(Solution) - Consider two nodes A and B that use the slotted -(2025 Original AI-Free Solution)

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Consider two nodes, A and B, that use the slotted ALOHA protocol to contend for a channel. Suppose node A has more data to transmit than node B. and node A's retransmission probability PAis greater than node B's retransmission probability, PB
a. Provide a formula for node A's average throughput. What is the total effciency of t.he protocol with these two nodes?
b. If PA = 2PB' is node A's average throughput twice as large as that of node S" Why or why not? If not, how can you choose PA and P8 to make that happen'.'
c. In general, suppose there are N nodes, among which node A has retransmission 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.