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

The cell loss probability is determined in order to investigate the call admission control problem in an asynchronous transfer mode (ATM) multiplexer loaded with a superposition of M independent and homogeneous bursty sources. The system is modeled as a single-server queuing system with finite buffer space and a deterministic service rate. The arrival process is approximated by a Markov modulated deterministic process (MMDP) in which cells arrive at a uniform rate determined by an m-state Markov process. Two approximation methods based on the MMDP approach are proposed. The first leads to an efficient iterative algorithm for computing the system steady-state probabilities from which the cell loss probability can be calculated. The second provides a closed-form formula for the cell loss probability. Comparison with simulation results shows that the first method is remarkably accurate for all cases examined, whereas the closed-form formula is accurate for cases in which the average burst length is relatively large