Donald Bren School of Information and Computer Sciences

This paper considers a queueing system with a finite buffer and multiple heterogeneous arrival streams. We focus on Markov Modulated Arrival Processes with differing burstiness and investigate the loss of individual arrival streams when the parameters of the heterogeneous arrival streams are varied.

Our analysis follows a new stochastic integral approach and extends existing results for continuous-time Markov Modulated Poisson Arrival Processes to include both continuous-time and discrete-time treatments of multiplexed heterogeneous Markov Modulated Arrivals. In addition, we derive loss probabilities for a priority packet discarding scheme (a congestion control mechanism suitable for high-speed networks). Several interesting numerical results are presented; we introduce a new characterization of an arrival stream, which we refer to as self-loss, and use this to qualitatively predict the effects of multiplexing bursty streams with non-bursty streams.