Given a network using slotted Aloha multiple access protocol with N users and each user attempting to access the channel with probability P. It is safe to assume that each user always has a frame of data to send and that it uses access probability for both first time frame access and access after a collision. The probability of a single node successfully accessing the channel is
\(P(1-P)^{n-1}\)
and the probability that anyone of the nodes successfully accesses the channel is
\(NP(1-P)^{n-1}\)
a)If there are 20 users,determine the value of P that maximizes the probability of any of the nodes accessing the channel. What is this probability that anyone of the nodes will successfully access the channel?
b)Consider problem 5again,but this time assume that instead of each user always having a frame to send, each user has a frame to send with probability q. Derive the expression for the probability that anyone of the nodes will successfully access the channel in terms of P, q, and N. If q < 1, will this probability be greater or less than the one found?