A Theoretical Performance Analysis of a Markovian Switching Node

Some important ingredients of a switching system are a switching network, a switching network controller, a set of receivers that will process the call before a connection is completed, and a receiver controller. Here a highly simplified analytically tractable mathematical model of such a system was studied to gain insight into performance limitations and to shed light on analytical difficulties in extending the analysis to more realistic systems. For simplicity, it is assumed that each call on arrival must be assigned to one of channels or paths or links (there is no concentration); if no channel is available, the call is cleared from the system. In addition, each call temporarily requires a receiver for setting up its further routing; if no receiver is available, calls queue until a receiver is available. The equilibrium probability of blocking and mean throughput rate, and the equilibrium waiting time distribution are found in terms of model parameters. Numerical results are presented as well as asymptotic analytic results. Using this analysis, the capacity of the switching node is analytically calculated, with the capacity determined by the joint choice of number of links and receivers. The analysis shows in terms of formulas and for selected numerical results that there are cases where one cannot independently choose the number of links and receivers to achieve a desired level of performance.