Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
A decomposition approach for stochastic reward net models
Performance Evaluation
Modeling and analysis of stochastic systems
Modeling and analysis of stochastic systems
An approximate method for generating asymmetric random variables
Communications of the ACM
Passage time distributions in large Markov chains
SIGMETRICS '02 Proceedings of the 2002 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Object-Oriented Implementation of Selected Numerical Methods: An Introduction with Java and Smalltalk
Response time densities in generalised stochastic petri net models
WOSP '02 Proceedings of the 3rd international workshop on Software and performance
Fast estimation of probabilities of soft deadline misses in layered software performance models
Proceedings of the 5th international workshop on Software and performance
Iterative convergence of passage-time densities in semi-Markov performance models
Performance Evaluation - Performance modelling and evaluation of high-performance parallel and distributed systems
Elements for response-time statistics in ERP transaction systems
Performance Evaluation
Numerical maximum log likelihood estimation for generalized lambda distributions
Computational Statistics & Data Analysis
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Response time densities and quantiles are important performance and quality of service metrics, but their analytical derivation is, in general, very expensive. This paper presents a technique for determining approximate response time densities in Markov and semi-Markov stochastic models that requires two orders of magnitude less computation than exact Laplace transform-based techniques. The method computes the first four moments of the desired response time and then makes use of Generalised Lambda Distributions to obtain an approximation of the corresponding density. Numerical results show good agreement over a range of response time curves, particularly for those that are unimodal.