Finding Optimal Timetables for Edinburgh Bus Routes

We present a novel application of stochastic simulation and model-checking methods to determining whether bus services are fulfilling their service-level agreement to provide on-time departures of buses from stops sufficiently often. We use open data on predicted bus arrival times to parameterise a stochastic model of a particular bus route from Edinburgh city centre out to suburban and rural areas to the south of the city. We validate and then analyse our stochastic model using both simulation and model-checking methods. Finally, we complete an optimisation study on the model and discover a better timetable for the service which would expose the bus service operator to less financial risk of penalties being applied by the regulatory authorities which define standards for bus service, punctuality and reliability.