Optimum Bus Scheduling

The paper presents a mathematical investigation into bus scheduling. The passenger arrival rate is supposed to be given; the problem is to determine the bus departure rate as a function of time. The primary objective is to minimize the number of buses that is needed. A secondary criterion is the minimization of the passenger waiting time, for which a calculus of variation technique is used. Although the paper deals mainly with a single busroute, it is also shown how the theory can be extended to the case of a pair of linked busroutes. The practical implications are illustrated by an example. The fleetsize formula that is used here is thought to be applicable to many transportation systems.