Loss probabilities and delay and jitter distributions in a finite buffer queue with heterogeneous batch Markovian arrival processes

We study a single server queue with finite buffer that may represent an ATM multiplexer. The input traffic is a superposition of independent heterogeneous batch Markovian arrival processes. Service durations are supposed to be exponential. We derive the loss probability and the delay and jitter distributions for each individual process, as well as for the superposed one. We show that there is a significant difference between performances of individual and global flows, justifying our work. The approach is based on martingale techniques