Suppose five active nodes A, B, C, D and E are competing for access to a channel using slotted ALOHA. Assume each node has an infinite number of packets to send. Each node attempts to transmit in each slot with probability p. The first slot is numbered slot 1, second slot is numbered slot 2 and so on

a. What is the probability that node B succeeds for the first time in slot 3. Think about what should happen for node B to succeed in slot 3 for first time. What should happen in slot 1 and 2? Workout the probabilities of these individual events. As these events are what we call mutually exclusive events, the overall probability of that event is the multiplication of individual events.

b. What is the probability that some node (either A, B, C, D or E) succeeds for the first time in slot 3?

c. What is the probability that the first success (for any of the nodes) occurs in slot 3? d. What is the efficiency/utilisation of this four node system?