The average velocity in a queue

Abstract

A number of cars drive along a narrow road that does not allow overtaking. Each driver has a certain maximum speed at which he or she will drive if alone on the road. As a result of slower cars ahead, many cars are forced to drive at speeds lower than their maximum ones. The average velocity in the queue offers a non-trivial example of a mean value calculation. Approximate and exact results are obtained using sampling, enumeration and calculations. The geometrical nature of the problem as well as the separate levels of averaging involved are emphasized. Further problems suitable for exploration in student projects are outlined.