Consider a router shown in the below figure. It serves $4$ users, and its outgoing link capacity is

$200$ Mbps$.$ The ith user has pi probability for being active. When active, the user generates data at

$100$ Mbps$.$ Suppose that p$1=0\mathrm{.}3,$ p$2=0\mathrm{.}5,$ p$3=0\mathrm{.}2,$ and p$4=0\mathrm{.}4.$ What is the probability of the

router being congested? Please provide your calculation det

ails.