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By this result we can write:
a ðw h Þ
inew
D ðw h Þ
i
C ðw h Þ
i
þ
t
0
;
where a ðw h Þ
inew
a ðw h Þ
i
¼
þ D
t
:
So, we obtain:
a ðw h Þ
i
D ðw h Þ
i
C ðw h Þ
i
þ D
t
þ
t
0
C ðw h Þ
i
a ðw h Þ
i
D ðw h Þ
i
) D
t
t
þ
:
Solution 5: Tolerate some non critical tasks k among (m + n) based on (m, n)
￿
firm model proposed by Hamdaoui and Ramanathan ( 1995 )
ðw h Þ
i
C ðw h Þ
i
D ðw h Þ
i
m ðw h Þ
i
I ðw h Þ
i
n ðw h Þ ¼ fs
ð
;
;
;
Þg;
i
¼
1tom
;
h
¼
1toM
:
m ðw h Þ
i
¼
;
;
1
it tolerates missing deadline
m ðw h Þ
i
it doesn 0 it tolerate missing deadline
ð 11 Þ
;
;
¼
0
I ðw h Þ
i
¼
H
;
Hard task
;
I ðw h Þ
i
¼
S
;
Soft task
;
￿
Solution 6: Removal of some non critical tasks (to be rejected)
n ðw h Þ ¼ fs ðw h Þ
i
C ðw h Þ
i
D ðw h Þ
i
m ðw h Þ
i
I ðw h Þ
i
ð
;
;
;
Þg;
i
¼
1tom
;
h
¼
1toM
:
m ðw h Þ
i
¼
1
;
it tolerates missing deadline
;
m ðw h Þ
i
it doesn 0 it tolerate missing deadline
ð 12 Þ
¼
0
;
;
I ðw h Þ
i
¼
H
;
Hard task
;
I ðw h Þ
i
¼
S
;
Soft task
;
For every solution the corresponding response time is:
Resp ðw h Þ
k
the response time calculated by the
first solution,
;
1
the response time calculated by the second solution,
Resp ðw h Þ
k ; 2
Resp ðw h Þ
k ;
the response time calculated by the third solution,
3
the response time calculated by the fourth solution,
Resp ðw h Þ
k ; 4
Resp ðw h Þ
k ; 5
the response time calculated by the
fifth solution,
Resp ðw h Þ
k
the response time calculated by the sixth solution,
;
6
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