A hybrid analysis method for multi-class queueing networks with multi-server nodes

There is no doubt that Rapid Modeling based on queueing theory serves the purpose of understanding complex manufacturing systems. It enables managers to integrate operational performance measures when evaluating alternative process designs. This helps decision-makers to avoid the mistake of focusing mainly on short-term financial results instead of finding sustainable solutions. However, we are facing several limitations of state-of-the-art algorithms for queueing systems. In particular, the precision of the estimates of the performance measures vary under different conditions, and information about the distribution of the output variables is available only for a few special cases. In this paper, we propose a set of recursive equations to describe the behavior of multi-class, multi-server queueing systems: ∑ Gi/Gi/m. We will show the application to simulation and propose a hybrid decomposition method for queueing networks of ∑ Gi/Gi/m stations. The proposed method is intended to deliver better estimates of the performance measures than the available decomposition algorithms and, at the same time, to be faster and easier to implement than full simulation. We illustrate the performance of the hybrid solution by comparing the results of discrete event simulation with the results of a software package implementing the hybrid algorithm and software packages applying alternative algorithms.