Divergent Quiescent Transition Systems (extended version)

Quiescence is a fundamental concept in modelling system behaviour, as it explicitly represents the fact that no output is produced in certain states. The notion of quiescence is also essential to model-based testing: if a particular implementation under test does not provide any output, then the test evaluation algorithm must decide whether or not to allow this behaviour. To explicitly model quiescence in all its glory, we introduce Divergent Quiescent Transition Systems (DQTSs). DQTSs model quiescence using explicit delta-labelled transitions, analogous to Suspension Automata (SAs) in the well-known ioco framework. Whereas SAs have only been defined implicitly, DQTSs for the first time provide a fully-formalised framework for quiescence. Also, while SAs are restricted to convergent systems (i.e., without tau-cycles), we show how quiescence can be treated naturally using a notion of fairness, allowing systems exhibiting divergence to be modelled as well. We study compositionality under the familiar automata-theoretical operations of determinisation, parallel composition and action hiding. We provide a non-trivial algorithm for detecting divergent states, and discuss its complexity. Finally, we show how to use DQTSs in the context of model-based testing, for the first time presenting a full-fledged theory that allows ioco to be applied to divergent systems

Deterioration modeling of sewer pipes via discrete-time Markov chains: A large-scale case study in the Netherlands

[For the latest version of this repository go to: https://gitlab.utwente.nl/fmt/degradation-models/dtmc_sewer_pipes.git] Sewer pipe network systems are an important part of civil infrastructure, and in order to find a good trade-off between maintenance costs and system performance, reliable sewer pipe degradation models are essential. In this paper, we present a large-scale case study in the city of Breda in the Netherlands. Our dataset has information on sewer pipes built since the 1920s and contains information on different covariates. We also have several types of damage, but we focus our attention on infiltrations, surface damage, and cracks. Each damage has an associated severity index ranging from 1 to 5. To account for the characteristics of sewer pipes, we defined 6 cohorts of interest. Two types of discrete-time Markov chains (DTMC), which we called Chain `Multi' and `Single' (where Chain `Multi'contains additional transitions compared to Chain `Single'), are commonly used to model sewer pipe degradation at the pipeline level, and we want to evaluate which suits better our case study. To calibrate the DTMCs, we define an optimization process using Sequential Least-Squares Programming to find the DTMC parameter that best minimizes the root mean weighted square error. Our results show that for our case study there is no substantial difference between Chain `Multi' and `Single', but the latter has fewer parameters and can be easily trained. Our DTMCs are useful to compare the cohorts via the expected values, e.g., concrete pipes carrying mixed and waste content reach severe levels of surface damage more quickly compared to concrete pipes carrying rainwater, which is a phenomenon typically identified in practice.This research has been partially funded by NWO under the grant PrimaVera (https://primavera-project.com) number NWA.1160.18.238, and has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 101008233