Clos Network

(a) Consider a 3-stage Clos network like the one we saw in class, with

N = 4, and k = n = m = 2, i.e. there is no expansion between the first

and second stage. Because k < 2n−1, the switch is not guaranteed to

be strictly non-blocking. Prove that it is in fact strictly non-blocking,

or find a counter-example to show that it isn’t.

(b) Joe Engineer believes that if we add connections according to the

following algorithm, a Clos network is strictly non-blocking when k =

n.

Algorithm: When adding new connections, if possible, use the center

stage block that already has the most connections through it. If not

possible, try the second most congested center stage block; and so on,

until a block is found. Ties are broken at random; and once added,

connections are never rearranged.

(i) With this algorithm, is the switch in part (a) strictly non-blocking?

(ii) Is the switch strictly non-blocking for N > 4? (Hint: Try N = 9,

k = n = m = 3.)