Consider three nodes, A, B and C, that adopt the slotted ALOHA protocol to contend for a channel. Suppose node A has more data than node B, and node B has more data than node C to be transmitted. Denote by pA, pB, pC the retransmission probability of nodes A, B, and C respectively, assuming that pA >= pB and pB >= pC. a. Calculate the average throughput of node A (i.e. probability of successful transmission for a given slot). What is the total efficiency of the protocol with these three nodes? (10 points) b. If pA = 3pB and pB=3pC, is node A’s average throughput nine times as large as that of node C? Why or why not? Justify your answer. If not, how can you choose pA and pC to make that happen? (10 points) c. In general, suppose there are N nodes, among the N nodes, there are x nodes with retransmission probability p, and y nodes with retransmission probability q, and the rest z nodes with retransmission probability r, where N=x+y+z and p+q+r=1. Provide expressions to compute the average throughput of any node with retransmission probability p, q or r, respectively. What is the overall throughput of the N nodes? (4 points)