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While visiting Haifa, Sid Resnick discovered that people who wish to travel from the port area up…


While visiting Haifa, Sid Resnick discovered that people who wish to travel from the port area up the mountain frequently take a shared taxi known as a sherut. The capacity of each car is five people. Potential customers arrive according to a Poisson process with rate λ. As soon as five people are in the car, it departs for The Carmel, and another taxi moves up to accept passengers on. A local resident (who has no need of a ride) wanders onto the scene. What is the distribution of the time he has to wait to see a cab depart?