Some Practical Aspects of Periodic Timetabling

Abstract

We consider the design of periodic timetables for public transportation networks. The used model is a digraph in which temporal restrictions on the arcs relate periodically recurring events. Solution methods are commonly based on an integer programming approach; the number of integer variables equals the cyclomatic number of the digraph.

In timetabling, one major question is how to order lines that share a common track. In our paper we show, that in this context we can cut off 2(V) — n! infeasible integer vectors, by adding only polynomially many well-known constraints.

Another point of interest is not to construct timetables that pay for short passengers’ waiting times by an exorbitant amount of rolling stock required to perform a timetable. We will show that both routing the rolling stock and periodic timetabling can be modelled within one ILP. Although this leads to a quadratic objective function, we’re able to derive a heuristic permitting good control of the considerable trade-off.