Cyclic schedules for r irregularly occurring events

In connection with railway scheduling problems Guldan [6] considered the problem to place Y regular polygons on a circle such that the minimum distance between two neighbouring vertices becomes as large as possible. This corresponds to the situation that trains which arrive in constant intervals at some railway station are scheduled such that the safety interval between two trains is as large as possible. In this paper we drop the assumption of regularly arriving trains. We consider trains arriving according to some fixed periodic pattern and optimize different objective functions: maximizing