1. In Section 6.3, we provided an outline of the derivation of the efficiency of slotted ALOHA. In this problem we’ll complete the derivation. a. Recall that when there are N active nodes, the...

1. In Section 6.3, we provided an outline of the derivation of the efficiency of slotted ALOHA. In this problem we’ll complete the derivation.

a. Recall that when there are N active nodes, the efficiency of slotted ALOHA is
Np(1 -
p)

^N-1

. Find the value of
p
that maximizes this expression.

b. Using the value of
p
found in (a), find the efficiency of slotted ALOHA by letting
N
approach infinity. Hint: (1 -
1/N)
N
approaches 1/e as
N
approaches infinity.