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 . 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?