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 ﬁnish 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

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

, M

, ..., M

) and Input/Output ports

, I

, ..., I

, O

, ..., O

• Each operation’s execution time (E

, E

, ..., E

)

where v = |V|.

• The number of distinct input ﬂuids (F

, F

, ..., F

)

• 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

u∈V

(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

v∈succ(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

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

is been assigned to task t

then proces-

sor p

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

then

that task t

will be inserted in that idle slot or gap on

processor p

. If task t

cannot ﬁnd any idle slot on pro-

cessor p

then it will be inserted after the last sched-

uled task on p

. 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

cannot be completed before operation v

and operation v

. Let us say that there are v oper-

ations namely v

, v

, ...., v

and q mixer modules

are there in DMFB namely p

, p

, ...., p

. 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

) = w

+ max

∈succ(v

)

(rank

)) (4)

Where succ(v

) is the set of successor nodes of opera-

tion v

, w

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

exit

) = w

exit

(5)

Before we can get ﬁnal schedule (Actual Start Time

AST(v

, p

) and Actual Finish Time AFT(v

, p

)) we

take help of partial schedule: (Earliest Start Time

EST(v

, p

) and Earliest Finish Time EFT(v

, p

)).

AST(v

, p

), AFT(v

, p

) are Actual start and ﬁnish

time of operation v

on processor p

. EST(v

, p

EFT(v

, p

) are earliest possible execution start and

ﬁnish times of operation v

on processor p

. 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

) = 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

. 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

is already executing on processor p

then

avail[j] is the AFT of v

. The other inner max block in

(7) refers to maximum AFT among all predecessor of

node v

. pred(v

) refers to set of all predecessor nodes

of particular node v

. If you want to calculate EST

of particular node v

then all it’s predecessor nodes

should have been already scheduled.

EST(v

, p

) = max{ max

∈pred(v

)

(AFT(v

)), avail[ j]}

(7)

EFT(v

, p

) is Earliest execution Finish Time of op-

eration v

on mixer p

. It is summation of EST(v

, p

)

and execution time of operation v

on mixer p

. 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

, p

) = w

i, j

+ EST(v

, p

) (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

compared to module

but, we have to consider only EFT because module

with lower EST for operation v

may be a smaller

module and module p

with higher EST for operation

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

, v

have same EFT on module p

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

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

in decreasing manner;

5 Take the current operation v

from CL;

6 for Each Available module p

in module

library p

∈ Q do

7 Compute EST(v

, p

), EFT(v

, p

)

8 end

9 Assign operation v

to Module p

that

gives minimum EFT;

10 Remove operation v

from CL;

11 Add v

’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

refers to Serum, S

refers

to Plasma and R

, R

refers to Glucose, Lactate,

Pyruvate respectively. All Input/Dispense operations

will take 2s, M

, M

, D

will take 3s and

, M

, D

will take 5s and all Output op-

erations are instantaneous.

As In-vitro2 is a DAG with 6 connected com-

d(I

) = 2s

d(M

1−3

) = 3s

d(M

4−6

) = 5s

d(D

1−3

) = 3s

d(D

4−6

) = 5s

d(O

) = 0s

Figure 2: In-vitro Assay with 2 Samples, 3 Reagents.

DT1

DT2

DT3

DT4

0 2 4

6 8 10 12 14 16 18 20

I10

I11

I12

D2 M6

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

BIODEVICES 2019 - 12th International Conference on Biomedical Electronics and Devices

180

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(v∗q)

is for selecting best available module p

from a mod-

ule library Q for operation v

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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