Performance analysis of a priority based ATM multiplexer with correlated arrivals

We consider the performance analysis of an ATM multiplexer supporting both delay sensitive (e.g. silence detected voice) and loss sensitive (e,g. data) traffic flows. The delay sensitive cells are stored in a finite (relatively small) buffer and are given service priority over loss sensitive cells in each slot. In our formulation, we allow both classes to have a general (Markovian) correlation structure. A simple matrix geometric solution for the state probability of the system is provided allowing simple computation of any desired performance metric such as loss probability and buffer requirements of high and low priority classes, respectively. We provide number of numerical results. In particular, we consider the superposition of Bernoulli on-off sources often used to model silence detected packetized voice-like traffic as a high priority class. The example for low priority traffic is taken to be i.i.d batches of geometric distribution and two-state correlated batches. The numerical results show that both the loss behavior and the buffer requirements are quite sensitive to the (average) burst size of high priority traffic. In particular, it is demonstrated that for any level of utilization, the buffer requirements for both classes appear to be almost proportional to the burst size of the high priority class. The performance of low priority traffic is shown to be quite sensitive to its correlation structure. This class suffers most if both low and high priority traffic are very bursty.