Checking Individual Agent Behaviours in Markov Population Models by Fluid Approximation

Bortolussi, Luca; Hillston, Jane

doi:10.1007/978-3-642-38874-3_4

Cited by 10 publications

(11 citation statements)

References 45 publications

(91 reference statements)

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“…From Table II, we see that the obtained reward converges to a fixed value with increasing model parameter N. Therefore, if one is interested in the value obtained if the model parameters go towards infinity, methods concerned with the limiting behaviour [7,8,40, 1] might be more appropriate. As discussed in the introduction, our method targets at finding conservative bounds for the model under consideration.…”

Section: Case Studiesmentioning

confidence: 99%

Transient Reward Approximation for Continuous-Time Markov Chains

et al. 2015

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We are interested in the analysis of very large continuoustime Markov chains (CTMCs) with many distinct rates. Such models arise naturally in the context of reliability analysis, e. g., of computer network performability analysis, of power grids, of computer virus vulnerability, and in the study of crowd dynamics. We use abstraction techniques together with novel algorithms for the computation of bounds on the expected final and accumulated rewards in continuous-time Markov decision processes (CTMDPs). These ingredients are combined in a partly symbolic and partly explicit (symblicit) analysis approach. In particular, we circumvent the use of multi-terminal decision diagrams, because the latter do not work well if facing a large number of different rates. We demonstrate the practical applicability and efficiency of the approach on two case studies.

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Section: Case Studiesmentioning

confidence: 99%

Transient Reward Approximation for Continuous-Time Markov Chains

et al. 2015

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“…Recent work on fluid model checking develops an analogous approach for collective systems [3]. CSL properties related to a single component can be checked with respect to a population.…”

Section: Extending Model Checking Capabilitiesmentioning

confidence: 99%

Challenges for Quantitative Analysis of Collective Adaptive Systems

Hillston

2014

Trustworthy Global Computing

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“…We need to set the initial conditions for the model. In [19] it was mentioned that CRv2 infected between 1 and 2 million out of a potential number of 6 million hosts. Therefore, to start with, we set the initial number of vulnerable hosts M 1 (0) equal to 6 million, minus the number of nodes initially infected, patched or inactive.…”

Section: Setting the Initial Conditions For The July Outbreakmentioning

confidence: 99%

“…The Fast Simulation Theorem [30] is used for the characterisation of the behaviour of a single object via the average system behaviour, as defined by the mean-field approximation. The proposed method is called fluid model-checking, it has been supplemented with next and steady-state operators in [19].…”

Section: Related Workmentioning

confidence: 99%

“…In this section we briefly discuss the complexity of the numerical (approximate) algorithms for checking CSL properties of a local mean-field model, presented above. The full discussion on the decidability and convergence can be found in [19], therefore, we will not provide it here. As was discussed above, the presented algorithms are computationally demanding, due to the need of iterative computations of the solution of Kolmogorov equations.…”

Section: Run Timementioning

confidence: 99%

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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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Checking Individual Agent Behaviours in Markov Population Models by Fluid Approximation

Cited by 10 publications

References 45 publications

Transient Reward Approximation for Continuous-Time Markov Chains

Transient Reward Approximation for Continuous-Time Markov Chains

Challenges for Quantitative Analysis of Collective Adaptive Systems

Model-checking mean-field models : algorithms & applications

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