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for the transportation. An efficient routing schedule (virtual route) is often required to
be developed to provide an optimal routing in terms of objectives such as latest arrival
time and overall cell utilization. Droplet routing problem in
DMFB
s is typically
modeled in terms of a 2D-grid (Figure 3). For each droplet, there exists a set of source
grid locations, a set of target grid locations, and (optionally) a set of mixers. Each
source-target combination is defined as a net. A 2-pin net has a single source and
single target. A combination of two Sources, one Mixer and one Target forms a 3-pin
net. While execution of routing of multiple nets within a 2D planar array of a DMFB
there are possibilities of intersection or overlapping of droplet routes during their
concurrent routing in time-multiplexed manner. To avoid such undesirable behaviors
following fluidic constraints are introduced.
Fig. 2.
Top down Design Methodology
Fig. 3.
Routing with 2-pin nets in a 2D Array For
DMFBs
Let
d
i
at
(x
t
i,
y
t
i
)
and
d
j
at
(
x
t
j
, y
t
j
)
denote two independent droplets at any given
timestamp
t
. Then, the following constraints, defined as Fluidic
Constraint
s are
required to be satisfied for any time
t
while routing [25]:
Static constraint
:
| x
t
i
- x
t
j
| >1
or
| y
t
i
- y
t
j
| >1
Dynamic constraint
: | x
t+1
i
- x
t
j
| >1
or,
| y
t+1
i
- y
t
j
| >1
or,
| x
t+1
j
- x
t
i
| >1
or
| y
t+1
j
- y
t
i
| >1
This implies that for any droplet at location
(x, y)
,
the locations
(x+1, y), (x-1, y),
(x, y+1), (x, y-1), (x+1, y+1), (x+1, y-1), (x-1, y-1),
and
(x-1, y+1)
are prohibited for
any other droplet to enter at timestamps
t
and
t+1
in order to maintain these fluidic
constraints. Hence, all the locations adjacent to
(x, y)
as stated above form a
Critical
Zone
(Figure 2) for any droplet at
(x, y)
at timestamp
t
. A predetermined time limit
called the
Timing
Constraint
defines the maximum allowed transportation time for a
given set of droplets.
