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Embedded Software for SoC - Grupo de Mecatrônica EESC/USP

Embedded Software for SoC - Grupo de Mecatrônica EESC/USP

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Adaptive Checkpointing with Dynamic Voltage Scaling 461<br />

is not correct to always <strong>de</strong>clare the job as unschedulable if its checkpointing<br />

<strong>de</strong>adline is missed. We overcome this problem by adopting the following<br />

solution: if the checkpointing <strong>de</strong>adline is missed but the actual job <strong>de</strong>adline<br />

is not missed, the job continues execution without inserting any more checkpoints.<br />

(2) Since the actual execution time of a job is affected by fault arrival<br />

pattern, it is necessary to adjust the starting time and slack of the next job<br />

during execution. In our proposed solution, during actual execution, once the<br />

current job finishes its execution, the adapchp procedure returns its completion<br />

time. The next job starts its execution based on the previous job’s<br />

completion time and its own pre-computed starting time, which is obtained<br />

off-line. Meanwhile, the pre-computed slack of the next job is adjusted<br />

accordingly. We explain this <strong>for</strong>mally below.<br />

Let the actual starting time of be and the actual execution time be<br />

Then the actual starting time of the next job can be calculated<br />

as:<br />

The actual slack time of is adjusted as:<br />

and the actual checkpointing <strong>de</strong>adline<br />

is adjusted as:<br />

Then we can apply adapchp C, k, to job the procedure<br />

returns the value which is the actual execution time of including<br />

checkpointing and fault recovery cost.<br />

5.3. Experimental results<br />

We consi<strong>de</strong>r two tasks<br />

and<br />

Here we assume that the single checkpointing cost is 10, and we require that<br />

at least 20 checkpoints are inserted <strong>for</strong> each slack.<br />

We compare the multi-task adaptive scheme, <strong>de</strong>noted by ADT_MUL, with<br />

the Poisson-arrival and k-fault-tolerant schemes in terms of the probability<br />

of timely completion. The experimental results are shown in Table 33-7. These<br />

results show that the adaptive scheme provi<strong>de</strong>s a higher probability of timely<br />

completion <strong>for</strong> multi-task systems than the other two schemes.<br />

6. CONCLUSIONS<br />

We have presented a unified approach <strong>for</strong> adaptive checkpointing and dynamic<br />

voltage scaling <strong>for</strong> a real-time task executing in an embed<strong>de</strong>d system. This

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