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the average completion time for reliability-oblivious error-recovery is higher when
more electrodes are defective. The completion time of the reliability-driven error-
recovery does not depend on the type of defect on the chip and keeps the minimum
completion time.
2.5.2
Protein Assays: Interpolating Mixing and
Exponential Dilution
Next we evaluate re-synthesis and error-recovery for two real-life protein assays.
These assays lead to the dilution of a protein sample by using two methods, namely
interpolating mixing and exponential dilution. Figure
2.20
shows the sequencing
graphs of these two protocols [
11
]. The protocols for these two bioassays are
described in [
11
].
The completion time of biochips with CCD camera-based sensing systems and
without error-recovery mechanism are shown in Fig.
2.21
when errors are injected in
the sample preparation of interpolating mixing. The bioassay is mapped to a 10
10
electrode array.
Figure
2.22
reports the completion time when multiple errors are inserted into
the interpolating mixing bioassay. Note that the completion time defined here only
includes the time spent on fluid-handling operations, and excludes the CPU time
consumed on resynthesis. From Fig.
2.22
, we see that the completion time achieved
by the PRSA-based algorithm and the greedy algorithm are almost the same, but
the CPU times for these two algorithms are different. The simulation is performed
on a 2.6-GHz, Intel i5 processor with 6 GB of memory. Both re-synthesis algorithm
are implemented on the basis of the same initial synthesis result. The CPU time
needed is around 33 min for computing the re-synthesis results using PRSA, which
was ten times higher than the bioassay completion time; while the CPU time is less
than 5 s for the greedy algorithm, which is only 2.5 % of the bioassay completion
time. The bioassay completion time derived by the greedy algorithm is only slightly
higher for the PRSA. Nevertheless, the greedy algorithm is more suitable for on-line
re-synthesis due to the low CPU time.
While the PRSA-based approach is less attractive for real-time decision making,
it provides a useful calibration point for the greedy algorithm and shows that the
latter's effectiveness for timely bioassay completion. Moreover, the PRSA-based
method can be served as the basis for future error-recovery methods based on pre-
computation and pre-loading of recovery schedules.
For the exponential dilution protocol introduced in [
11
], we compare the comple-
tion time for the reliability-driven and reliability-oblivious error-recovery methods
in Fig.
2.23
. First we randomly select one operation
opt
fe
as the first instance of
error in the execution of bioassay, where
opt
fe
is a dilution operation performed on a
1
4 electrode sub-array. Then for subsequent operations that are performed on this
electrode array with defects, we set P
fail
as the probability that the operation will fail
