Automatic verification of finite-state concurrent systems using temporal logic specifications
ACM Transactions on Programming Languages and Systems (TOPLAS)
Computing Poisson probabilities
Communications of the ACM
Self-similarity in World Wide Web traffic: evidence and possible causes
IEEE/ACM Transactions on Networking (TON)
Model-checking continuous-time Markov chains
ACM Transactions on Computational Logic (TOCL)
Performance Analysis of Communication Systems with Non-Markovian Stochastic Petri Nets
Performance Analysis of Communication Systems with Non-Markovian Stochastic Petri Nets
Faster and Symbolic CTMC Model Checking
PAPM-PROBMIV '01 Proceedings of the Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Beyond Memoryless Distributions: Model Checking Semi-Markov Chains
PAPM-PROBMIV '01 Proceedings of the Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Probabilistic Symbolic Model Checking with PRISM: A Hybrid Approach
TACAS '02 Proceedings of the 8th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Approximate Symbolic Model Checking of Continuous-Time Markov Chains
CONCUR '99 Proceedings of the 10th International Conference on Concurrency Theory
Model Checking Continuous-Time Markov Chains by Transient Analysis
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Verifying Continuous Time Markov Chains
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
Automated Performance and Dependability Evaluation Using Model Checking
Performance Evaluation of Complex Systems: Techniques and Tools, Performance 2002, Tutorial Lectures
Formal Methods for Dynamic Power Management
Proceedings of the 2003 IEEE/ACM international conference on Computer-aided design
Consecutive customer loss probabilities in M/G/1/n and GI/M(m)//n systems
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
Consecutive customer losses in regular and oscillating MX/G/1/n systems
Queueing Systems: Theory and Applications
Moments of the duration of busy periods of mx/g/1/n systems
Probability in the Engineering and Informational Sciences
Analysis of GI/M/s/c queues using uniformisation
Computers & Mathematics with Applications
Model checking expected time and expected reward formulae with random time bounds
Computers & Mathematics with Applications
SFM'07 Proceedings of the 7th international conference on Formal methods for performance evaluation
Algorithms for computing moments of the length of busy periods of single-server systems
ICCOMP'06 Proceedings of the 10th WSEAS international conference on Computers
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Continuous Time Markov Chains (CTMCs) are widely used as the underlying stochastic process in performance and dependability analysis. Model checking of CTMCs against Continuous Stochastic Logic (CSL) has been investigated previously by a number of authors [2,4,13]. CSL contains a time-bounded until operator that allows one to express properties such as "the probability of 3 servers becoming faulty within 7.01 seconds is at most 0.1". In this paper we extend CSL with a random time-bounded until operator, where the time bound is given by a random variable instead of a fixed real-valued time (or interval). With the help of such an operator we can state that the probability of reaching a set of goal states within some generally distributed delay while passing only through states that satisfy a certain property is at most (at least) some probability threshold. In addition, certain transient properties of systems which contain general distributions can be expressed with the extended logic. We extend the efficient model checking of CTMCs against the logic CSL developed in [13] to cater for the new operator. Our method involves precomputing a family of coefficients for a range of random variables which includes Pareto, uniform and gamma distributions, but otherwise carries the same computational cost as that for ordinary time-bounded until in [13].We implement the algorithms in Matlab and evaluate them by means of a queueing system example.