Model-checking mean-field models : algorithms & applications

Abstract

Large systems of interacting objects are highly prevalent in today's world. In this thesis we primarily address such large systems in computer science. We model such large systems using mean-field approximation, which allows to compute the limiting behaviour of an infinite population of identical objects. This thesis aims at formulating and analysing advanced properties of large systems of interacting objects using fast, efficient, and accurate algorithms. We propose to apply model-checking techniques to mean-field models. This allows (i) defining advanced properties of mean-field models, such as survivability, steady-state availability, conditional instantaneous availability using logic; and (ii) automatically checking these properties using model-checking algorithms. Existing model-checking logics and algorithms cannot directly be applied to mean-field models since the model consist of two layers: the local level, describing the behaviour of a randomly chosen individual object in a large system, and the global level, which addresses the overall system of all interacting objects. Therefore, we define two logics, called Mean Field Continuous Stochastic Logic (MF-CSL), and Mean-Field Logic (MFL), for describing properties of systems composed of many identical interacting objects, on both the local and the global level. We present model-checking algorithms for checking both MF-CSL and MFL properties, and illustrated these algorithms using an extensive example on virus propagation in a computer network. We discuss the differences in the expressiveness of these two logics as well as their possible combination. Additionally, we combine the mean-field method with parameter fitting techniques in order to model real-world large systems, and obtain a better understanding of the behaviour of such systems. We explain how to build a mean-field model of the system, and how to estimate the corresponding parameter values, so as to find the best fit between the available data and the model prediction. To illustrate the approach we estimate the parameter values for the outbreak of the real-world computer worm Code-Red. The techniques presented in this thesis allow an involved analysis of large systems of interacting objects, including (i) obtaining parameter values of mean-field model using measurements; (ii) defining advanced properties of the model; and (iii) automatically checking such properties.