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Embedded Software for SoC - Grupo de Mecatrônica EESC/USP

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462 Chapter 33<br />

Table 33-7. Results on adaptive checkpointing <strong>for</strong> five jobs: variation of P with <strong>for</strong> (a) C =<br />

10, and k = 5. (b) C = 20, and k = 5.<br />

Fault arrival rate<br />

Probability of timely completion of tasks, P<br />

Poisson-arrival<br />

k-fault-tolerant<br />

ADT_MUL<br />

(a)<br />

6<br />

10<br />

14<br />

18<br />

0.996<br />

0.967<br />

0.870<br />

0.647<br />

1.000<br />

0.983<br />

0.899<br />

0.610<br />

1.000<br />

0.987<br />

0.914<br />

0.696<br />

(b)<br />

6<br />

10<br />

14<br />

18<br />

0.884<br />

0.487<br />

0.149<br />

0.018<br />

0.815<br />

0.370<br />

0.086<br />

0.013<br />

0.930<br />

0.542<br />

0.153<br />

0.028<br />

approach provi<strong>de</strong>s fault tolerance and facilitates dynamic power management.<br />

The proposed energy-aware adaptive checkpointing scheme uses a dynamic<br />

voltage scaling criterion that is based not only on the slack in task execution<br />

but also on the occurrences of faults during task execution. We have presented<br />

simulation results to show that the proposed approach significantly reduces<br />

power consumption and increases the probability of tasks completing correctly<br />

on time <strong>de</strong>spite the occurrences of faults. We have also exten<strong>de</strong>d the adaptive<br />

checkpointing scheme to a set of multiple tasks. A linear-programming mo<strong>de</strong>l<br />

is employed in an off-line manner to obtain the relevant parameters that are<br />

used by the adaptive checkpointing procedure. Simulation results show that<br />

the adaptive scheme is also capable of providing a high probability of timely<br />

completion in the presence of faults <strong>for</strong> a set of multiple tasks.<br />

We are currently investigating checkpointing <strong>for</strong> distributed systems with<br />

multiple processing elements, where data <strong>de</strong>pen<strong>de</strong>ncies and inter-no<strong>de</strong> communication<br />

have a significant impact on the checkpointing strategy. We are<br />

examining ways to relax the restrictions of zero rollback and state restoration<br />

costs, as well as the assumption of no fault occurrence during checkpointing<br />

and rollback recovery. It is quite straight<strong>for</strong>ward to mo<strong>de</strong>l nonzero<br />

rollback and state restoration cost, but it appears that the assumption of no<br />

faults during checkpointing is difficult to relax.<br />

REFERENCES<br />

1.<br />

2.<br />

3.<br />

P. Pop, P. Eles and Z. Peng. “Schedulability Analysis <strong>for</strong> Systems with Data and Control<br />

Depen<strong>de</strong>ncies.” Proceedings of Euromicro RTS, pp. 201–208, June 2000.<br />

T. Ishihara and H. Yasuura. “Voltage Scheduling Problem <strong>for</strong> Dynamically Variable Voltage<br />

Processors.” Proceedings of International Symposium on Low Power Electronics and<br />

Design, August 1998.<br />

Y. Shin, K. Choi, and T. Sakurai. “Power Optimization of Real-Time <strong>Embed<strong>de</strong>d</strong> Systems

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