Exercise $1.$ Imagine you are a Network engineer in charge of setting up the network between UC Irvine and UC Berkeley. You are given two options for network configurations as given below: $($a$)$ A direct link from Irvine to Berkeley has a link of approximately $660$ km with a propagation speed of $2108$m$/$s and a transmission Exercise $2.$ A company has a dedicated link of $150$ Mbps$.$ Each employee, when online, transmits

continuously at $12$ Mbps when active, but each user is active only $25$ percent of the time.

Circuit Switching: a dedicated path or circuit is established between the sender and receiver for the

duration of the transmission.

Packet Switching: data is divided into small units called packets. Each packet is sent independently

through the network. Packets can take different paths to reach the destination where they are reassembled

into the original message.

$1.$ How many users can the link support when circuit switching is used?

$2.$ For the remainder of this problem, suppose packet switching is used and that the number of users

is what you calculated in the previous question. What is the probability that more than $4$ users are

transmitting at the same time?

$3.$ Now suppose that the system will drop any packets if it is being utilized at $100\%$ capacity without

queuing them. If we need to guarantee a probability of at most $0\mathrm{.}05$ of messages being lost, what is

the maximum number of users we can support under packet switching.