You have trained your dog, Bernie, to carry twenty 64Gbytes USBs instead of a flask of wine. You consider it an emergency when your disk fills up. The dog can travel to your side, wherever you may be, at 25 km/hour. For what range of distances does Bernie have a higher data rate than a transmission line whose data rate (excluding overhead) is 1Gbps? How does your answer change if (i) Bernie’s speed is halved; (ii) each USBs capacity is doubled; (iii) the data rate of the transmission line is halved.
Expert Answer
Suppose in the range of “x km” Bernie has higher data rate than transmission line.
To reach “X km ” Bernie will take t= x/(25km/hour) time
Traveling speed of Benie in Km/second is 25/3600= 1/144 seconds (in one hour there are 3600 second)
t=x/(1/144)=x*144 secomds {t= x/v in second, v is speed of Bernie}
Bernie can fetch 12 * 64Gbytes in x*144 seconds
So the transmission arte of Bernie is (12*64)/(x*144) Gbps
and this must be higher tha the transmision line
i.e. (12 * 64) / (x * 144) Gbps > 1Gbps
x < 5.33 Km
So in the range of 5.33 km Bermie have a higher data rate than a transmission line whose data rate (excluding overhead) is 1Gbps.
(i)
If the bernie seed is halved than t = x / (1/(2*144))=x /(1/288) = x*288 seconds
So
(12 * 64) / (x * 288) Gbps > 1Gbps
x < 2.66 Km
So in the range of 2.66 km (half of original ) Bermie have a higher data rate than a transmission line whose data rate (excluding overhead) is 1Gbps.
(ii) each USBs capacity is doubled
than
(12 * 128) / (x * 144) Gbps > 1Gbps
x < 10.66 Km
So in the range of 10.66 km (double of original ) Bermie have a higher data rate than a transmission line whose data rate (excluding overhead) is 1Gbps.
(iii)
(12 * 64) / (x * 144) Gbps > .5Gbps
x < 10.66 Km
So in the range of 10.66 km (double of original ) Bermie have a higher data rate than a transmission line whose data rate (excluding overhead) is 0.5 Gbps.