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Planes arrive at a circular sector of airspace according to a Poisson process with rate 20 arrivals per hour. The radius of the sector is 40 miles. Each plane travels at a speed of 400 miles per hour. There are 4 possible entrance / exit points in the sector, as shown. An aircraft is equally like to arrive and depart from any of points A, B, C, and D (but an aircraft cannot enter and exit from the same point). For example, the probability that an aircraft arrives at point A is 1/4. Given that an aircraft arrives at A, the probability that it exits at B, C, or Dis 1/3 cach. Assume that aircraft flights are straight paths and there are no collisions or conflict avoidance maneuvers in the sector. (a) What is the average path length across the sector? (b) What is the average number of aireraft in the sector? (c) If we suppose that aircraft sometimes execute avoidance maneuvers to prevent conflicts/collisions, would the answer in (b) go up or down? D. 40 miles

Planes arrive at a circular sector of airspace according to a Poisson process with rate 20 arrivals per hour. The radius of the sector is 40 miles. Each plane travels at a speed of 400 miles per hour. There are 4 possible entrance / exit points in the sector, as shown. An aircraft is equally like to arrive and depart from any of points A, B, C, and D (but an aircraft cannot enter and exit from the same point). For example, the probability that an aircraft arrives at point A is 1/4. Given that an aircraft arrives at A, the probability that it exits at B, C, or Dis 1/3 cach. Assume that aircraft flights are straight paths and there are no collisions or conflict avoidance maneuvers in the sector. (a) What is the average path length across the sector? (b) What is the average number of aireraft in the sector? (c) If we suppose that aircraft sometimes execute avoidance maneuvers to prevent conflicts/collisions, would the answer in (b) go up or down? D. 40 miles

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Planes arrive at a circular sector of airspace according to a Poisson process with rate 20 arrivals per hour. The radius of the sector is 40 miles. Each plane travels at a speed of 400 miles per hour. There are 4 possible entrance / exit points in the sector, as shown. An aircraft is equally like to arrive and depart from any of points A, B, C, and D (but an aircraft cannot enter and exit from the same point). For example, the probability that an aircraft arrives at point A is 1/4. Given that an aircraft arrives at A, the probability that it exits at B, C, or D is 1/3 each. Assume that aircraft flights are straight paths and there are no collisions or conflict avoidance maneuvers in the sector. (a) What is the average path length across the sector? (b) What is the average number of aircraft in the sector? (c) If we suppose that aircraft sometimes execute avoidance maneuvers to prevent conflicts/collisions, would the answer in (b) go up or down?
Transcribed Image Text:Planes arrive at a circular sector of airspace according to a Poisson process with rate 20 arrivals per hour. The radius of the sector is 40 miles. Each plane travels at a speed of 400 miles per hour. There are 4 possible entrance / exit points in the sector, as shown. An aircraft is equally like to arrive and depart from any of points A, B, C, and D (but an aircraft cannot enter and exit from the same point). For example, the probability that an aircraft arrives at point A is 1/4. Given that an aircraft arrives at A, the probability that it exits at B, C, or D is 1/3 each. Assume that aircraft flights are straight paths and there are no collisions or conflict avoidance maneuvers in the sector. (a) What is the average path length across the sector? (b) What is the average number of aircraft in the sector? (c) If we suppose that aircraft sometimes execute avoidance maneuvers to prevent conflicts/collisions, would the answer in (b) go up or down?
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