Circuit & Packet Switching $(15$ points$)$

Consider the example in $$Packet vs$.$ Circuit Switching$$ slide with the following variation. Each user, when active, needs $400$ Kbps bandwidth. There are total $30$ such users wanting to get connected, where each user will be active with probability $0\mathrm{.}2,$ all going through a link of $6$ Mbps$.$

a$.$

Under circuit switching, up to how many users can be supported on this link? $(5$ points$)$

b$.$

Under packet switching, write down the probability that there are k active users out of $30.$ What is the average number of active users? What is the probability that the link is overloaded, i$.$e$.,$ when the link cannot support the bandwidth requirement of all active users? $(10$ points$)$

$($Just write down the mathematical expression. You don't need to compute the exact number.$)$

Hint: Use binomial$$distribution$.$