The Fourier-series method for inverting transforms of probability distributions
Queueing Systems: Theory and Applications - Numerical computations in queues
Using MPI: portable parallel programming with the message-passing interface
Using MPI: portable parallel programming with the message-passing interface
Queueing networks and Markov chains: modeling and performance evaluation with computer science applications
An efficient disk-based tool for solving large Markov models
Performance Evaluation - Special issue on tools for performance evaluation
Numerical Inversion of Laplace Transforms Using Laguerre Functions
Journal of the ACM (JACM)
A probabilistic dynamic technique for the distributed generation of very large state spaces
Performance Evaluation - Special issue on modelling techniques and tools for performance evaluation
Computational algorithms for closed queueing networks with exponential servers
Communications of the ACM
Performance Modelling of Communication Networks and Computer Architectures (International Computer S
Performance Modelling of Communication Networks and Computer Architectures (International Computer S
Response time densities in generalised stochastic petri net models
WOSP '02 Proceedings of the 3rd international workshop on Software and performance
WOSP '04 Proceedings of the 4th international workshop on Software and performance
Efficient approximation of response time densities and quantiles in stochastic models
WOSP '04 Proceedings of the 4th international workshop on Software and performance
Journal of Parallel and Distributed Computing
Iterative convergence of passage-time densities in semi-Markov performance models
Performance Evaluation - Performance modelling and evaluation of high-performance parallel and distributed systems
Future Generation Computer Systems - Systems performance analysis and evaluation
Uniformization with representatives: comprehensive transient analysis of infinite-state QBDs
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
Asymptotic Variance Of Passage Time Estimators In Markov Chains
Probability in the Engineering and Informational Sciences
Information flow modeling based on diffusion rate for prediction and ranking
Proceedings of the 16th international conference on World Wide Web
Approximate queueing network analysis of patient treatment times
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Tackling large state spaces in performance modelling
SFM'07 Proceedings of the 7th international conference on Formal methods for performance evaluation
Approximating passage time distributions in queueing models by Bayesian expansion
Performance Evaluation
A formal language toward the unification of model checking and performance evaluation
ASMTA'10 Proceedings of the 17th international conference on Analytical and stochastic modeling techniques and applications
Provisioning multi-tier cloud applications using statistical bounds on sojourn time
Proceedings of the 9th international conference on Autonomic computing
| Hi-index | 0.00 |
Probability distributions of response times are important in the design and analysis of transaction processing systems and computer-communication systems. We present a general technique for deriving such distributions from high-level modelling formalisms whose state spaces can be mapped onto finite Markov chains. We use a load-balanced, distributed implementation to find the Laplace transform of the first passage time density and its derivatives at arbitrary values of the transform parameter s. Setting s = 0 yields moments while the full passage time distribution is obtained using a novel distributed Laplace transform inverter based on the Laguerre method. We validate our method against a variety of simple densities, cycle time densities in certain overtake-free (tree-like) queueing networks and a simulated Petri net model. Our implementation is thereby rigorously validated and has already been applied to substantial Markov chains with over 1 million states. Corresponding theoretical results for semi-Markov chains are also presented.