D.P. Reijsbergen

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 Edinburghs city centre.

Formal Punctuality Analysis of Frequent Bus Services Using Headway Data

We evaluate the performance of frequent bus services in Edinburgh using the punctuality metrics identified by the Scottish Government. We describe a methodology for evaluating each of these metrics that only requires measurements of bus ‘headways’ — the time between subsequent bus arrivals. Our methodology includes Monte Carlo simulation and time series analysis. Since one metric is given in ambiguous language, we provide a formal description of the two most plausible interpretations. The automated nature of our method allows public transport operators to continuously assess whether the performance of their network meets the targets set by government regulators. We carry out a case study using Automatic Vehicle Location (AVL) data involving two frequent services, including the AirLink service to and from Edinburgh airport.

Hypothesis testing for rare-event simulation : limitations and possibilities

One of the main applications of probabilistic model checking is to decide whether the probability of a property of interest is above or below a threshold. Using statistical model checking (SMC), this is done using a combination of stochastic simulation and statistical hypothesis testing. When the probability of interest is very small, one may need to resort to rare-event simulation techniques, in particular importance sampling (IS). However, IS simulation does not yield 0/1-outcomes, as assumed by the hypothesis tests commonly used in SMC, but likelihood ratios that are typically close to zero, but which may also take large values. In this paper we consider two possible ways of combining IS and SMC. One involves a classical IS-scheme from the rare-event simulation literature that yields likelihood ratios with bounded support when applied to a certain (nontrivial) class of models. The other involves a particular hypothesis testing scheme that does not require a-priori knowledge about the samples, only that their variance is estimated well.

Moment-based Probabilistic Prediction of Bike Availability for Bike-Sharing Systems

We study the problem of future bike availability prediction of a bike station through the moment analysis of a PCTMC model with time-dependent rates. Given a target station for prediction, the moments of the number of available bikes in the station at a future time can be derived by a set of moment equations with an initial set-up given by the snapshot of the current state of all stations in the system. A directed contribution graph with contribution propagation method is proposed to prune the PCTMC to make it only contain stations which have significant contribution to the journey flows to the target station. The underlying probability distribution of the available number of bikes is reconstructed through the maximum entropy approach based on the derived moments. The model is parametrized using historical data from Santander Cycles, the bike-sharing system in London. In the experiments, we show our model outperforms the classic time-inhomogeneous queueing model on several performance metrics for bike availability prediction.

Path-ZVA: General, Efficient, and Automated Importance Sampling for Highly Reliable Markovian Systems

We introduce Path-ZVA: an efficient simulation technique for estimating the probability of reaching a rare goal state before a regeneration state in a (discrete-time) Markov chain. Standard Monte Carlo simulation techniques do not work well for rare events, so we use importance sampling; i.e., we change the probability measure governing the Markov chain such that transitions “towards” the goal state become more likely. To do this, we need an idea of distance to the goal state, so some level of knowledge of the Markov chain is required. In this article, we use graph analysis to obtain this knowledge. In particular, we focus on knowledge of the shortest paths (in terms of “rare” transitions) to the goal state. We show that only a subset of the (possibly huge) state space needs to be considered. This is effective when the high dependability of the system is primarily due to high component reliability, but less so when it is due to high redundancies. For several models, we compare our results to well-known importance sampling methods from the literature and demonstrate the large potential gains of our method.

Moment-based Availability Prediction for Bike-Sharing Systems

Abstract We study the problem of predicting the future availability of bikes in a bike station through the moment analysis of a PCTMC model with time-dependent rates. Given a target station for prediction, the moments of the number of available bikes in the station at a future time can be derived by a set of moment equations with an initial set-up given by the snapshot of the current state of all stations in the system. A directed contribution graph is constructed, and a contribution propagation method is proposed to prune the PCTMC so that it only contains stations which have significant contribution to the journey flows to the target station. Once the moments have been derived, the underlying probability distribution of the available number of bikes is reconstructed through the maximum entropy approach. We illustrate our approach on Santander Cycles, the bike-sharing system in London. The model is parameterized using historical data from Santander Cycles. Experimental results show that our model outperforms a time-inhomogeneous Markov queueing model with respect to several performance metrics for bike availability prediction.

Probabilistic Modelling of Station Locations in Bicycle-Sharing Systems

We present a simulation methodology for generating the locations of stations in Bicycle-Sharing Systems. We present several methods that are inspired by the literature on spatial point processes. We evaluate how the artificially generated systems compare to existing systems through a case study involving 11 cities worldwide. The method that is found to perform best is a data-driven approach in which we use a dataset of places of interest in the city to ‘rate’ how attractive city areas are for station placement. The presented methods use only non-proprietary data readily available via the Internet.

Transient and Steady-State Statistical Analysis for Discrete Event Simulators

We extend the model checking tool MultiVeStA with statistical model checking of steady-state properties. Since MultiVeStA acts as a front-end for simulation tools, it confers this ability onto any tool with which it is integrated. The underlying simulation models are treated as black-box systems. We will use an approach based on batch means using the ASAP3 algorithm. We motivate the work using two case studies: a biochemical model written in the Bio-PEPA language and an application from transport logistics.

Proceedings of iFM 2017: 13th International Conference on integrated Formal Methods

Search-based testing is widely used to find bugs in models of complex Cyber-Physical Systems. Latest research efforts have improved this approach by casting it as a falsification procedure of formally specified temporal properties, exploiting the robustness semantics of Signal Temporal Logic. The scaling of this approach to highly complex engineering systems requires efficient falsification procedures, which should be applicable also to black box models. Falsification is also exacerbated by the fact that inputs are often time-dependent functions. We tackle the falsification of formal properties of complex black box models of CyberPhysical Systems, leveraging machine learning techniques from the area of Active Learning. Tailoring these techniques to the falsification problem with time-dependent, functional inputs, we show a considerable gain in computational effort, by reducing the number of model simulations needed. The effectiveness of the proposed approach is discussed on a challenging industrial-level benchmark from automotive.

Validation of Automatic Vehicle Location Data in Public Transport Systems

Performance metrics for public transport systems can be calculated from automatic vehicle location (AVL) data but data collection subsystems can introduce errors into the data which would invalidate these calculations, giving rise to misleading conclusions. In this paper we present a range of methods for visualising and validating AVL data before performance metrics are computed. We illustrate our presentation with the specific example of the Lothian Buses Airlink bus, a frequent service connecting Edinburgh city centre and Edinburgh airport. Performance metrics for frequent services are based on headways, the separation in space and time between subsequent buses serving a route. This paper provides a practical experience report of working with genuine vehicle location data and illustrates where care and attention is needed in cleaning data before results are computed from the data which could incorrectly reflect the true level of service provided.