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1-Consider the car-caravan analogy from Section 4 in Chapter 1. In this problem,

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Question

1-Consider the car-caravan analogy from Section 4 in Chapter 1. In this problem, assume a propagation speed of 60 km/hr and that each toll booth takes 12 seconds to service a car. a) (7 points) Suppose the caravan of 10 cars begins immediately in front of the first toll booth, travels 40 km to a second toll booth, then another 40 km to a third toll booth, and finally stops immediately after the third tool booth. Thus, they travel a total of 80 km. What is the total end- to-end delay? b) (3 points) Where is the last car in the caravan after 30 minutes? Your answer must include a distance/specific location, and not only a relative direction.

Explanation / Answer

a.)

The cars start at front of first toll booth and ends after the third toll booth.

Transmission delay or dtrans at toll booth = 12 seconds at each toll booth for each car.

There are 10 cars. So total transmission delay at each toll booth = 120 seconds = 2 minutes.

Propagation delay or dprop = distance travelled / propagation speed

Total distance = 80 km.

dprop = 80 km/ 60 kmh = (80/60) * 60 minutes = 80 minutes.

Total end to end delay = dprop + (time taken at each of the three toll booths)

= dprop + 3 * dtrans (because there are 3 booths)

= 80 + 2*3 = 86 minutes.

b.)

The last car in the caravan leaves the first toll booth after 120 seconds or 2 minutes. Therefore, the distance of the last car from the first toll booth after 30 minutes will be equal to distance travelled by it in (30 - 2) or 28 minutes

28 minutes = (28/60) hours.

Distance travelled = speed * time

= 60 km/hour * (28/60) hours

= 28 km.

Hence the last car will be 28 kilometers away from the first toll booth.