class6atc

class6atc - Too Close for Comfort: Geometrical Probability...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Too Close for Comfort: Geometrical Probability in the Sky Suppose that two aerial routes--one Eastbound and one Northbound--cross at an altitude of 35,000 feet at junction J (Figure 1). In the absence of air-traffic control, the times at which eastbound planes would arrive at the junction would reflect a Poisson process with parameter λ E (per minute). Likewise, northbound planes would arrive under an independent Poisson process with parameter λ N . All planes move at a speed of 600 miles per hour along their routes. J Figure1:Eastbound and Northbound Air Routes Cross at J The Federal Aviation Administration thinks it dangerous if two planes cruising at the same altitude get within 5 miles of one another (in which case they are said to conflict ). The idea is that, if a conflict arises, the planes are traveling so fast that they could collide if one of them deviates from its course. With the FAA standard in mind, we calculate the probabilities of three interesting events: E: the chance that an eastbound plane that has just reached J is in conflict at that moment with a northbound plane N: the chance that a northbound plane that has just reached J is at that moment in conflict with an eastbound plane
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
EE: the chance that a given eastbound plane that passes through J is at any time in conflict with a northbound plane that passes through J. P(E) To find P(E), we note that the conflict occurs if, at the time the eastbound plane reaches J, there is a northbound plane within five miles of J. If E* is the complement of E, then E* requires that there be no northbound plane within five miles of the junction. It is easier to find P(E*) than P(E), so we will do so and then invoke the rule P(E) = 1 - P(E*). We aren’t told anything about planes that are not at the junction, so how can we
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 5

class6atc - Too Close for Comfort: Geometrical Probability...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online