Consider two nodes, A and B, that use the slotted ALOHA protocol to con- tend for a channel. Suppose node A has more data to transmit than node B, and node A's retransmission probability p, is greater than node B's retrans- mission probability, PB. a. Provide a formula for node A's average throughput. What is the total effi- ciency of the protocol with these two nodes? b. If pA= 2pg, is node A's average throughput twice as large as that of node B? Why or why not? If not, how can you choose p, and pg to make that happen? c. In general, suppose there are N nodes, among which node A has retrans- mission probability 2p and all other nodes have retransmission probability p. Provide expressions to compute the average throughputs of node A and of any other node.

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