Proof of Theorem 1
v When a packet arrives in a time slot it must choose
a memory not chosen by
1. The N – 1 other packets that arrive at that timeslot.
2. The N other packets that depart at that timeslot.
3. The N - 1 other packets that can depart at the same time
as this packet departs (in future).
v Proof:
Ø By the pigeon-hole principle, 3N –1  memories that can
perform at most one memory operation per time slot are
sufficient for the router to be work-conserving
10