P$1(20$ points$).$ Consider an application that transmits data at a steady rate $($for example, the sender generates an $N-$bit unit of data every $k$ time units, where $k$ is small and fixed$).$ Also, when such an application starts, it will continue running for a relatively long period of time. Answer the following questions, briefly justifying your answer:

a$.$ Would a packet$-$switched network or a circuit$-$switched network be more appropriate for this application? Why? $(10$ points$)$

b$.$ Suppose that a packet$-$switched network is used and the only traffic in this network comes from such applications as described above. Furthermore, assume that the sum of the application data rates is less than the capacities of each and every link. Is some form of congestion control needed? Why?

points$)$

P$2(20$ points$).$ This elementary problem begins to explore propagation delay and transmission delay, two central concepts in data networking. Consider two hosts, A and B$,$ connected by a single link of rate $R$ bps$.$ Suppose that the two hosts are separated by $m$ meters, and suppose the propagation speed along the link is $s$ meters$/$sec$.$ Host A is to send a packet of size $L$ bits to Host B$.$

a$.$ Express the propagation delay, $d_{\text{p}\text{r}\text{o}\text{p}\text{,}in\text{t}\text{e}\text{r}\text{m}\text{s}ofm}m$ and $s.(2$ points$)$

b$.$ Determine the transmission time of the packet, $d_{\text{t}\text{r}\text{a}\text{n}\text{s}\text{,}in\text{t}\text{e}\text{r}\text{m}\text{s}ofL\text{a}\text{n}\text{d}R.(2\text{p}\text{o}\text{i}\text{n}\text{t}\text{s})}$

c$.$ Ignoring processing and queuing delays, obtain an expression for the end to$-$end delay. $(2$ points$)$

d$.$ Suppose Host A begins to transmit the packet at time $t=0.$ At time $t=d_{\text{t}\text{r}\text{a}\text{n}\text{s}\text{,}\text{w}\text{h}\text{e}\text{r}\text{e}is}$ bit of the packet? $(3$ points$)$

e$.$ Suppose points$)$

f$.$ Suppose $d_{\text{p}\text{r}\text{o}\text{p}\text{i}\text{s}\text{l}\text{e}\text{s}\text{s}\text{t}\text{h}\text{a}\text{n}}{d}_{\text{t}\text{r}\text{a}\text{n}\text{s}\text{.}At\text{t}\text{i}\text{m}\text{e}}t=d_{\text{t}\text{r}\text{a}\text{n}\text{s}\text{,}\text{w}\text{h}\text{e}\text{r}\text{e}is\text{t}\text{h}\text{e}\text{f}\text{i}\text{r}\text{s}\text{t}\text{b}\text{i}\text{t}of\text{t}\text{h}\text{e}\text{p}\text{a}\text{c}\text{k}\text{e}\text{t}\text{?}}(3$ points$)$

g$.$ Suppose $s=2\mathrm{.}5*{10}^8,L=1500$ bytes, and $R=10Mbps.$ Find the distance $m$ so that $d_{\text{p}\text{r}\text{o}\text{p}}$ equals $d_{\text{t}\text{r}\text{a}\text{n}\text{s}\text{.}(5\text{p}\text{o}\text{i}\text{n}\text{t}\text{s})}$

P$3(20$ points$).$ In this problem, we consider sending real$-$time voice from Host A to Host B over a packet$-$switched network $($VoIP$).$ Host A converts analog voice to a digital $64kbps$ bit stream on the fly. Host A then groups the bits into $56-$byte packets. There is one link between Hosts A and B; its transmission rate is $10Mbps$ and its propagation delay is $10$msec. As soon as Host A gathers a packet, it sends it to Host B$.$ As soon as Host B receives an entire packet, it converts the packet's bits to an analog signal. How much time elapses from the time a bit is created $($from the original analog signal at Host A$)$ until the bit is decoded $($as part of the analog signal at Host B$)?$