Model Checking Continuous-Time Markov Chains by Transient Analysis

Baier, Christel; Haverkort, Boudewijn R.; Hermanns, Holger; Katoen, Joost-Pieter

doi:10.1007/10722167_28

Cited by 120 publications

(182 citation statements)

References 22 publications

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“…A (labelled) CTMC C is a tuple (S, R, L) where S and L are as for DTMCs, and R : S × S → IR 0 is the rate matrix. (We adopt the same conventions as in [6,7], i.e. we do allow self-loops.)…”

Section: The Continuous-time Settingmentioning

confidence: 99%

“…CSL model checking [7,6] is performed in the same way as for CTL [11] and PCTL [17], by recursively computing the set Sat(Φ). For the boolean operators this is exactly as for CTL and for unbounded until this is exactly as for PCTL.…”

Section: The Continuous-time Settingmentioning

confidence: 99%

“…It has been shown in [6] that for a given CTMC C and state s in C, the measure Prob C (s, Φ U t Ψ ) can be calculated by means of a transient analysis of the CTMC C , which can easily be derived from C using the [·] operator. Let π C (s, t)(s ) denote the probability of being in state s at time t given that the system started in state s, i.e.…”

Section: The Continuous-time Settingmentioning

confidence: 99%

“…Approximate CSL model-checking algorithms have been studied in [7] where the satisfaction of time-bounded until formulas is shown to be based on solving a (recursive) Volterra equation system. More recently, Baier et al [6] reduced verifying time-bounded until formulas to the problem of computing transient-state probabilities for CTMCs. This significant result employs a formula-dependent transformation of the CTMC and -more importantlyallows one to adopt efficient techniques like uniformisation [16,23] for verifying time-bounded until-formulas.…”

Section: Introductionmentioning

confidence: 99%

“…Verifying time-bounded until formulas using transient analysis of CTMCs [6] suggests that uniformisation should be applied to each individual state separately. This results in a worst case time complexity of O(M ·N ), where N is the number of states in the CTMC and M the number of transitions.…”

Section: Introductionmentioning

confidence: 99%

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Faster and Symbolic CTMC Model Checking

Katoen

Kwiatkowska

Norman

et al. 2001

Process Algebra and Probabilistic Methods. Performance Modelling and Verification

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Abstract. This paper reports on the implementation and the experiments with symbolic model checking of continuous-time Markov chains using multi-terminal binary decision diagrams (MTBDDs). Properties are expressed in Continuous Stochastic Logic (CSL) [7] which includes the means to express both transient and steady-state performance measures. We show that all CSL operators can be treated using standard operations on MTBDDs, thus allowing a rather straightforward implementation of symbolic CSL model checking on existing MTBDD-based platforms such as the verifier PRISM. The main result of the paper is an improvement of O(N ) in the time complexity of checking time-bounded until-formulas, where N is the number of states in the CTMC under consideration. This result yields a drastic speed-up in the verification time of model checking CTMCs, both in the symbolic and non-symbolic case.

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Section: The Continuous-time Settingmentioning

confidence: 99%

Section: The Continuous-time Settingmentioning

confidence: 99%

Section: The Continuous-time Settingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stochastic modeling and analysis of the bitcoin protocol in the presence of block communication delays

Bistarelli

Nicola

Galletta

et al. 2021

Concurrency and Computation

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We analyze the protocol of the Bitcoin blockchain by using the PRISM probabilistic model checker. In particular, we (i) extend PRISM with the ledger data type, (ii) model the behaviour of the key participants in the protocol -the miners -and (iii) describe the whole protocol as a parallel composition of processes. The probabilistic analysis of the model highlights how forks happen and how they depend on specific parameters of the protocol, such as the difficulty of the cryptopuzzle and the network communication delays. Our results confirm that considering transactions in blocks at depth larger than 5 as permanent is reasonable because the majority of miners have consistent blockchains up-to that depth with probability of almost 1. We also study the behaviour of networks with churn miners, which may leave the network and rejoin afterwards, and with different topologies.

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Fault masking as a service

et al. 2014

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Due to copyright restrictions, the access to the full text of this article is only available via subscription.In SOA, composite services depend on a set of partner services to perform their tasks. These partner services may become unavailable because of system and/or network faults, leading to an increased error rate for the composite service. In this paper, we propose an approach to prevent the occurrence of errors that result from the unavailability of partner services. We introduce an external Web service, dubbed Fault Avoidance Service (FAS), to which composite services can register at will. After registration, FAS periodically checks the partner links, detects unavailable partner services, and updates the composite service with available alternatives. Thus, in case of a partner service error, the composite service will have been updated before attempting an ill-destined request. We provide mathematical analysis regarding the error rate and the false positive rate with respect to the monitoring frequency of FAS for two models. We obtained empirical results by conducting several tests on the Amazon Elastic Compute Cloud to evaluate our mathematical analyses. We also introduce an industrial case study for improving the quality of a service-oriented system from the broadcasting and content delivery domain.Vestel Electronics ; Turkish Ministry of Science, Industry and Technolo

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Model Checking Continuous-Time Markov Chains by Transient Analysis

Cited by 120 publications

References 22 publications

Faster and Symbolic CTMC Model Checking

Faster and Symbolic CTMC Model Checking

Stochastic modeling and analysis of the bitcoin protocol in the presence of block communication delays

Fault masking as a service

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