Embedded Software for SoC - Grupo de Mecatrônica EESC/USP

Adaptive Checkpointing with Dynamic Voltage Scaling 453
is given by
from which it follows that
To decrease the checkpointing cost, we set the checkpointing
interval to in our adaptive scheme.
A similar threshold on the execution time can easily be calculated for the
k-fault-tolerant scheme. In order to satisfy the k-fault-tolerant requirement,
the worst-case re-execution time is incorporated. The following inequality
must hold:
This implies the following
threshold on E:
If the execution time E exceeds the k-fault-tolerant checkpointing
scheme cannot provide a deterministic guarantee to tolerate k faults.
3.1. Checkpointing algorithm
The adaptive checkpointing algorithm attempts to maximize the probability
that the task completes before its deadline despite the arrival of faults as a
Poisson process with rate A secondary goal is to tolerate, as for a possible,
up to k faults. In this way, the algorithm accommodates a pre-defined faulttolerance
requirement (handle up to k faults) as well as dynamic fault arrivals
modeled by the Poisson process. We list below some notation that we use in
our description of the algorithm:
1.
denotes the checkpointing interval for the Poisson-arrival
approach.
2.
denotes the checkpointing interval for the k-faulttolerant
approach.
3.
denotes the checkpointing interval
if the Poisson-arrival approach is not feasible for timely task completion.
4. denotes the remaining execution time. It is obtained by subtracting from
E the amount of time the task has executed (not including checkpointing
and recovery).
5. denotes the time left before the deadline. It is obtained by subtracting
the current time from D.
6. denotes an upper bound on the remaining number of faults that must be
7.
tolerated.
The threshold is obtained by replacing D with in (1).
8. The threshold is obtained by replacing D with and k with
in (2).
The procedure interval
for calculating the checkpointing
interval is described in Figure 33-2(a), and the adaptive checkpointing scheme
adapchp(D, E, C, k, is described in Figure 33-2(b). The adaptive checkpointing
procedure is event-driven and the checkpointing interval is adjusted
when a fault occurs and rollback recovery is performed.