Parameter Synthesis for Markov Models: Faster Than Ever

Quatmann, Tim; Dehnert, Christian; Jansen, Nils; Junges, Sebastian; Katoen, Joost-Pieter

doi:10.1007/978-3-319-46520-3_4

Cited by 79 publications

(123 citation statements)

References 22 publications

Supporting

Mentioning

117

Contrasting

Order By: Relevance

“…Setup. In our first set of benchmarks, we adopt parametric MDPs and MCs from [32]. Essentially, the technique from that paper allows to approximate the percentage of instantiations that satisfy (or do not satisfy) a specification.…”

Section: Parameter Synthesis Benchmarksmentioning

confidence: 99%

Scenario-Based Verification of Uncertain MDPs

Cubuktepe

Jansen

Junges

et al. 2020

Tools and Algorithms for the Construction and Analysis of Systems

Self Cite

View full text Add to dashboard Cite

We consider Markov decision processes (MDPs) in which the transition probabilities and rewards belong to an uncertainty set parametrized by a collection of random variables. The probability distributions for these random parameters are unknown. The problem is to compute the probability to satisfy a temporal logic specification within any MDP that corresponds to a sample from these unknown distributions. In general, this problem is undecidable, and we resort to techniques from so-called scenario optimization. Based on a finite number of samples of the uncertain parameters, each of which induces an MDP, the proposed method estimates the probability of satisfying the specification by solving a finite-dimensional convex optimization problem. The number of samples required to obtain a high confidence on this estimate is independent from the number of states and the number of random parameters. Experiments on a large set of benchmarks show that a few thousand samples suffice to obtain high-quality confidence bounds with a high probability.

show abstract

Section: Parameter Synthesis Benchmarksmentioning

confidence: 99%

Scenario-Based Verification of Uncertain MDPs

Cubuktepe

Jansen

Junges

et al. 2020

Tools and Algorithms for the Construction and Analysis of Systems

Self Cite

View full text Add to dashboard Cite

show abstract

“…Our approach can be easily extended to also support timeunbounded properties by using the method of [25] for parameter synthesis of discrete-time Markov models and properties expressed by time-unbounded formulae of probabilistic computation tree logic.…”

Section: A Computing Safe Property Bounds For Pctmcsmentioning

confidence: 99%

“…Fig. 2 shows the resulting model, encoded in the PRISM modelling language extended with the evolve constructs from Section IV-C. As in [31], we model separately the software and hardware failures and repairs, for both the master server (lines [22][23][24][25] and the chunk servers (lines [26][27][28][29][30][31], and assume that loss of chunk copies due to chunk server failures leads to further chunk replications, which is an order of magnitude slower if c = 0 and a backup of the chunk must be used (line 32).…”

Section: Case Studiesmentioning

confidence: 99%

“…Finally, research on parameter synthesis for probabilistic systems from temporal logic specifications focuses on deriving symbolic expressions for the satisfaction probability of the specification as a function of the parameters [20], [38], [39] or on computing safe enclosures of the satisfaction probability for given intervals of parameter values [12], [25]. In contrast to this work, our robust design synthesis directly integrates sensitivity analysis into the automated design process.…”

Section: Case Studiesmentioning

confidence: 99%

See 1 more Smart Citation

Designing Robust Software Systems through Parametric Markov Chain Synthesis

Călinescu

Češka

Gerasimou

et al. 2017

2017 IEEE International Conference on Software Architecture (ICSA)

View full text Add to dashboard Cite

Abstract-We present a method for the synthesis of software system designs that satisfy strict quality requirements, are Paretooptimal with respect to a set of quality optimisation criteria, and are robust to variations in the system parameters. To this end, we model the design space of the system under development as a parametric continuous-time Markov chain (pCTMC) with discrete and continuous parameters that correspond to alternative system architectures and to the ranges of possible values for configuration parameters, respectively. Given this pCTMC and required tolerance levels for the configuration parameters, our method produces a sensitivity-aware Pareto-optimal set of designs, which allows the modeller to inspect the ranges of quality attributes induced by these tolerances, thus enabling the effective selection of robust designs. Through application to two systems from different domains, we demonstrate the ability of our method to synthesise robust designs with a wide spectrum of useful tradeoffs between quality attributes and sensitivity.Keywords-software performance and reliability engineering; probabilistic model synthesis; multi-objective optimisation I. INTRODUCTION Evaluating the performance, reliability and other quality attributes of alternative designs is essential for the cost-effective engineering of software [1], [2]. Delaying this evaluation until integration or system testing can greatly increase engineering costs, as defects identified late in the development lifecycle require much more effort to fix [3]. A common method to avoid this delay uses model-based simulation [4] or formal verification [5] to predict the quality attributes of alternative designs. Models that meet the quality requirements of the system under development are then used as a basis for its implementation. Models based on queueing networks [6], probabilistic models [2], [5] and timed automata [7] have been used for this purpose, together with tools for their simulation (e.g. Palladio [8]) and verification (e.g. PRISM [9]). Furthermore, recently proposed approaches automate the search for suitable designs. Probabilistic model repair [10], [11] automatically modifies the transition probabilities of Markov models that violate a quality requirement, generating new models that meet the requirement. Precise parameter synthesis [12] identifies transition rates that enable continuous Markov models to satisfy a quality requirement or to optimise a quality attribute of the modelled system. Finally, probabilistic model synthesis [13] starts from a design template that captures alternative system designs, and uses multiobjective optimisation to generate the Pareto-optimal set of Markov models associated with the quality requirements of the system.

show abstract

“…Despite the significant progress in the last years in analysing pMCs [10,15,41], the scalability of algorithms severely lacks behind methods for ordinary MCs.…”

Section: Introductionmentioning

confidence: 99%

Are Parametric Markov Chains Monotonic?

Spel

Junges

Katoen

2019

Automated Technology for Verification and Analysis

Self Cite

View full text Add to dashboard Cite

This paper presents a simple algorithm to check whether reachability probabilities in parametric Markov chains are monotonic in (some of) the parameters. The idea is to construct-only using the graph structure of the Markov chain and local transition probabilities-a pre-order on the states. Our algorithm cheaply checks a sufficient condition for monotonicity. Experiments show that monotonicity in several benchmarks is automatically detected, and monotonicity can speed up parameter synthesis up to orders of magnitude faster than a symbolic baseline.

show abstract

Parameter Synthesis for Markov Models: Faster Than Ever

Cited by 79 publications

References 22 publications

Scenario-Based Verification of Uncertain MDPs

Scenario-Based Verification of Uncertain MDPs

Designing Robust Software Systems through Parametric Markov Chain Synthesis

Are Parametric Markov Chains Monotonic?

Contact Info

Product

Resources

About