Optimal service synchronization in public transport

In this paper two schedule synchronization problems in public transit network are formulated and solved. The first is concerned with a transfer synchronization when passengers changing transit lines at transfer points. The stochastic version of QSAP (Quadratic Semi-Assignment Problem) formulation is developed together with the efficient computer solution method. The second is concerned with the headways harmonization problem i.e. synchronization of different transit Lines on a common segment of routes. Illustrative real-life bus lines examples demonstrate the utility of these two proposals.