CS$4470$ Homework $1$

$1.$ Calculate the latency $($from first bit sent to last bit received$)$ for the following:

$($a$)10-$Mbps Ethernet with a single store$-$and$-$forward switch in the path, and a packet

size of $5000$ bits. Assume that each link introduces a propagation delay of $10$ us and

that the switch begins retransmitting immediately after it has finished receiving the

packet.

$($b$)$ Same as $($a$)$ but with three switches.

$($c$)$ Same as $($a$)$ but assume the switch implements $$cut$-$through$$ circuit switching: It

is able to begin transmitting the packet after the first $200$ bits have been received.

$2.$ Consider two hosts, A and B$,$ directly connected by a link of $40,000$ Km$,$

propagation speed $2\mathrm{.}5*108$ m$/$s$,$ and transmission rate R$=5$ Mbps$.$ Assume zero

queuing delay.

$($a$)$ How long does it take to move a packet of length $1000$ bytes from one A to B$?$

$($b$)$ Generally, how long does it take to move a packet of length L over a link of

distance d$,$ propagation speed s$,$ and transmission rate R bps$?$

$($c$)$ Assume the transmission time of the packet is dtrans and the propagation delay

dprop. Suppose that host A begins to transmit a packet at time t$=0.$ At time t$=$ dtrans

where is the last bit of the packet?

$($d$)$ Suppose dprop is greater than dtrans. At time t$=$ dtrans, where is the first bit of

the packet? $($e$)$ Suppose dprop is less than dtrans. At time t$=$ dtrans, where is the first

bit of the packet?

$($f$)$ Calculate the bandwidth$-$delay product R$*$ dprop.

$($g$)$ Consider sending a file of $1,200,000$ bits from host A to host B$.$ Suppose the file is

sent continuously as a large message. What is the maximum number of bits that will

be in the link at any time?

$($h$)$ What is the width $($in meters$)$ of a bit in the link?