Suppose two hosts, A and B, are separated by 20,000 kilometers and are connected by a direct link of R = 2 Mbps. Suppose the propagation speed over the link is 2.5 108 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?

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Answer:

a. (210^6)((210^7)/(2.510^8)) = 1.610^5 bits or 160,000 bits

b. 1.6*10^5 bits or 160,000 bits

c. Bandwidth delay product of link is maximum number of bits that can be in the link

d. Width of bit = Length of link / bandwidth-delay product so 1 bit is 125 meters long. Yes, this is longer than a football field.

e. Width of bit = s/R

Hope this helps :)

For point a:

The distance from of the two hosts A to B = 20,000 km

[tex]=2\times 10^{7} meters \left ( since\ 1km=10^{3}m \right )[/tex]

Direct connection rate (R) from A to B =2Mbps

[tex]=2\times 10^{6}bps \left ( 1Mbps =10^{6}bps \right )[/tex]

Speed(S) of propagation of a link from A to B [tex]=2.5\times 10^{8} meters/sec[/tex]

Calculate the time limit for propagation:

[tex]d_{prog}=\frac{Distance}{Speed} =\frac{2\times 10^{7}}{2.5\times10^{8} } =0.08sec[/tex]

bandwidth-delay product calculation:

[tex]R \times d_{prog} =2\times 10^{6}\times 0.08 =16\times 10^{4}bits[/tex]

The delay product is therefore [tex]160000\ bit[/tex]

For point b:

File size[tex]=800000\ bits =8\times 10^{5} \ bits[/tex]

Direct connection rate (R) from A to B =2Mbps

[tex]=2\times 10^{6}\ bps \left ( 1Mbps =10^{6}bps \right )[/tex]

product bandwidth-delay:

[tex]R \times d_{prog} =2\times 10^{6}\times 0.08 =16\times 10^{4}\ bits[/tex]

The maximum number of bits will thus be [tex]160000\ bit[/tex] at a given time.

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