Probabilistic Modelling of the Impact on Bus Punctuality of a Speed Limit Proposal in Edinburgh

We propose a data-driven methodology for evaluating the impact of the introduction of a speed limit on the punctuality of bus services. In particular, we use high-frequency Automatic Vehicle Location data to parameterise a model that represents the movement of a bus along predefined patches of the route. We fit the probability distributions of the time spent in each patch to two classes of probability distributions: hyper-Erlang distributions, for which we use the tool HyperStar, and a variation of the three-parameter gamma distributions recommended by the Traffic Engineering Handbook. In both cases we obtain models that can be expressed using the framework of Probabilistic Timed Automata, allowing us to evaluate bus punctuality using the model checking tool UPPAAL. We conduct a case study involving a proposed speed limit in Edinburgh.