Circuit Switching and Packet Switching:

Consider a network with a capacity of C $=8$ Mbps$.$ Suppose that each user requires a

fixed rate R $=200$ Kbps when transmitting, but each user independently transmits only

$25\%$ of the time or with probability p $=0\mathrm{.}25.$

a$)(1$ pt$)$ Using circuit switching, what is the maximum number of users that can be

supported?

b$)(2$ pts$)$ What is the above circuit$-$switched network$$s expected utilization, i$.$e$.,$ the

fraction of its resources being used on average?

c$)(2$ pts$)$ Assume packet switching is used with a total of N $=40$ users. What is the

probability the users $1,3,$ and $7$ are active and the rest inactive?