Aircraft arrive for takeoff at an airport runway according to a Poisson process at an average speed
Question:
Aircraft arrive for takeoff at an airport runway according to a Poisson process at an average speed of 20 per hour. The time required for an aircraft to take off has an exponential distribution with a mean of 2 minutes, and this process must be completed before the next aircraft can begin to take off.
Because a brief storm just started, all the planes that have not started takeoff have just been temporarily grounded. However, planes continue to arrive on the runway during the storm to await its end.
Assuming steady-state operation before the storm, determine the expected number of planes that will be waiting to take off at the end of the storm if it lasts 30 minutes.
Introduction to Operations Research
ISBN: 978-1259162985
10th edition
Authors: Frederick S. Hillier, Gerald J. Lieberman