Problem $3[15$ points$]$: Consider the network depicted in the figure below where nodes

$\frac{?}{\text{b}\text{a}\text{r}}(A)$ and B are hosts, and node S is a store$-$and$-$forward switch. The switch has a very large

buffer and never loses packets.

Suppose that link $AS$ has a bandwidth of $1M\frac{b}{s}$ and propagation delay of $1$ ms $,$ and

link $SB$ has a bandwidth of $2M\frac{b}{s}$ and propagation delay of $2$ ms $.$

$($a$)$ Assume that node A has a data message of size $10,000$ bits that it wishes to transmit

to node B $.$ What is the end$-$to$-$end delay if node A sends the entire message as a single

packet?

$($b$)$ Now, assume that node A divides data into $10$ equal$-$sized packets $($i$.$e$.,$ each packet

has $1,000$ bits$).$ In this case, what is the end$-$to$-$end delay between A and B$?$ Assume

a packet enters the switch as soon as the first bit arrives, and leaves the switch only

when the last bit is transmitted. Assume that the packets are sent back$-$to$-$back.

$($c$)$ Plot the number of packets stored in switch $S$ as a function of time.