Automatic verification of finite-state concurrent systems using temporal logic specifications
ACM Transactions on Programming Languages and Systems (TOPLAS)
Stochastic ordering for Markov processes on partially ordered spaces
Mathematics of Operations Research
Model-checking continuous-time Markov chains
ACM Transactions on Computational Logic (TOCL)
An Algorithmic Approach to Stochastic Bounds
Performance Evaluation of Complex Systems: Techniques and Tools, Performance 2002, Tutorial Lectures
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
Model Checking of Continuous-Time Markov Chains by Closed-Form Bounding Distributions
QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
Stochastic model checking with stochastic comparison
EPEW'05/WS-FM'05 Proceedings of the 2005 international conference on European Performance Engineering, and Web Services and Formal Methods, international conference on Formal Techniques for Computer Systems and Business Processes
Accuracy of strong and weak comparisons for network of queues
MMB&DFT'10 Proceedings of the 15th international GI/ITG conference on Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance
Strong and Weak orderings for an accurate resource dimensioning
VECoS'11 Proceedings of the Fifth international conference on Verification and Evaluation of Computer and Communication Systems
Strong and weak stochastic bounds for multidimensional Markov chains
International Journal of Critical Computer-Based Systems
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The probabilistic model checking provides a precise formalism for the performance and reliability verification of telecommunication systems modeled by Markov chains. We study a queueing system similar to a Jackson network except that queues have a finite capacity. We propose to study in this paper (state and path) formulas from the Continuous Stochastic Logic (CSL), in order to verify performability properties. Unfortunately, transient and stationary analysis is very complex for multidimensional Markov processes. So we propose to use the stochastic comparisons in the sense of weak orderings to define bounding processes. Bounding processes are represented by independent M/M/1 queues for which transient and stationary distributions can be computed as the product of probability distributions of each queue. We use the increasing set method, and we develop an intuitive formalism based on events to establish weak stochastic comparisons.