Applying the reduction approach to EQNM2L large models

At a time when complexity becomes a major issue in system modeling, it becomes necessary to simplify, as much as possible, complex systems to be modeled. The inherent complexity of this latter obstructs understanding of their models. In turn, the number of components, interactions between them and the size of the model, increase when complexity increases. As a result, visualization and comprehension become difficult. As well, the analysis or the simulation of large models becomes time consuming tasks. For these reasons, there is a need to reduce the system size, which reduces the number of components and time analysis or simulation. In this field, there is a wide range of methodologies for reducing large models, but they are often specialized according to modeling languages. In this work, we are interested to queueing networks reduction methodologies. This article gives an approach for reducing EQNM2L (Extended Queuing Networks Modeling and Markup Language) large model to a smaller one. The objective is to reduce the analysis time as well as the simulation time of the network. The basic idea is to divide the model into a set of submodels which are analyzed in isolation. In this work, we propose to substitute each submodel by a single M/G/^∞ station. The main conclusion of this work is that this adopted rule provides exact results for the mean number of clients at the network and the mean time spent at the whole network. For other parameters, approximated results are obtained.