ðw h Þ
i

¼ :

d ðw h Þ
i

þ h ðw h Þ
i

C ðw h Þ
i

So ; t 0

) h ðw h Þ
i

C ðw h Þ
i

d ðw h Þ
i

t þ :