Consider the following idealiz

Consider the following idealized WiMAX scenario. The downstream sub-frame (see Figure 6. 17)is slotted in time, with N downstream slots per sub-frame, with all time slots of equal length in time. There are four nodes, A, B,C, and D, reachable from the base station at rates of 10 Mbps, 5 Mbps, 2.5 Mbps, and 1 Mbps, respectively, on the downstream channel. The base station has an infinite amount of data to send to each of the nodes, and can send to any one of these four nodes during any time slot in the downstream sub-frame.
a. what is the maximum rate at which the base station can send to the nodes, assuming it can send to any node it chooses during each time slot? Is your solution fair? Explain and define what you mean by "fair."
b. If there is a fairness requirement that each node must receive an equal amount of data during each downstream sub-frame, what is the average transmission rate by the base station (to all nodes) during the downstream sub-frame? Explain how you arrived at your answer.
c. Suppose that the fairness criterion is that any node can receive at most twice as much data as any other node during the sub-frame. What is the average transmission rate by the base station (to all nodes during the sub-frame? Explain how you arrived at your answer.