A Function-Equivalent Components Based Simplification Technique for PEPA Models ⋆

Abstract. PEPA has recently been extended with functional rates [1][2]. These functions allow the specification of indirect interaction between components in such a way that the rate of an activity may be made dependent on the local state currently exhibited by one or more components. In this paper we demonstrate that these rates allow a systematic simplification of models in which there is appropriate indirect interaction between components. We investigate the interplay between this style of simplification and aggregation based on bisimulation, and establish a heuristic for applying both techniques in a complementary fashion.

Process algebra for epidemiology: evaluating and enhancing the ability of PEPA to describe biological systems

Modelling is a powerful method for understanding complex systems, which works by simplifying them to their most essential components. The choice of the components is driven by the aspects studied. The tool chosen to perform this task will determine what can be modelled, the maximum number of components which can be represented, as well as the analyses which can be performed on the system. Performance Evaluation Process Algebra (PEPA) was initially developed to tackle computer systems issues. Nevertheless, it possesses some interesting properties which could be exploited for the study of epidemiological systems. PEPA's main advantage resides in its capacity to change scale: the assumptions and parameter values describe the behaviour of a single individual, while the resulting model provides information on the population behaviour. Additionally, stochasticity and continuous time have already proven to be useful features in epidemiology. While each of these features is already available in other tools, to find all three combined in a single tool is novel, and PEPA is proposed as a useful addition to the epidemiologist's toolbox. Moreover, an algorithm has been developed which allows converting a PEPA model into a system of Ordinary Differential Equations (ODEs). This provides access to countless additional software and theoretical analysis methods which enable the epidemiologist to gain further insight into the model. Finally, most existing tools require a deep understanding of the logic they are based on and the resulting model can be difficult to read and modify. PEPA's grammar, on the other hand, is easy to understand since it is based on few, yet powerful concepts. This makes it a very accessible formalism for any epidemiologist. The objective of this thesis is to determine precisely PEPA's ability to describe epidemiological systems, as well as extend the formalism when required. This involved modelling two systems: the bubonic plague in prairie dogs, and measles in England and Wales. These models were chosen as they exhibit a good range of typical features, allowing to thoroughly test PEPA. All features required in each of these models have been analysed in detail, and a solution has been provided for representing each of these features. While some of them could be expressed in a straightforward manner, PEPA did not provide the tools to express others. In those cases, we determined methods to approach the desired behaviour, and the limitations of said methods were carefully analysed. In the case of models with a structured population, PEPA was extended to simplify their expression and facilitate the writing process of the PEPA model. The work also required the development of an algorithm to derive ODEs adapted to the type of models encountered. Finally, the PEPAdum software was developed to assist the modeller in the generation and analysis of PEPA models, by simplifying the process of writing a PEPA model with compartments, performing the average of stochastic simulations and deriving and explicitly providing the ODEs using the Stirling Amendment

Investigation of a Novel Formal Model for Mobile User Interface Design

Mobile user interfaces are becoming increasingly complex due to the expanding range of functionalities that they incorporate, which poses significant difficulties in software development. Formal methods are beneficial for highly complex software systems, as they enable the designed behaviour of a mobile user interface (UI) to be modelled and tested for accuracy before implementation. Indeed, assessing the compatibility between the software specification and user requirements and verifying the implementation in relation to the specification are essential procedures in the development process of any type of UI. To ensure that UIs meet users‘ requirements and competences, approaches that are based on interaction between humans and computers employ a variety of methods to address key issues. The development of underlying system functionality and UIs benefit from formal methods as well as from user-interface design specifications. Therefore, both approaches are incorporated into the software development process in this thesis. However, this integration is not an easy task due to the discrepancies between the two approaches. It also includes a method, which can be applied for both simple and complex UI applications. To overcome the issue of integrating both approaches, the thesis proposes a new formal model called the Formal Model of Mobile User Interface Design (FMMUID). This model is devised to characterise the composition of the UI design based on hierarchical structure and a set theory language. To determine its applicability and validity, the FMMUID is implemented in two real-world case studies: the quiz game iPlayCode and the social media application Social Communication (SC). A comparative analysis is undertaken between two case studies, where each case study has three existing applications with similar functionality in terms of structure and numbers of elements, functions and colours. Furthermore, the case studies are also assessed from a human viewpoint, which reveals that they possess better usability. The assessment supports the viability of the proposed model as a guiding tool for software development. The efficiency of the proposed model is confirmed by the result that the two case studies are less complex than the other UI applications in terms of hierarchical structure and numbers of elements, functions and colours, whilst also presenting acceptable usability in terms of the four examined dimensions: usefulness, information quality, interface quality, and overall satisfaction. Hence, the proposed model can facilitate the development process of mobile UI applications