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Analyzing Energy-Efficient and Kubernetes-Based Autoscaling of Microservices Using probabilistic model checking

JOURNAL OF GRID COMPUTING 2025年第1期23卷 1-26页

作者： Agos Jawaddi, Siti Nuraishah Ismail, Azlan Sulaiman, Mohd Suffian Cardellini, Valeria Univ Teknol MARA UiTM Coll Comp Informat & Math Sch Comp Sci Shah Alam 40450 Selangor Malaysia Univ Teknol MARA UiTM Inst Big Data Analyt & Artificial Intelligence IBD Selangor Malaysia Univ Roma Tor Vergata Dept Civil Engn & Comp Sci Engn DICII Rome Italy

Microservices are widely used to enable agility and scalability in modern software systems, while cloud computing offers cost-effective ways to provision computing resources on demand. However, ensuring the correctness of scaling decisions and their impact on energy consumption is a challenging problem that has not been sufficiently addressed in previous research. Thus, in this paper, we present an innovative approach for analyzing host energy consumption and energy violations influenced by microservice autoscaling policies using probabilistic model checking (PMC). We propose four variations of the Markov Decision Process (MDP) models that incorporate various scaling constraints inspired by Kubernetes-based Horizontal Pod Autoscaler, and we encode these models using two different approaches, namely, bounded-by-action (BBA) and bounded-by-state (BBS). We use PMC to verify the scaling policies in terms of host energy consumption and energy violations, and we conduct sensitivity analysis to demonstrate the effectiveness of our models in generating energy-efficient scaling policies. Our results show that the latency and energy-based MDP model offers the most suitable policies for ensuring energy efficiency in microservice systems. Additionally, the number of pods and the scale-out action significantly affect energy consumption and violations. Sensitivity analysis also reveals that incorporating latency into scaling decisions is key to energy efficiency, while variations in the maximum pod threshold significantly influence energy consumption and violation. Our approach provides a formal method for ensuring the correctness of microservice autoscaling decisions in cloud environments at design time and can help reduce energy consumption and violations while ensuring service-level objectives are met.

关键词： Microservices Energy-driven microservice autoscaling Markov decision process Formal verification probabilistic model checking Kubernetes

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Time Table Scheduling for Single Track Railways by probabilistic model checking and Genetic Algorithms

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INTERNATIONAL JOURNAL OF INTELLIGENT TRANSPORTATION SYSTEMS RESEARCH 2025年 1-18页

作者： Mohagheghi, Mohammadsadegh Vali E Asr Univ Rafsanjan Rafsanjan Iran

Finding optimal train scheduling is one of the most important challenges in railway logistics. Providing a pre-defined timetable is a prevalent response to manage this challenge in many developing countries. Single line track is widely used in these countries where old infrastructures may cause unforeseen delays. Such train delays can affect the fixed timetables and postpone destination arrival times, which bring economical side effects. Delay propagation may influence other trains in both directions of a track. To minimize the total propagated delays in a single-track railway network and maximize its performance, optimal timetabling should be provided. In this paper, we rely on the stochastic nature of train failures and propose a new framework to approximate the expected propagated delays in a railway network for a given timetable. Our approach is to reduce the problem of minimizing the total expected propagated delays to a probabilistic model checking of the corresponding MDP model. We apply the PRISM modeling language to provide a high-level description of a given railway system and apply the PRISM model checker engines to analyze the related problem. To overcome the state and time complexities of computing the problem for complex railway systems we utilize the statistical methods to approximate optimal solutions. Using this framework, we follow two approaches for computing a near-optimal timetable. These approaches include the lightweight smart sampling and genetic algorithm and in both cases statistical model checking is used to analyse the proposed timetable solutions. The north-west part of Iranian railways is considered as an empirical benchmark. The proposed approach reduces the total delays for this case study to less than half.

关键词： Railway scheduling Optimal timetable Markov decision process probabilistic model checking

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Synchronisation in Language-Level Symmetry Reduction for probabilistic model checking 30th

Synchronisation in Language-Level Symmetry Reduction for Pro...

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30th International Symposium on model checking Software

作者： Valkov, Ivaylo Donaldson, Alastair F. Miller, Alice Univ Glasgow Glasgow Lanark Scotland Imperial Coll London London England

ISBN: (纸本)9783031661488;9783031661495

The generic representatives (or counter abstraction) approach has been shown to be an effective symmetry reduction method for model checking. This method was extended to a probabilistic setting via a specialised language, Symmetric probabilistic Specification Language (SPSL) and an associated tool, GRIP, for use with the PRISM model checker. However, SPSL does not support synchronisation-based communication, making this method inapplicable to systems that require synchronisation. We show how synchronisation can be added to SPSL, and develop new counter abstraction translation rules for synchronous statements. We extend GRIP accordingly and demonstrate the feasibility and effectiveness of the new abstraction rules via a range of examples. This extends the applicability of the generic representatives technique to the wide class of probabilistic systems that rely on synchronisation. Experimental results show that our approach works well for systems that are composed of a large number of simple symmetric modules that feature a small amount of synchronisation-based communication.

关键词： probabilistic model checking Symmetry reduction Generic representatives Counter abstraction Synchronisation PRISM

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probabilistic model checking of the One-Dimensional Ising model

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IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS 2009年第5期E92D卷 1003-1011页

作者： Sekizawa, Toshifusa Tsuchiya, Tatsuhiro Takahashi, Koichi Kikuno, Tohru Osaka Univ Grad Sch Informat Sci & Technol Suita Osaka 5650871 Japan Natl Inst Adv Ind Sci & Technol Res Ctr Verificat & Semant Toyonaka Osaka 5600083 Japan

probabilistic model checking is an emerging verification technology for probabilistic analysis. Its use has been started not only in computer science but also in interdisciplinary fields. In this paper, we show that probabilistic model checking allows one to analyze the magnetic behaviors of the one-dimensional Ising model, which describes physical phenomena of magnets. The Ising model consists of elementary objects called spins and its dynamics is often represented as the Metropolis method. To analyze the Ising model with probabilistic model checking, we build Discrete Time Markov Chain (DTMC) models that represent the behavior of the Ising model. Two representative physical quantities, i.e., energy and magnetization, are focused on. To assess these quantities using model checking, we devise formulas in probabilistic real time Computation Tree Logic (PCTL) that represent the quantities. To demonstrate the feasibility of the proposed approach, we show the results of an experiment using the PRISM model checker.

关键词： verification probabilistic model checking the Ising model Discrete Time Markov Chain

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probabilistic model checking for the quantification of DoS security threats

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COMPUTERS & SECURITY 2009年第6期28卷 450-465页

作者： Basagiannis, Stylianos Katsaros, Panagiotis Pombortsis, Andrew Alexiou, Nikolaos Aristotle Univ Thessaloniki Dept Informat Thessaloniki 54124 Greece

Secure authentication features of communication and electronic commerce protocols involve computationally expensive and memory intensive cryptographic operations that have the potential to be turned into denial-of-service (DoS) exploits. Recent proposals attempt to improve DoS resistance by implementing a trade-off between the resources required for the potential victim(s) with the resources used by a prospective attacker. Such improvements have been proposed for the Internet Key Exchange (IKE), the just Fast Keying (JFK) key agreement protocol and the Secure Sockets Layer (SSL/TLS) protocol. In present article, we introduce probabilistic model checking as an efficient tool-assisted approach for systematically quantifying DoS security threats. We model a security protocol with a fixed network topology using probabilistic specifications for the protocol participants. We attach into the protocol model, a probabilistic attacker model which performs DoS related actions with assigned cost values. The costs for the protocol participants and the attacker reflect the level of some resource expenditure (memory, processing capacity or communication bandwidth) for the associated actions. From the developed model we obtain a Discrete Time Markov Chain (DTMC) via property preserving discrete-time semantics. The DTMC model is verified using the PRISM model checker that produces probabilistic estimates for the analyzed DoS threat. in this way, it is possible to evaluate the level of resource expenditure for the attacker, beyond which the likelihood of widespread attack is reduced and subsequently to compare alternative design considerations for optimal resistance to the analyzed DoS threat. Our approach is validated through the analysis of the Host Identity Protocol (HIP). The HIP base-exchange is seen as a cryptographic key-exchange protocol with special features related to DoS protection. We analyze a serious DoS threat, for which we provide probabilistic estimates, as well as r

关键词： Denial of service Secure authentication probabilistic model checking Resource exhaustion Attacker model

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probabilistic model checking of biological systems with uncertain kinetic rates

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THEORETICAL COMPUTER SCIENCE 2012年 419卷 2-16页

作者： Barbuti, Roberto Levi, Francesca Milazzo, Paolo Scatena, Guido IMT Lucca Inst Adv Studies I-55100 Lucca Italy Univ Pisa Dip Informat I-56127 Pisa Italy

In this paper, we present a formalization of biological systems based on multiset rewriting and we investigate the use of abstract interpretation on its semantics. We consider a probabilistic semantics, which is well suited to represent the non-deterministic evolution of real biological systems. Abstract interpretation allows us to deal with systems in which the kinetic rates of the evolution rules are not precisely known. On the (abstract) systems, we perform probabilistic model checking obtaining lower and upper bounds for the probabilities of reaching states satisfying the given properties. We apply abstract probabilistic model checking to verify reachability properties in a model of tumor growth. (C) 2011 Elsevier B.V. All rights reserved.

关键词： probabilistic model checking Systems biology Uncertain kinetic rates Abstract interpretation Interval Markov chains

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probabilistic model checking of Regenerative Concurrent Systems

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IEEE TRANSACTIONS ON SOFTWARE ENGINEERING 2016年第2期42卷 153-169页

作者： Paolieri, Marco Horvath, Andras Vicario, Enrico Univ Florence Dept Informat Engn Via Santa Marta 3 I-50139 Florence Italy Univ Turin Dept Comp Sci Corso Svizzera 185 I-10149 Turin Italy

We consider the problem of verifying quantitative reachability properties in stochastic models of concurrent activities with generally distributed durations. models are specified as stochastic time Petri nets and checked against Boolean combinations of interval until operators imposing bounds on the probability that the marking process will satisfy a goal condition at some time in the interval [alpha, beta] after an execution that never violates a safety property. The proposed solution is based on the analysis of regeneration points in model executions: a regeneration is encountered after a discrete event if the future evolution depends only on the current marking and not on its previous history, thus satisfying the Markov property. We analyze systems in which multiple generally distributed timers can be started or stopped independently, but regeneration points are always encountered with probability 1 after a bounded number of discrete events. Leveraging the properties of regeneration points in probability spaces of execution paths, we show that the problem can be reduced to a set of Volterra integral equations, and we provide algorithms to compute their parameters through the enumeration of finite sequences of stochastic state classes encoding the joint probability density function (PDF) of generally distributed timers after each discrete event. The computation of symbolic PDFs is limited to discrete events before the first regeneration, and the repetitive structure of the stochastic process is exploited also before the lower bound a, providing crucial benefits for large time bounds. A case study is presented through the probabilistic formulation of Fischer's mutual exclusion protocol, a well-known real-time verification benchmark.

关键词： probabilistic model checking reachability stochastic Petri net Markov regenerative process Markov renewal theory

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probabilistic model checking Analysis of Palytoxin Effects on Cell Energy Reactions of the Na⁺/K⁺-ATPase

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2013年第6期10卷 1530-1541页

作者： Braz, Fernando A. F. Cruz, Jader S. Faria-Campos, Alessandra C. Campos, Sergio V. A. Univ Fed Minas Gerais Dept Comp Sci BR-30123970 Belo Horizonte MG Brazil Univ Fed Minas Gerais Dept Biochem & Immunol BR-30123970 Belo Horizonte MG Brazil

probabilistic model checking (PMC) is a technique used for the specification and analysis of complex systems. It can be applied directly to biological systems which present these characteristics, including cell transport systems. These systems are structures responsible for exchanging ions through the plasma membrane. Their correct behavior is essential for animal cells, since changes on those are responsible for diseases. In this work, PMC is used to model and analyze the effects of the palytoxin toxin (PTX) interactions with one of these systems. Our model suggests that ATP could inhibit PTX action. Therefore, individuals with ATP deficiencies, such as in brain disorders, may be more susceptible to the toxin. We have also used heat maps to enhance the kinetic model, which is used to describe the system reactions. The map reveals unexpected situations, such as a frequent reaction between unlikely pump states, and hot spots such as likely states and reactions. This type of analysis provides a better understanding on how transmembrane ionic transport systems behave and may lead to the discovery and development of new drugs to treat diseases associated to their incorrect behavior.

关键词： probabilistic model checking systems biology sodium-potassium pump palytoxin

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probabilistic model checking of complex biological pathways

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THEORETICAL COMPUTER SCIENCE 2008年第3期391卷 239-257页

作者： Heath, John Kwiatkowska, Marta Norman, Gethin Parker, David Tymchyshyn, Oksana Univ Oxford Comp Lab Oxford OX1 3QD England Univ Birmingham Sch Biosci Birmingham B15 2TT W Midlands England Univ Birmingham Sch Comp Sci Birmingham B15 2TT W Midlands England

probabilistic model checking is a formal verification technique that has been successfully applied to the analysis of systems from a broad range of domains, including security and communication protocols, distributed algorithms and power management. In this paper we illustrate its applicability to a complex biological system: the FGF (Fibroblast Growth Factor) signalling pathway. We give a detailed description of how this case study can be modelled in the probabilistic model checker PRISM, discussing some of the issues that arise in doing so, and show how we can thus examine a rich selection of quantitative properties of this model. We present experimental results for the case study under several different scenarios and provide a detailed analysis, illustrating how this approach can be used to yield a better understanding of the dynamics of the pathway. Finally, we outline a number of exact and approximate techniques to enable the verification of larger and more complex pathways and apply several of them to the FGF case study. (C) 2007 Elsevier B.V. All rights reserved.

关键词： probabilistic model checking probabilistic verification biological pathways biological modelling

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probabilistic model checking of complex biological pathways

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International Conference on Computational Methods in Systems Biology

ISBN: (纸本)3540461663

关键词： probabilistic model checking probabilistic verification biological pathways biological modelling

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