On-chip Networks for Manycore Architecture Myong ... - People - MIT

Uniform PROM
Uniform PROM weighs the routing probabilities so that each
possible minimal path has an equal chance of being chosen.
Let’s suppose that a
packet on the way to node D is currently at node S, where x and y indicate the
number of hops from S to D along the X and Y dimensions, respectively.
When
either x or y is zero, the packet is going straight in one direction and S simply moves
the packet to the direction of D. If both x and y are positive, on the other hand, S
can send the packet either along the X dimension to node S 0 x, or the Y dimension to
node S 0 y. Then, for each of the possible next hops,
N S 0 x !D = {(x 1) + y}!
(x 1)! · y!
N S 0 y !D =
{x +(y 1)}!
x! · (y 1)!
where N A!B represents the number of all minimal paths from node A to node B.
In order that each minimal path has the same probability to be taken, we need
to set the probability of choosing Sx 0 and Sy 0 proportional to N S 0 x !D and N S 0 y !D,
respectively. Therefore, we calculate P x , the probability for S to move the packet
along the X dimension as
P x =
N S 0 x !D
N S 0 x !D + N S 0 y !D
=
x · (x + y 1)!
x · (x + y 1)! + y · (x + y 1)! = x
x + y
and similarly, P y =
y . In this configuration, PROM is equivalent to n-phase ROMM
x+y
with each path being chosen at the source with equal probability. 4
Parametrized PROM The two configurations above are, in fact, two extremes of
a continuous family of PROM algorithms parametrized by a single parameter f, as
shown in Figure 2-2(b). At the source node, the router forwards the packet towards
the destination on either the horizontal link or the vertical link randomly according
to the ratio x + f : y + f, where x and y are the distances to the destination along
the corresponding axes. At intermediate nodes, two possibilities exist: if the packet
4 again, modulo di↵erences in virtual channel allocation
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