Stochastic convexity and concavity of Markov processes
Mathematics of Operations Research
Bounding of performance measures for a threshold-based queueing system with hysteresis
SIGMETRICS '97 Proceedings of the 1997 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
IEEE Transactions on Computers
Computing Performance Bounds of Fork-Join Parallel Programs Under a Multiprocessing Environment
IEEE Transactions on Parallel and Distributed Systems
Computing Closed-Form Stochastic Bounds on Transient Distributions of Markov Chains
SAINT-W '05 Proceedings of the 2005 Symposium on Applications and the Internet Workshops
An Algorithmic Approach to Stochastic Bounds
Performance Evaluation of Complex Systems: Techniques and Tools, Performance 2002, Tutorial Lectures
Generalized Class 𝒞 Markov Chains And Computation Of Closed-Form Bounding Distributions
Probability in the Engineering and Informational Sciences
CSRL model checking with closed-form bounding distributions
Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools
Closed form absorption time bounds
EPEW'07 Proceedings of the 4th European performance engineering conference on Formal methods and stochastic models for performance evaluation
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We propose a particular class of transition probability matrices for discrete-time Markov chains with a closed form to compute the stationary distribution. The stochastic monotonicity properties of this class are established. We give algorithms to construct monotone, bounding matrices belonging to the proposed class for the variability orders. The accuracy of bounds with respect to the underlying matrix structure is discussed through an example.