On the evolution of traffic characteristics inside multistage switching systems

In this paper, a method is developed to analyze the evolution of the traffic characteristics of information streams crossing the consecutive stages of an ATM multistage switching structure. Specifically, we develop a generic model for characterizing the traffic streams at the input of the consecutive stages, based on the assumption that the queueing processes in subsequent stages are independent. In our model, the parameters that determine the arrival process on the inlets of a switching element in a given stage solely depend on the output process on the outlets of the switching elements belonging to the previous stage. As a result, we are able to calculate the mean value and variance, as well as the whole distribution of the buffer contents and the packet delay in a tagged switching element, anywhere in the structure, based on earlier work. Furthermore, we can prove that, under the assumptions of the model, the traffic characteristics converge to a spatial steady state after a few stages in the system, i.e., the traffic parameters reach limiting values which are independent of the characteristics of the traffic sources at the entrance of the first stage. Although the present study focuses on the specific case of ATM switching systems, the authors believe similar results to hold also for more general multistage structures in which routing and multiplexing occurs in each stage.