(Minimizing the Number of Encounters) Suppose that cars enter a one-way highway in accordance with a Poisson process with rate λ. The cars enter at point a and depart at point b (see Figure 5.2). Each car travels at a
Figure 5.2. Cars enter at point a and depart at b.
constant speed that is randomly determined, independently from car to car, from the distribution G. When a faster car encounters a slower one, it passes it with no time being lost. If your car enters the highway at time s and you are able to choose your speed, what speed minimizes the expected number of encounters you will have with other cars, where we say that an encounter occurs each time your car either passes or is passed by another car?