Minimizing the waiting time for a one-way shuttle service

Consider a terminal in which users arrive continuously over a finite period of time at a variable rate known in advance. A fleet of shuttles has to carry the users over a fixed trip. What is the shuttle schedule that minimizes their waiting time? This is the question addressed in the present paper. We propose efficient algorithms for several variations of this question with proven performance guarantees. The techniques used are of various types (convex optimization, shortest paths,...). The paper ends with numerical experiments showing that most of our algorithms behave also well in practice.