Consider a user who needs to transmit $1\mathrm{.}5$ gigabytes of data to a server. The

user lives in a small town where only dial$-$up access is available. A bus visits

the small town once a day from the closest city, located $150$ km away, and stops

in front of the user$’$s house. The bus has a $100-$Mbps WiFi connection. It can

collect data from users in rural areas and transfer them to the Internet through a

$1$ Gbps link once it gets back to the city. Suppose the average speed of the bus is

$60$ km$/$h$.$ What is the fastest way the user can transfer the data to the server?

P$25.$ Suppose two hosts, A and B$,$ are separated by $20,000$ kilometers and are con$-$

nected by a direct link of R $=2$ Mbps$.$ Suppose the propagation speed over

the link is $2\mathrm{.}5$ # $108$

meters$/$sec$.$

a$.$ Calculate the bandwidth$-$delay product, R # dprop

$.$

b$.$ Consider sending a file of $800,000$ bits from Host A to Host B$.$ Suppose

the file is sent continuously as one large message. What is the maximum

number of bits that will be in the link at any given time?

c$.$ Provide an interpretation of the bandwidth$-$delay product.

d$.$ What is the width $($in meters$)$ of a bit in the link? Is it longer than a

football field?

e$.$ Derive a general expression for the width of a bit in terms of the propaga$-$

tion speed s$,$ the transmission rate R$,$ and the length of the link m$.$

P$26.$ Consider problem P$25$ but now with a link of R $51$ Gbps$.$ 

a$.$ Calculate the bandwidth$-$delay product, R $?$ dprop

$.$

b$.$ Consider sending a file of $800,000$ bits from Host A to Host B$.$ Suppose

the file is sent continuously as one big message. What is the maximum

number of bits that will be in the link at any given time?

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

P$27.$ Consider the scenario illustrated in Figure $1\mathrm{.}19($a$).$ Assume Rs

is $20$ Mbps$,$ 

Rc

is $10$ Mbps$,$ and the server is continuously sending traffic to the client.

Also assume the router between the server and the client can buffer at most

four$$messages$.$ After how many messages sent by the server will packet loss

starts occurring at the router?

P$28.$ Generalize the result obtained in Problem P$27$ for the case where the router

can buffer m messages.

P$29.$ Suppose there is a $10-$Mbps microwave link between a geostationary satellite

and its base station on Earth. Every minute the satellite takes a digital photo and

sends it to the base station. Assume a propagation speed of $2\mathrm{.}4$ # $108$

meters$/$sec$.$

a$.$ What is the propagation delay of the link?

b$.$ What is the bandwidth$-$delay product, R # dprop?

c$.$ Let x denote the size of the photo. What is the minimum value of x for the

microwave link to be continuously transmitting?