Probabilistic Model Checking for Continuous-Time Markov Chains via Sequential Bayesian Inference

Milios, Dimitrios; Sanguinetti, Guido; Schnoerr, David

doi:10.1007/978-3-319-99154-2_18

Cited by 7 publications

(7 citation statements)

References 36 publications

(70 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We compare our approach with two baseline approaches. The first on is called Automatic Elasticity-Fuzzy Based System ''AE_FBS'' algorithm [24], [27], which is a fuzzy rule-based controller linked with a reinforcement learning algorithm that learns and modifies elasticity policies at runtime for auto-configuration of VMs in a cloud environment. The second approach is called ''CTMC'' [18], which uses an analytical model based on Continuous-Time Markov Chain (CTMC)to estimate the number of virtual machines needed to adjust the resource elasticity value of a cloud platform.…”

Section: Resultsmentioning

confidence: 99%

“…One of the most important points is how to fine and encourage selective action. In each cycle, after action selection, if the Scale Up, Scale Down or No Op action is selected, respectively the equations ( 25), (26) or (27) of the β -reinforcement signal will be calculated. If β = 1, then, the selected operation is fined by equation (25); otherwise, if β = 0, then it is rewarded according to equation (26).…”

Section: E Elasticity Managermentioning

confidence: 99%

“…If β = 1, then, the selected operation is fined by equation (25); otherwise, if β = 0, then it is rewarded according to equation (26). If R_Ci is the mean of the response time of the i-th layer and C_Ci is the average cost of the i-th layer, then it is rewarded according to equation (27).…”

Section: E Elasticity Managermentioning

confidence: 99%

See 2 more Smart Citations

ControCity: An Autonomous Approach for Controlling Elasticity Using Buffer Management in Cloud Computing Environment

et al. 2019

View full text Add to dashboard Cite

Cloud computing has been one of the most popular distributed computing paradigms. Elasticity is a crucial feature that distinguishes cloud computing from other distributed computing models. It considers the resource provisioning and allocation processes can be implemented automatically and dynamically. Elasticity feature allows cloud platforms to handle different loads efficiently without disrupting the normal behavior of the application. Therefore, providing a resource elasticity analytical model can play a significant role in cloud resource management. This paper presents Controlling Elasticity (ControCity) framework for controlling resources elasticity through using ''buffer management'' and ''elasticity management''. In the proposed framework, there are two essential components called buffer manager and elasticity manager in the application layer and middleware layer, respectively. The buffer management controls the input queue of the user's request and the elasticity management controls the elasticity of the cloud platform using learning automata technique. In the application layer, applications are received by cloud applications and, then, placed in the control of the buffer. Buffer manager controls the queue of requests, and elasticity manager of the middleware layer using the learning automata provides a solution for controlling the elasticity of the cloud platform. The experimental results indicate that the ControCity reduces the response time by up to 3.7%, and increases the resource utilization and elasticity by up to 8.4% and 5.4%, respectively, compared with the other approaches.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: E Elasticity Managermentioning

confidence: 99%

See 1 more Smart Citation

ControCity: An Autonomous Approach for Controlling Elasticity Using Buffer Management in Cloud Computing Environment

et al. 2019

View full text Add to dashboard Cite

show abstract

“…As demonstrated in Section 4, such highly accurate approximations can provide valuable insights into the dynamics of biochemical networks and interacting populations. Although our examples were biological, computing these measures is important to other fields, for instance, to quantify customer waiting times [38,39], modelling computer-communication and transaction processing systems [34], computing reliability measures of complex systems [14], or in model checking [43]. (i) Because Q and Q r coincide on S r , Lemma 2.3 tells us that both X and X r leave for the first time S r at the same moment (namely, τ r ).…”

Section: Fixation Statistics In Population Dynamicsmentioning

confidence: 99%

The Exit Time Finite State Projection Scheme: Bounding Exit Distributions and Occupation Measures of Continuous-Time Markov Chains

Kuntz¹,

Thomas²,

Stan³

et al. 2019

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

We introduce the exit time finite state projection (ETFSP) scheme, a truncationbased method that yields approximations to the exit distribution and occupation measure associated with the time of exit from a domain (i.e., the time of first passage to the complement of the domain) of time-homogeneous continuous-time Markov chains. We prove that: (i) the computed approximations bound the measures from below; (ii) the total variation distances between the approximations and the measures decrease monotonically as states are added to the truncation; and (iii) the scheme converges, in the sense that, as the truncation tends to the entire state space, the total variation distances tend to zero. Furthermore, we give a computable bound on the total variation distance between the exit distribution and its approximation, and we delineate the cases in which the bound is sharp. We also revisit the related finite state projection scheme and give a comprehensive account of its theoretical properties. We demonstrate the use of the ETFSP scheme by applying it to two biological examples: the computation of the first passage time associated with the expression of a gene, and the fixation times of competing species subject to demographic noise.

show abstract

“…The only approach dealing with more general subsets, [19], imposes restrictions on the behaviour of the mean-field approximation, whose trajectory has to enter the reachability region in a finite time. Another interesting approach has been developed in [47,42], where model checking of time-bounded properties for CTMCs is expressed as a Bayesian inference problem, and approximated model checking algorithms are derived. However, no guarantees on the convergence of the resulting algorithms is given.…”

Section: Introductionmentioning

confidence: 99%

Central Limit Model Checking

Bortolussi

Cardelli

Kwiatkowska

et al. 2019

ACM Trans. Comput. Logic

View full text Add to dashboard Cite

We consider probabilistic model checking for continuoustime Markov chains (CTMCs) induced from Stochastic Reaction Networks (SRNs) against a fragment of Continuous Stochastic Logic (CSL) extended with reward operators. Classical numerical algorithms for CSL model checking based on uniformisation are limited to finite CTMCs and suffer from exponential growth of the state space with respect to the number of species. On the other hand, approximate techniques such as mean-field approximations and simulations combined with statistical inference are more scalable, but can be time consuming and do not support the full expressiveness of CSL. In this paper we employ a continuousspace approximation of the CTMC in terms of a Gaussian process based on the Central Limit Approximation (CLA), also known as the Linear Noise Approximation (LNA), whose solution requires solving a number of differential equations that is quadratic in the number of species and independent of the population size. We then develop efficient and scalable approximate model checking algorithms on the resulting Gaussian process, where we restrict the target regions for probabilistic reachability to convex polytopes. This allows us to derive an abstraction in terms of a time-inhomogeneous discrete-time Markov chain (DTMC), whose dimension is independent of the number of species, on which model checking is performed. Using results from probability theory, we prove the convergence in distribution of our algorithms to the corresponding measures on the original CTMC. We implement the techniques and, on a set of examples, demonstrate that they allow us to overcome the state space explosion problem, while still correctly characterizing the stochastic behaviour of the system. Our methods can be used for formal analysis of a wide range of distributed stochastic systems, including biochemical systems, sensor networks and population protocols.

show abstract

Probabilistic Model Checking for Continuous-Time Markov Chains via Sequential Bayesian Inference

Cited by 7 publications

References 36 publications

ControCity: An Autonomous Approach for Controlling Elasticity Using Buffer Management in Cloud Computing Environment

ControCity: An Autonomous Approach for Controlling Elasticity Using Buffer Management in Cloud Computing Environment

The Exit Time Finite State Projection Scheme: Bounding Exit Distributions and Occupation Measures of Continuous-Time Markov Chains

Central Limit Model Checking

Contact Info

Product

Resources

About