The Benefits of Sometimes Not Being Discrete

Hillston, Jane

doi:10.1007/978-3-662-44584-6_2

Cited by 3 publications

(3 citation statements)

References 65 publications

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“…In the last decade there have been efforts to alleviate the problems of state space explosion for very large systems by the use of fluid approximations [11]. In this approach an approximation of the underlying discrete CTMC is constructed as a set of ordinary differential equations that capture the average behaviour of the system when a large population of entities is involved.…”

Section: Challenges In Modelling Collective Adaptive Systemsmentioning

confidence: 99%

Quantitative Analysis of Collective Adaptive Systems

Hillston

2016

Lecture Notes in Computer Science

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Section: Challenges In Modelling Collective Adaptive Systemsmentioning

confidence: 99%

Quantitative Analysis of Collective Adaptive Systems

Hillston

2016

Lecture Notes in Computer Science

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“…With the scalable, virtualised services which are in use today components are replicated to provide resilience and application scalability to serve growing numbers of clients using the service. In order to reason about systems with replicated components it is essential to move away from discrete-state models and use representations which provide efficient representations of populations of components [3].…”

Section: Introductionmentioning

confidence: 99%

Abstract Interpretation of PEPA Models

Gilmore

Hillston

Zoń

2015

Semantics, Logics, and Calculi

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General rightsCopyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policyThe University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorer content complies with UK legislation. If you believe that the public display of this file breaches copyright please contact openaccess@ed.ac.uk providing details, and we will remove access to the work immediately and investigate your claim. Abstract. This paper relates the fluid-flow semantics of the stochastic process algebra PEPA (Performance Evaluation Process Algebra) to the static analysis technique of abstract interpretation. The explanation in the paper is illustrated through the example of a distributed denial of service (DDoS) attack which is being launched against a server. DDoS attacks are mounted by a large population of attackers, who are coordinating and working together in attacking a specific server. The scale of the attack is crucial to its success, but the resulting large number of states in the system makes it difficult to model and analyse using the conventional discrete-state interpretation of PEPA.

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“…Hence, modelchecking mean-field models is considered a valuable continuation. For an overview we refer to [58].…”

Section: Related Workmentioning

confidence: 99%

Model-checking mean-field models : algorithms & applications

Kolesnichenko¹

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Large systems of interacting objects are highly prevalent in today's world. Such system usually consist of a large number of relatively simple identical objects, and can be observed in many different field as, e.g., physics (interactions of molecules in gas), chemistry (chemical reactions), epidemiology (spread of the infection), etc. In this thesis we primarily address large systems of interacting objects in computer science, namely, computer networks. Analysis of such large systems is made difficult by the state space explosion problem, i.e., the number of states of the model grows exponentially with the number of interacting objects. In this thesis we tackle the state-space explosion problem by applying meanfield approximation, which was originally developed for models in physics, like the interaction of molecules in a gas. The mean-field method works by not considering the state of each individual object separately, but only their average, i.e., what fraction of the objects are in each possible state at any time. It allows to compute the exact limiting behaviour of an infinite population of identical objects, and this limiting behaviour is a good approximation, even when the number of objects is not infinite but sufficiently large. In this thesis we provide the theoretical background necessary for applying the mean-field method and illustrate the approach by a peer-to-peer Botnet case study. 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 can not 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 viii interacting objects. Therefore, we motivate and 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 valu...

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The Benefits of Sometimes Not Being Discrete

Cited by 3 publications

References 65 publications

Quantitative Analysis of Collective Adaptive Systems

Quantitative Analysis of Collective Adaptive Systems

Abstract Interpretation of PEPA Models

Model-checking mean-field models : algorithms & applications

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