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Application-Specific Network-on-Chip Synthesis
• Variable for flow of traffic out of a port: For each edge (v i ,v j )  ∊  E, let O i,j,k,l
be a {0,1} variable that is 1, if traffic from node v i to node v j flows out
of port p k,l ; otherwise it is 0.
• Variable for flow of traffic into a port: For each edge (v i ,v j )  ∊  E, let I i,j,k,l be
a {0,1} variable that is 1, if traffic from node v i to node v j flows into
port p k,l ; otherwise it is 0.
9.5.1.2 Derived Variables
• Variable for total traffic flowing out of a port: Let BO k,l represent the total
traffic flowing out of port p k,l . It can be written as
BO k l
, = ∑ ω(e m )×O , , ,
i j k l
∀em ={vi ,vj }∈E
• Variable for total traffic flowing into a port: Let BI k,l represent the total
traffic flowing into port p k,l . It can be written as
BI k l
, = ∑ ω(e m )× I , , ,
i j k l
∀em ={vi ,vj }∈E
• Variable for flow of traffic on a link: Let Z i,j,k,l,m,n be a {0,1} variable that
is 1, if traffic (v i , v j ) leaves port l of router k and that port is connected
to port n of router m. It can be represented as
Z i j k l m n
, , , , , = O i j k l
, , , × RR k l m n
, , ,
• The equation can be linearized using the following two rules:
O i j k l
, + RR , , , 2 i j k l m n
, ,
k l m n ≥ × Z , , , , ,
O
+ RR , , ≤ Z i j k l m n + 1
i j k l
, , ,
k l m n
,
, , , , ,
9.5.2 Objective Function
The objective is to minimize the power consumption of the NoC due to
cumulative traffic flowing through all routers. The overall function is as
follows:
Minimize (P R + P L ), P R being the router power and P L being the link power,
is given by
P R = Ψ i ×
BI i j
, + Ψ o ×
BO i j
,
∑ ∑
∑ ∑
r R p
∀ ∈ R ∀
∀ ∈ ∀
r
p
i
i j
,
i
i j
,