Suppose users share a 3 Mbps link. Also suppose each user requires 150 kbps when transmitting, but each user transmits only 10 percent of the time. (See the discussion of packet switching versus circuit switching in textbook)

a. When circuit switching is used, how many users can be supported? Why?

b. For the remainder of this problem, suppose packet switching is used. Find the probability that a given user is transmitting.

c. Suppose there are 120 users. Find the probability that at any given time; exactly n users are transmitting simultaneously, provide a generic form of your expression using n (Hint: Use the binomial distribution.) Now, consider the following values for n: 10, 20, 50, 100. Do you see a trend? Discuss.

d. Now consider a problem of finding the probability that there is k or more users transmitting simultaneously out of 120 users. Value of k could be 2, 3 or 4. For this problem, you dont need to find the exact answer, but rather discuss how you would approach this problem. What would one of the ways to possibly find the answer. [ hint: if P(x) + P(y) = 1, so P(x) = 1 P(y) ] [If you feel comfortable in finding the result, please do so to show your work; however that wont add or subtract any points]