A novel approach to estimating the cell loss probability of an ATM multiplexer loaded with homogeneous bursty sources

We are interested in determining the cell loss probability in order to investigate the call admission control problem in an ATM multiplexer loaded with a superposition of M independent and homogeneous bursty sources. We model the above system as a single-server queueing system with finite buffer space and a deterministic service rate. In this paper, we approximate the arrival process by a Markov modulated deterministic process (MMDP) in which cells arrive at a uniform rate determined by an m-state Markov process. We propose two approximation methods based on the MMDP approach. The first method leads to an efficient iterative algorithm for computing the system steady-state probabilities from which the cell loss probability can be easily calculated. The second method provides a closed-form formula for the cell loss probability. By comparing with simulation results, we find that the first method is remarkably accurate for all cases we have examined, whereas the closed-form formula is accurate for cases in which the average burst length is relatively large.