Performance analysis of statistical multiplexing of heterogeneous discrete-time Markovian arrival processes in an ATM network

The cell loss probability and the mean cell delay are major performance metrics in analyzing a statistical multiplexer loaded with a superposition of independent and heterogeneous bursty sources. In this paper, we model each arrival process by a two-state discrete-time Markovian arrival process (D-MAP). We discuss that this traffic modeling is more realistic than the other ones in ATM networks. Then we model the superposition of r types of the two-state D-MAPS into a discrete-time batch Markovian arrival process (D-BMAP) with 2’ states. By using the steady-state analysis of the D-BMAPIDIlIKqueueing model, we obtain the exact cell loss probabilities and the mean cell delays for each type of traffic in the statistical multiplexer. In particular, we derive the formulas concerned with these performance metrics under two buffer access strategies of the simultaneous cell arrivals at the same slot: (1) fair access, and (2) priority access. From some numerical examples, we show that the performance of each traffic at the statistical multiplexer may be severely affected by its own traffic characteristics and priority of buffer access, as well as the traffic characteristics of the others.