Consider a random access network with slotted ALOHA. Define the following parameters: S = average throughput: average number of successful transmissions per unit time G = total traffic load: average number of transmissions attempted per unit time, including new packets as well as retransmissions of old packets Assume that: (1) all packets have the same length; (2) nodes cannot generate a packet while trans- mitting or trying to transmit; and (3) the number of nodes attempting to transmit (both new packets and old packets that collided) follow a Poisson distribution. (a) What is the average throughput of the network? (b) At which traffic load is the average throughput maximum? (c) What is the main reason that slotted ALOHA outperforms pure ALOHA in terms the average throughput? What is the cost to achieve the average throughput gain?