Patch-based Modelling of City-centre Bus Movement with Phase-type Distributions

We propose a methodology for constructing a stochastic performance model of a public transportation network using real-world data. Our main data source consists of Automatic Vehicle Location (AVL) measurements of buses in the Edinburgh region. Although the data has a relatively low frequency, we can use it to parameterise a model in which a bus moves between predefined patches in the city. We fit the probability distributions of the sojourn times in the patches to phase-type distributions using the tool HyperStar. We then translate the output from HyperStar to a model of a complete part of a bus route expressed in the reactive modules language of the PRISM model checker. Finally, we demonstrate how we can use the numerical techniques implemented in PRISM to answer meaningful questions about the performance of the bus network in the context of a case study involving the addition of trams to a busy section of Edinburgh's city centre.