The Uniformization method computes the probability distribution of a CTMC of maximum rate \$\$\backslashmu \$\$ $\mu$ at the time a general event with PDF f(x) fires. Usually, f(x) is taken as the deterministic distribution, leading to the computation of the CTMC probability at time t, but Uniformization may be extended to use other distributions. The extended Uniformization does not manipulate directly the distribution, as the whole computation is based on the alpha-factors of f(x), and the maximum CTMC rate \$\$\backslashmu \$\$ $\mu$ . This tool paper describes alphaFactory, a tool that computes the series of alpha-factors of a general distribution function starting from f(x). The main goal of alphaFactory is to provide a freely available implementation for the computation of alpha-factors, to be used inside any extended Uniformization method implementation. Truncation of the infinite series of alpha-factors is determined by a novel error bound, which provides a reliable truncation point also in case of defective PDFs. alphaFactory can be easily integrated into other existing tools, and we show its integration inside the GreatSPN framework, to solve Markov Regenerative Stochastic Petri Nets.

### alphaFactory: A Tool for Generating the Alpha Factors of General Distributions

#### Abstract

The Uniformization method computes the probability distribution of a CTMC of maximum rate \$\$\backslashmu \$\$ $\mu$ at the time a general event with PDF f(x) fires. Usually, f(x) is taken as the deterministic distribution, leading to the computation of the CTMC probability at time t, but Uniformization may be extended to use other distributions. The extended Uniformization does not manipulate directly the distribution, as the whole computation is based on the alpha-factors of f(x), and the maximum CTMC rate \$\$\backslashmu \$\$ $\mu$ . This tool paper describes alphaFactory, a tool that computes the series of alpha-factors of a general distribution function starting from f(x). The main goal of alphaFactory is to provide a freely available implementation for the computation of alpha-factors, to be used inside any extended Uniformization method implementation. Truncation of the infinite series of alpha-factors is determined by a novel error bound, which provides a reliable truncation point also in case of defective PDFs. alphaFactory can be easily integrated into other existing tools, and we show its integration inside the GreatSPN framework, to solve Markov Regenerative Stochastic Petri Nets.
##### Scheda breve Scheda completa Scheda completa (DC)
14th International Conference, QEST 2017
Berlino
September 5-7, 2017
Quantitative Evaluation of Systems
Springer International Publishing
36
51
978-3-319-66335-7
Amparore Elvio Gilberto ; Donatelli Susanna
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1663776