The Fourier-series method for inverting transforms of probability distributions
Queueing Systems: Theory and Applications - Numerical computations in queues
Passage time distributions in large Markov chains
SIGMETRICS '02 Proceedings of the 2002 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Response time densities in generalised stochastic petri net models
WOSP '02 Proceedings of the 3rd international workshop on Software and performance
The ipc/HYDRA Tool Chain for the Analysis of PEPA Models
QEST '04 Proceedings of the The Quantitative Evaluation of Systems, First International Conference
Journal of Parallel and Distributed Computing
MapReduce: simplified data processing on large clusters
OSDI'04 Proceedings of the 6th conference on Symposium on Opearting Systems Design & Implementation - Volume 6
MapReduce for Data Intensive Scientific Analyses
ESCIENCE '08 Proceedings of the 2008 Fourth IEEE International Conference on eScience
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Generalized stochastic Petri nets (GSPNs) are widely used in the performance analysis of computer and communications systems. Response time densities and quantiles are often key outputs of such analysis. These can be extracted from a GSPN's underlying semi-Markov process using a method based on numerical Laplace transform inversion. This method typically requires the solution of thousands of systems of complex linear equations, each of rank n, where n is the number of states in the model. For large models substantial processing power is needed and the computation must therefore be distributed. In this paper we describe the implementation of a response time analysis module for the Platform Independent Petri net Editor (PIPE2) which interfaces with Hadoop, an open-source implementation of Google's MapReduce distributed programming environment, to provide distributed calculation of response time densities in GSPN models. The software is validated with results calculated analytically as well as simulated results for larger models. Excellent scalability is shown.