##### Achieving desired throughput in Slotted ALOHA protocol

You have two computers, A and B, sharing a wireless network in your room. The network

runs the slotted Aloha protocol with equal-sized packets. You want B to get twice the throughput over the wireless network as A whenever both nodes are backlogged. You configure A to send packets with probability p. What should you set the transmission probability of B to, in order to achieve your throughput goal?

(A) p / 1+p

(B) p / 1+2p

(C) 2p / 1+p

(D) 1/2

Let B’s transmission probability be p_{b}.

The utilization is equal to p(1−p_{b})+(1−p)p_{b}.

A’s throughput is the first term, p(1 − p_{b}),

and B’s throughput is the second term, p_{b}(1 − p).

Using the fact that we want B to get twice the throughput of A, and solving for p_{b} in terms of p,

2. p(1 − p_{b}) = p_{b}(1 − p)

solving**, p _{b} = 2p/1+p**