Analysis of a closed‐loop manufacturing system with finite buffers

In this paper, we are interested in the analysis of a closed loop manufacturing system with finite buffers. More precisely, the system we consider is a production line consisting of a series of machines separated by buffers of finite capacity. In addition, parts need to be mounted onto pallets during their processing through the production line. Our aim is to develop an analytical method for performance evaluation of this class of manufacturing systems. The main performance parameter of interest when designing such a system is the production capacity, i.e. the maximal production rate that can be obtained. It is a function of the processing times at the different machines, the buffer sizes, as well as the total number of pallets that are available. For this purpose, we model the system as a closed queuing network with finite capacity queues. We propose a new approximation method to calculate the performance of such queuing networks. The principle is to decompose the closed queuing network into a set of subsystems, each subsystem modelling the flow of material in one of the buffers of the network. The population constraint of the closed network is taken into account by ensuring that the sum of the average queue lengths of the different subsystems is equal to the number of the customers of the network. We present numerical results that show that the method has a fairly good qualitative as well as quantitative behaviour.