An Optimal On Line Scheduling Algorithm for Overloaded Real Time Systems
An Optimal On Line Scheduling Algorithm for Overloaded Real Time Systems
Gilad Koren
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This means that the index of the last deadline after which the tasks has zero value is [log2{imp{Ti))\ - 1 = [/off2(^)J - 1- For notational convenience any task T, will have associated descending tasks denoted by rpO rpl rp2 rp\log2(imp(Ti))\-l where the release times and the computation times of all these tasks are equal to the release time and the computation time of T, . Tf has a firm deadline at 'i) '" section 5 42 • Every other task, T, where j L — e ■ V, , by assumption 3. 2 c, ,mar X -... e • (1 + y/k) • achievedvalue(/), by lemma 5. 4 ^ (l+>/fc) achieved value (/) — k The "loss" from scheduling T. During BUSY is at least k ■ (i+>/fc)achievedvalue(/) ^j^^ value obtained by scheduling T, is at most (1 + \/k) ■ achievedvalue(/) (lemma 5. 4). Hence the net gain is less than or equal to zero.
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