Heterogeneous Earliest Finish Time based Scheduling for Digital
Microfluidic Biochips
Rajesh Kolluri, J. V. Phani Kumar and Sumanta Pyne
Department of Computer Science and Engineering, National Institute of Technology Rourkela, Odisha 769008, India
Keywords:
Lab-on-chip, Microfluidics, DMFB, MEMS, Scheduling, DMHEFT.
Abstract:
One of the recent emerging technology in biochemical analysis field is Lab-on-chip (LOC) technology which
uses digital microfluidics property to manipulate droplets discretely. LOC efficiently carries out all biochem-
ical operations we do in traditional laboratories on a single reconfigurable chip called as Digital Microfluidic
Biochip (DMFB). DMFBs helps to achieve parallelism and miniaturization compared to traditional labora-
tory methods in terms of samples and equipment used. One of the important problem in DMFB synthesis is
scheduling. We present a simple method called as Heterogeneous Earliest Finish Time for digital microflu-
idics (DMHEFT) for scheduling DMFB. It is a greedy heuristic based list scheduling. HEFT is previously
used for task scheduling where multiple heterogeneous processors are available for solving inter-dependent
tasks depicted as DAG. In this paper, it is applied to Microfluidic biochips. DMHEFT uses Upward rank value
to prioritize the tasks or operations and earliest nish time to assign tasks to different modules like mixers,
heaters and detectors etc. Simulation results show that it produces better assay lengths and run time compared
to existing algorithms.
1 INTRODUCTION
Digital Microfluidics is small part of bio-MEMS (Mi-
cro Electro Mechanical Systems) or Lab-On-Chip
(Verpoorte and De Rooij, 2003). Basic agenda of
Digital Microfluidic Biochips (DMFBs) is to integrate
all required functions of biochemical analysis onto a
single small-sized chip using microfluidics. In other
words DMFBs are specially designed chips for bio-
logical and chemical analysis. Digital Microfluidics
explores so many advantages compared to traditional
laboratory techniques or methods. The main advan-
tages opting for DMFB rather than traditional labora-
tory analysis of samples are DMFB reduces time, cost
and achieves automation, miniaturization. DMFB
has applications in the area of clinical diagnostics
(Schulte et al., 2002), Analyzing human physiolog-
ical fluids like saliva, urine, sweat, serum, plasma,
blood and tears (Srinivasan et al., 2003), DNA se-
quence analysis and it can also be used to test some
fluids related to terrorist activities using bio-samples
(Su and Chakrabarty, 2008) and fluorescence detec-
tion (Bhardwaj and Jha, 2018).
DMFB works by manipulating discrete level
droplets on biochip. Unlike the continuous-flow
microfluidics or analog-digital microfluidics which
uses pumps and valves to make fluids flow contin-
uously and mix them with reagents (Verpoorte and
De Rooij, 2003). Digital microfluidics uses Elec-
tro wetting on Dielectric (EWoD) property to make
droplets move discretely and mix them with reagents
on 2-Dimensional array of electrodes (Pollack et al.,
2002). DMFB consists of two glass plates placed
one above the other and droplets will move between
these plates. Upper glass plate consists of coating
of hydrophobic layer which prevents fluids stick to
the surface of the plate and one ground electrode that
spreads across the entire upper plate. In addition
to hydrophobic layer, lower plate has m n control
electrodes and a dielectric layer which works as an
insulator. A droplet will move from one electrode
to another electrode by activating one of the adja-
cent electrode where you want to move the droplet
while deactivating the electrode which is holding the
droplet now. DMFB is capable of performing various
operations on droplets like dispensing, dilute, mix-
ing, merging two droplets into one droplet, splitting
a droplet, storage and detection of change in a droplet
in terms of color, heating, volume etc. by putting a
LED and photo diode on the corresponding electrode
(Su and Chakrabarty, 2004). DMFB is dynamically
reconfigurable which means all the operations can be
Kolluri, R., Kumar, J. and Pyne, S.
Heterogeneous Earliest Finish Time based Scheduling for Digital Microfluidic Biochips.
DOI: 10.5220/0007367101750182
In Proceedings of the 12th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2019), pages 175-182
ISBN: 978-989-758-353-7
Copyright
c
2019 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
175
done on-chip and there is no permanent designated
place for any operation, operations can be done any-
where, anytime on the chip one at a time. Various
biological, chemical assays are specified as directed
acyclic graphs (DAGs) depicting the different type of
operations and dependencies between them (Su and
Chakrabarty, 2008).
Figure 1: Digital Microfluidic Biochip structure (Grissom
and Brisk, 2012b).
Synthesis of DMFB consists of three steps namely
Scheduling, Placement and Routing (Grissom and
Brisk, 2012b). Also called as DMFB compiler.
Scheduling is allocating absolute start, stop time slots
to every operation depicting that when an operation
has to occur pertaining to resource constraints en-
suring there are enough resources to process certain
bioassay. In this paper we emphasize on scheduling.
In conjunction to this placer and router algorithm can
be used to finish the synthesis step. Scheduling is
more important than placement and routing part of
synthesis because of operations (mixing and detec-
tion) take more time compared to actual placing of
operations and transportation of droplets.
2 RELATED WORK
Some of the significant scheduling algorithms are
based on Heuristic based List Scheduling variants,
Genetic Algorithms and Integer Linear Programming
(ILP).
List Scheduling (LS) (Micheli, 1994) is a heuris-
tics based greedy scheduling algorithm. LS generates
a prioritized sequence of tasks and allocates proces-
sor to tasks in the sequence of their priority which
minimizes some predefined objective function. Mod-
ified List Scheduling (MLS) (Su and Chakrabarty,
2008),(Su and Chakrabarty, 2004) algorithm is an
augmentation to List Scheduling algorithm. Unlike
LS, MLS has a rescheduling step which effects in
achieving legal schedule under resource constraints.
It is a polynomial time executed greedy based heuris-
tic algorithm.
Force-directed List Scheduling (FDLS) (O’Neal
et al., 2012) is also based on List Scheduling not on
MLS. It modifies/replaces priority function (which is
used to prioritize tasks for execution sequence) of List
Scheduling. First, this method was used for the high
level synthesis of digital signal processing. FDLS
computes the priorities of tasks at every scheduling
step in response to the dependencies underlying be-
tween tasks (vertices) as shown in DAG which were
already scheduled in earlier calculation of priorities
and also Force calculation which considers the fewest
steps at which the operations can be scheduled which
will be known by As Soon As Possible (ASAS) and
As Late As Possible (ALAP). FDLS produces better
assay lengths than MLS but runs slower than MLS
because of complex rank calculation mechanism.
Path Scheduling (PS) (Grissom and Brisk, 2012b)
schedules the DAG, path after path unlike node by
node in List Scheduling. All operations on a path
are scheduled contiguously. Path scheduling works
by calculating two priorities Critical path priority and
Independent path priority. By calculating node pri-
orities, it only explores paths with the lowest prior-
ity thereby reducing the number of droplets stored in
DMFB. If storage droplets are more on-chip it ad-
versely affects the performance of chip because it is
indirectly reducing functional area of chip. When a
large assay has to be scheduled on small DMFB then
PS works better than LS and FDLS. But, PS only
works for trees/forests, failed to schedule other type
of DAGs.
Two Genetic List Scheduling Algorithms GA1
(Su and Chakrabarty, 2008), GA2 (Ricketts et al.,
2006) were there which takes long run time but con-
verge to locally optimal solutions. These two also
based on List scheduling. Which initially use LS to
produce a legal initial schedule and randomly varying
operation priorities using crossover, mutation. Ge-
netic algorithms gives lesser bio-assay lengths but
runs slower compared to LS, PS and FDLS. Some
Integer Linear Programming (ILP) based scheduling
algorithms (Ding et al., 2001), (Su and Chakrabarty,
2004), (Su and Chakrabarty, 2008), are there same as
Genetic algorithms achievesoptimal solutions but has
exponential running time.
3 SCHEDULING OVERVIEW
3.1 Scheduling Preliminaries
Scheduling of a DMFB is an NP-Complete problem.
Scheduling DMFB operations is actually scheduling
a DAG. Scheduling determines each operation’s start-
ing execution time slot and finishing execution time
slot sticking to resource constraints and operation de-
pendences derived from DAG. We cannot say that a
particular schedule that we get is legal at all times be-
cause there is a chance that resource requirements of
BIODEVICES 2019 - 12th International Conference on Biomedical Electronics and Devices
176
bio-assay may exceed the existing resource or mod-
ules of a DMFB. The goal of scheduling algorithm is
to reduce the bio-assay execution time.
DMFB consists of Different modules like Gen-
eral modules to execute normal operations like mix,
merge, split and Specialized modules to execute spe-
cial operations like detection, heating and Input ports
to implement dispense operations and Output ports to
yield output or to vent waste. Each input fluid will
have at least one input port.
3.1.1 Input
Inputs to scheduling algorithm are
A Bio-assay represented as a DAG G=(V,E), V
represents different bio-assay operations and E
represents dependencies between them.
Module library consists of number of reconfig-
urable modules like mixers, heaters or detec-
tors etc. (M
1
, M
2
, ..., M
q
) and Input/Output ports
(I
1
, I
2
, ..., I
e
, O
1
, O
2
, ..., O
f
).
Each operation’s execution time (E
1
, E
2
, ..., E
v
)
where v = |V|.
The number of distinct input fluids (F
1
, F
2
, ..., F
x
)
Number of droplets allowed to be stored on a
module at any time-step t is (k)
3.1.2 Output
Each operation in DAG will be assigned a starting and
finishing time slot. Final task’s finishing time is called
as assay length or assay execution time.
3.1.3 Objective
The objective of scheduling algorithm is to reduce the
assay length or assay execution time under resource
constraints and adhering to operation dependencies as
depicted in DAG.
Obj = min{max
uV
(AFT(u))} (1)
Assay length is the Actual Finish time of the last ex-
ecuting operation or task. Scheduling objective is to
decrease the assay length, that is to minimize the fin-
ish time of the last executing task in assay.
3.1.4 Droplet Storage
The droplet produced by operation u must be stored
for time interval H(u), if any of it’s successor opera-
tion not starting immediately after it’s finishing time.
Some work module must be available to store u dur-
ing H(u).
H(u) = { max
vsucc(u)
AST(v)} AFT(u) (2)
3.1.5 Legality
A legal schedule must satisfy precedence constraints
as specified in DAG.
(u, v) E, AST(v) AFT(u) (3)
At any time-step t in the schedule, the number of
operations scheduled should not exceed the number
of available work modules present on the chip.
3.2 Scheduling Assumptions
In DMFB scheduling, we have to schedule the differ-
ent DMFB operations to particular available modules
on the chip. Reconfigurable nature of DMFB is any
operation of the assay can be performed anywhere on
the chip (any module of DMFB). The execution time
of mixing or detecting operation depends on the size
of the mixer or detector module. If the size of the
module is large then execution time will be less and
if the size of the module is small then execution time
will be more (Su and Chakrabarty, 2004). We can
conclude that execution time is inversely proportional
to the size of the module. This property of DMFB
causes problems, those are scheduling cannot be sep-
arated from placement and placement cannot be sepa-
rated from scheduling (O’Neal et al., 2012). Suppose
if we start with a placement then in the middle of exe-
cution on demand if we change the size of the module
then the placement that we start with becomes illegal.
Hence, in scheduling the main assumption is all the
modules are of fixed size, they don’t change their size
in the middle of assay execution. That is the reason
we will declare the module library, that is a number
of modules and their sizes and their execution time
before we start scheduling.
The second assumption is all the scheduling oper-
ations we perform are non-preemptive in nature un-
like in digital computing. Once a droplet is moved
on to chip for an operation, it cannot be taken back to
reservoirs at any cost. Droplet has to wait, if any ob-
stacle in its path or if any further move of that droplet
causes deadlock.
The third assumption is unlike in parallel or dis-
tributed computing there is no communication cost
between modules or operations of the chip because
in distributed system processors are arranged at dif-
ferent places and operate together, there is a need
for communication between different processors and
that communication will take a reasonable amount of
time. But in Microfluidic Biochips as it is a single
chip and modules are virtual processors there is no
need for communication between them. Hence, there
will be no communication cost between modules (Su
and Chakrabarty, 2004).
Heterogeneous Earliest Finish Time based Scheduling for Digital Microfluidic Biochips
177
The fourth assumption is that single chip is used
for both assay operations and storage. In distributed
computing processors and memory are decoupled and
treated as different resources, But in Microfluidic
Biochips any part of the chip can be used for any op-
eration like mixing, detection or storage at different
times. Here we just designate some selected area of a
chip to function as different modules as a mixer, de-
tector, heater and storage of droplets pertaining to flu-
idic constraints for droplet routing (Su et al., 2006).
Work modules are derived from chip size. Means
based on chip size we deterministically decide what
are the optimal number of work modules we can put
in biochip (Micheli, 1994).
4 HEFT BACKGROUND
Heterogeneous Earliest Finish Time (HEFT) is a
scheduling algorithm used for achieving high per-
formance with low complexity in heterogeneous dis-
tributed systems where there are different heteroge-
neous processors available for solving tasks which
are interdependent. Operations and the interdepen-
dencies between operations are shown using a DAG.
So, HEFT schedules those tasks on the available pro-
cessors in such a way that Actual Finish Time of the
exit tasks is minimized as low as possible using the
available processor set. HEFT follows insertion based
scheduling policy which means that if two or more
tasks are scheduled on a processor p
j
then when we
are scheduling another task on that processor, then we
will search for a gap between the two scheduled pro-
cesses on that processor if that gap is adequate enough
to accommodate the execution time requirement of
that process then that process will be inserted between
those already scheduled processes. For example, a
processor p
j
is been assigned to task t
i
then proces-
sor p
j
will look for idle slots in its own schedule such
that it will calculate the difference between EFT and
EST of every two consecutive tasks. If that difference
is greater than or equal to the execution time w
i
then
that task t
i
will be inserted in that idle slot or gap on
processor p
j
. If task t
i
cannot find any idle slot on pro-
cessor p
j
then it will be inserted after the last sched-
uled task on p
j
. When first assigning a processor to a
task, HEFT will look for a processor which will take
least execution time for that process or in other terms
look for a processor which will give the earliest finish
time for that task (Topcuoglu et al., 2002).
4.1 Implementation Differences
DMHEFT modifies HEFT to work for DMFB envi-
ronments by modifying DAG attributes and calcula-
tions according to DMFB specifications. DMHEFT
don’t use insertion based scheduling policy as HEFT
does. This reduces overhead of checking all the idle
gaps on already scheduled processor. DMHEFT uses
least recently used policy when allocating modules to
operations to avoid deadlocks. In HEFT scheduling
sequence will be generated once, but in DMHEFT we
use Candidate list and it is modified after every iter-
ation. Other modifications and detailed algorithm is
described in Section 5.
5 HEFT FOR DIGITAL
MICROFLUIDICS
Heterogeneous Earliest Finish Time for Digital Mi-
crofluidics (DMHEFT) is a scheduling algorithm
which is a heuristic based list scheduling method to
produce better assay execution times. As it is a list
scheduling heuristic the whole process divides into
two phases operation prioritization and module allo-
cation to a particular operation based on operation se-
quence prioritized for scheduling obtained in the first
phase. To do the above mentioned two phases we
need some heuristics which are mentioned below and
based on attributes used in (Topcuoglu et al., 2002).
5.1 Graph Attributes used in DMHEFT
A process of any biochemical analysis in digital mi-
crofluidics is represented by a DAG G=(V,E) where
V represents a set of different operations and E rep-
resents a set of dependencies between operations like
operation v
3
cannot be completed before operation v
1
and operation v
2
. Let us say that there are v oper-
ations namely v
1
, v
2
, v
3
, ...., v
j
and q mixer modules
are there in DMFB namely p
1
, p
2
, p
3
, ...., p
q
. Any op-
eration with no parent (predecessor) is called as an
entry operation and operation with no child (succes-
sor) is called as an exit operation. Some distributed
systems require single entry single exit operation sys-
tem but in digital microfluidics we can have multiple
entry and multiple exit DAGs. As the first phase is
task prioritization, to do that we use upward rank of a
node. Upward rank of a node in a graph is the length
of the longest path from that particular node to exit
task including execution time of that particular opera-
tion. Upward rank of a node in the graph is calculated
by summing up execution time of that operation and
rank of the successor which is having the maximum
BIODEVICES 2019 - 12th International Conference on Biomedical Electronics and Devices
178
rank value in all it’s successor set. Upward rank of a
node is calculated recursively.
rank
u
(v
i
) = w
i
+ max
v
j
succ(v
i
)
(rank
u
(v
j
)) (4)
Where succ(v
i
) is the set of successor nodes of opera-
tion v
i
, w
i
is the execution time of operation i. As the
exit tasks don’t have any successor, upward rank for
that nodes is only the execution time of that particular
operation.
rank
u
(v
exit
) = w
exit
(5)
Before we can get final schedule (Actual Start Time
AST(v
i
, p
j
) and Actual Finish Time AFT(v
i
, p
j
)) we
take help of partial schedule: (Earliest Start Time
EST(v
i
, p
j
) and Earliest Finish Time EFT(v
i
, p
j
)).
AST(v
i
, p
j
), AFT(v
i
, p
j
) are Actual start and finish
time of operation v
i
on processor p
j
. EST(v
i
, p
j
),
EFT(v
i
, p
j
) are earliest possible execution start and
finish times of operation v
i
on processor p
j
. EST for
first tasks we execute on chip is zero because there
are no other operations executing on chip and they
can start immediately whenever they arrive.
EST(v
entry
, p
j
) = 0 (6)
EST for other nodes excluding entry nodes will be
calculated recursively. EST is maximum value be-
tween processor available time and maximum AFT
of all predecessor nodes of node v
i
. avail[j] is the
time at which mixer will be ready for execution of
another task if it is executing any task or any tasks are
queued on that mixer for execution. In other words if
operation v
k
is already executing on processor p
j
then
avail[j] is the AFT of v
k
. The other inner max block in
(7) refers to maximum AFT among all predecessor of
node v
i
. pred(v
i
) refers to set of all predecessor nodes
of particular node v
m
. If you want to calculate EST
of particular node v
m
then all it’s predecessor nodes
should have been already scheduled.
EST(v
i
, p
j
) = max{ max
v
m
pred(v
i
)
(AFT(v
m
)), avail[ j]}
(7)
EFT(v
i
, p
j
) is Earliest execution Finish Time of op-
eration v
i
on mixer p
j
. It is summation of EST(v
i
, p
j
)
and execution time of operation v
i
on mixer p
j
. EFT
also calculated recursively and if EFT of particular
node has to be calculated all its immediate predeces-
sor operations should have already been scheduled.
EFT(v
i
, p
j
) = w
i, j
+ EST(v
i
, p
j
) (8)
After a operation is scheduled on a mixer then we
can get AST and AFT of that task. Main objective of
scheduling is to reduce the AFT of exit task or the last
task in the prioritized scheduling sequence generated
using upward rank values.
AssayLength = max{AFT(n
exit
)} (9)
5.2 Proposed Algorithm HEFT for
Digital Microfluidic Biochips
DMHEFT is an operation scheduling algorithm based
on algorithm proposed in (Topcuoglu et al., 2002)
for task scheduling on heterogeneous processors.
DMHEFT is a heuristic based list scheduling algo-
rithm. As it is list scheduling algorithm it divides the
process into two main phases: Operation prioritizing
phase to prioritize operations based on upward rank
values calculated and Module selection phase for
selecting a best available module for a particular
operation in scheduling sequence.
Operation Prioritizing Phase: In DMFB Schedul-
ing we assume that all operations of a bio-assay
are available before we start scheduling, there are
no operations coming in between the intermediate
stages of assay execution. As all operations are
available beforehand we will prioritize operations so
as to let the system know which operation sequence
it has to execute. To prioritize operations we first
calculate upward rank of each operation starting from
nodes in last level of a DAG to first level of DAG
according to (4),(5). Now priority of a node is the
respective upward rank of that node. Now as we have
priority of all nodes we sort the operations based on
their priorities (upward rank values) in a decreasing
manner, this will be scheduling sequence that has to
be executed by DMFB. When two or more nodes
have same priority then tie-breaking will be done
randomly. The prioritized scheduling sequence is
a topological order of operations which abides all
precedence constraints in DAG.
Module Selection Phase: From the prioritized
scheduling sequence of operations select operation
one by one and allocate an available module which
has minimum mixing time/detection time for that par-
ticular operation. DMHEFT uses a different strategy
for selecting a module for operations unlike original
HEFT which uses insertion based scheduling. Gener-
ally as mixer area (number of cells) increases, mixing
time decreases and vice versa. So, every time a mix-
ing operation comes it selects a larger mixer available.
Normally in HEFT for multiple processors with in-
tercommunication between them uses insertion based
scheduling policy for selecting a processor for a task.
But in Microfluidic Biochips there is no communi-
cation between modules needed, because they all are
placed on a single chip. As there is no communication
between modules needed, there will not be any gaps
between two scheduled operations on a module ex-
cept for precedence constraints (an operation cannot
Heterogeneous Earliest Finish Time based Scheduling for Digital Microfluidic Biochips
179
start until an operation finishes). An operation may
have better EST on module p
i
compared to module
p
j
but, we have to consider only EFT because module
p
i
with lower EST for operation v
x
may be a smaller
module and module p
j
with higher EST for operation
v
x
is a larger module and even if starts late also it will
take less time to execute. Another case is that if two
operations v
x
, v
y
have same EFT on module p
j
then
the module that is not used recently will be selected
because if scheduler keep on assigning a module be-
cause it is having less mixing time, droplets may get
congested and may lead to deadlocks and stalling of
droplets which causes overhead in routing. Algorithm
of DMHEFT for digital microfluidic biochips is given
in Algorithm 1.
Algorithm 1: DMHEFT (HEFT for Digital Mi-
crofluidics).
1 Compute rank
u
for all operations by
traversing DAG bottom-up manner starting
with exit tasks;
2 Assign child operations of nodes with EST=0
to candidate list (CL);
3 while u CL unscheduled do
4 Sort the operations in CL in the order of
their rank
u
in decreasing manner;
5 Take the current operation v
i
from CL;
6 for Each Available module p
k
in module
library p
k
Q do
7 Compute EST(v
i
, p
k
), EFT(v
i
, p
k
)
8 end
9 Assign operation v
i
to Module p
j
that
gives minimum EFT;
10 Remove operation v
i
from CL;
11 Add v
i
s successors to CL;
12 (u, v) E if AST(v) > AFT(u) then
13 Store droplet from Operation u in
available module for H(u) interval
14 end
15 end
5.3 An Example
Here our proposed DMHEFT method has been ex-
plained with an example on In-vitro diagnostics assay
with 2 samples and 3 reagents on a 15× 13 DMFB
with four 3× 4 modules. S
1
refers to Serum, S
2
refers
to Plasma and R
1
, R
2
, R
3
refers to Glucose, Lactate,
Pyruvate respectively. All Input/Dispense operations
will take 2s, M
1
, M
2
, M
3
, D
1
, D
2
, D
3
will take 3s and
M
4
, M
5
, M
6
, D
4
, D
5
, D
6
will take 5s and all Output op-
erations are instantaneous.
As In-vitro2 is a DAG with 6 connected com-
I
1
I
2
I
3
I
4
I
5
I
6
I
7
I
8
I
9
I
10
I
11
I
12
S
1
S
1
S
1
S
2
S
2
S
2
R
1
R
2
R
3
R
1
R
2
R
3
M
1
M
2
M
3
M
4
M
5
M
6
D
1
D
2
D
3
D
4
D
5
D
6
O
1
O
2
O
3
O
4
O
5
O
6
d(I
i
) = 2s
d(M
13
) = 3s
d(M
46
) = 5s
d(D
13
) = 3s
d(D
46
) = 5s
d(O
i
) = 0s
Figure 2: In-vitro Assay with 2 Samples, 3 Reagents.
S1
S2
R1
R2
R3
DT1
DT2
DT3
DT4
0 2 4
6 8 10 12 14 16 18 20
I2
I4
I8
I10
I1
I5
I7
I11
I6
I9
I12
I3
M2
D2 M6
D6
M1 D1
M3 D3
M4 D4
M5 D5
Figure 3: Gantt chart for In-vitro Assay with 2 Samples, 3
Reagents.
ponents/trees, priorities are calculated differently for
each connected component. For three trees we will
get priorities as 8,8,6,3,0 and for rest three trees we
get 12,12,10,5,0. Operations are added to ready queue
based on root nodes priority. Every tree is processed
completely if it has been taken for execution because
if we stop that in between, we have to store that
droplet in some working module until the next op-
eration in that tree uses that droplet. if we allow
interleaving then there will be more droplets stored
on chip. Operations will be executed based on the
availability of input ports because we cannot sched-
ule two operations simultaneously which uses same
input port. So, if two operations with same priority
which uses same input port are in ready queue then
operation which uses different input port will be cho-
sen for simultaneous execution. And DMHEFT fol-
lows greedy strategy in executing operations so al-
ways allow the highest rank valued operation when
two operations with different rank values are queued.
DMHEFT will not schedule dispense operations until
the subsequent mix operations gets scheduled.
6 EXPERIMENTAL RESULTS
6.1 Simulation Setup
DMHEFT algorithm is implemented in C++ pro-
gramming on Intel(R) Core i7 3.40 GHz processor
with 4GB RAM and 500GB hard disk. DMHEFT’s
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Table 1: Scheduling Assay Lengths for Different Benchmarks by Various Scheduling Algorithms.
Benchmark
No.of
Operations
Scheduling Assay Length (in time-steps)
LS PS FDLS GA1 GA2 ILP DMHEFT
PCR 15 12 12 12 12 12 12 12
In-Vitro 1 16 15 15 15 15 15 15 15
In-Vitro 2 24 21 19 18 18 19 19 19
In-Vitro 3 36 25 27 25 23 23 23 25
In-Vitro 4 48 31 33 31 29 29 29 31
In-Vitro 5 64 45 45 41 39 39 39 41
Protein 103 198 187 182 179 194 180 198
scheduling assay lengths are compared with 6 existing
algorithms, those are ILP based formulation (Rick-
etts et al., 2006), LS (Grissom and Brisk, 2012a), PS
(Grissom and Brisk, 2012b), FDLS (O’Neal et al.,
2012), GA1 (Ricketts et al., 2006), GA2 (Su and
Chakrabarty, 2008). All these scheduling algorithms
were already implemented in UCR DMFB Static Sim-
ulator (Grissom et al., 2012), (Grissom et al., 2015)
and made publicly available. We executed all of
these scheduling algorithms on three famous bench-
marks for DMFB synthesis as provided in (Su and
Chakrabarty, 2006) namely PCR, In-Vitro Diagnos-
tics with 5 different variants and Protein synthesis as-
say. In-Vitro Diagnostics assays have 5 different as-
says based on number of samples which varies from 2
to 4 and number of reagents in reactions which also
varies from 2 to 4. All of these assays are repre-
sented in DAG form and readily available in UCR
DMFB Static Simulator. Each bioassay requires dif-
ferent number of I/O ports and has different number
of operations like mixing, storage, split, heating or
detection.
All of the scheduling algorithms are implemented
on a 15× 13 DMFB with different configuration (I/O
ports and Module library) based on assay. PCR assay
has 8 input ports and 1 output ports and In-Virto as-
say has 12 input ports and 1 output port and Protein
Synthesis assay has 5 input ports and 1 output port
and all of the three assays have four 3× 4 reconfig-
urable modules placed on 15 × 13 DMFB. Modules
are placed according to virtual topology presented
in (Grissom and Brisk, 2012a), (Grissom and Brisk,
2014) so that in future no placement and routing fail-
ures should occur. Number of droplets allowed to be
stored on each module(k) are 4.
6.2 Time Complexity
DMHEFT runs with complexity O(v q) where v is
number of bioassay operations and q is number of
modules in the chip. Where O(v) is for calculating
priority of everyvertex/operationin DAG and O(vq)
is for selecting best available module p
j
from a mod-
ule library Q for operation v
i
.
6.3 Assay Length Results
Table 1 reports the scheduling assay lengths in time
steps (1 time step= 1 s) of different scheduling al-
gorithms including DMHEFT on each of the above
mentioned benchmarks. All In-vitro assays got same
assay length for k=2 and k=4 but, Protein assay got
lesser assay lengths when k=4 than k=2. And all as-
says gets lower assay lengths if we increase the num-
ber of modules. DMHEFT performed well on PCR,
In-Vitro assays but not so compromising over Pro-
tein assay. DMHEFT generates better schedules than
LS in two cases and produces schedules no longer
than LS in all other cases. DMHEFT runtime com-
plexity is also polynomial as LS. Compared to PS,
DMHEFT produces shorter schedules in three cases
and in other three cases same length schedules and
in one case slightly larger schedule than PS. PS only
works on trees/forests but, DMHEFT can be applied
to any kind of DAG. Compared to FDLS, DMHEFT
produces five equal length schedules and two longer
schedules. But, DMHEFT rank calculation mecha-
nism is simpler than FDLS and that is why it runs
faster than FDLS. And Compared to GA1, GA2 and
ILP DMHEFT produces equal length schedules in
few cases and longer schedules in most of the cases
because obviously they run for more amount of time
and verify nearly 2000 random generated schedules
and pick local optimal solution and ILP also runs for a
time limit of four hours to get these assay lengths. But
DMHEFT within much shorter time gives schedules
with little difference in the assay length compared to
GA1, GA2, ILP.
7 CONCLUSION
We proposed a simple scheduling algorithm
DMHEFT for digital microfluidics which is based
Heterogeneous Earliest Finish Time based Scheduling for Digital Microfluidic Biochips
181
on HEFT proposed by (Topcuoglu et al., 2002).
DMHEFT is a list scheduling based greedy heuristic
works in two phases, operation prioritization for
generating scheduling sequence and module allo-
cation. DMHEFT schedules each vertex only once
unlike ILP and iterative improvement methods. It
uses upward rank value for prioritizing the operations
and determining scheduling sequence. Module with
earliest finish time is chosen for operations in the
queue. DMHEFT uses Least Recently Used policy
when scheduling operations on modules to avoid
deadlocks in future steps. DMHEFT can schedule
all types of DAGs unlike PS which only works
on trees/forests. Produces shorter or equal length
schedules than LS in all cases. Gives shorter or
equal length schedules than PS except in one case.
DMHEFT’s rank calculation mechanism is simpler
than FDLS’s, that is why it runs faster than FDLS.
Although DMHEFT produces longer schedules than
GA1, GA2 and ILP it runs much faster than them
with small difference in assay lengths.
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