Dealing with Zero Density Using Piecewise Phase-type Approximation

Every probability distribution can be approximated up to a given precision by a phase-type distribution, i.e. a distribution encoded by a continuous time Markov chain (CTMC). However, an excessive number of states in the corresponding CTMC is needed for some standard distributions, in particular most distributions with regions of zero density such as uniform or shifted distributions. Addressing this class of distributions, we suggest an alternative representation by CTMC extended with discrete-time transitions. Using discrete-time transitions we split the density function into multiple intervals. Within each interval, we then approximate the density with standard phase-type fitting. We provide an experimental evidence that our method requires only a moderate number of states to approximate such distributions with regions of zero density. Furthermore, the usage of CTMC with discrete-time transitions is supported by a number of techniques for their analysis. Thus, our results promise an efficient approach to the transient analysis of a class of non-Markovian models.Comment: extended version of paper with same name accepted to 11th European Workshop on Performance Engineering (EPEW 2014

List of requirements on formalisms and selection of appropriate tools

This deliverable reports on the activities for the set-up of the modelling environments for the evaluation activities of WP5. To this objective, it reports on the identified modelling peculiarities of the electric power infrastructure and the information infrastructures and of their interdependencies, recalls the tools that have been considered and concentrates on the tools that are, and will be, used in the project: DrawNET, DEEM and EPSys which have been developed before and during the project by the partners, and M\uf6bius and PRISM, developed respectively at the University of Illinois at Urbana Champaign and at the University of Birmingham (and recently at the University of Oxford)

The DSPNexpress 2.000 performance and dependability modeling environment

This paper describes the latest version of the software package DSPNexpress, a tool for modeling with deterministic and stochastic Petri nets (DSPNs). Novel innovative features of DSPNexpress 2.000 constitute an efficient numerical method for transient analysis of DSPNs with and without concurrent deterministic transitions. In particular, DSPNexpress 2.000 can perform transient analysis of DSPNs without concurrent deterministic transitions in three orders of magnitude less computational effort than the previously known method. Furthermore, DSPNexpress 2.000 contains an effective numerical method for steady-state analysis of DSPNs with concurrent deterministic transitions. 1. Innovative Features of DSPNexpress To effectively employ model-based evaluation of computer and communication systems, software environments are needed that simplify model specification, modification, as well as automate quantitative analysis. Due to the complexity of practical modeling applications requiring sophisticated solution methods, the development of effective software tool support for stochastic Petri nets is an active research area. Software packages for stochastic Petri nets includ