A novel approach to estimating the cell loss probability in an ATM multiplexer loaded with homogeneous on-off sources

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Abstract
Estimating the cell loss probability in an ATM multiplexer is one of the most important problems concerning congestion control and bandwidth management in an ATM-based BISDN. We propose a new approach to estimating the cell loss probability in an ATM multiplexer. We use the Markov modulated deterministic process (MMDP) to approximate the actual arrival process and then model the ATM multiplexer as an MMDP/D/1/K queueing system. Using queueing analysis, we derive a formula for the cell loss probability expressed in terms of the limiting probabilities of a Markov chain. We propose two approximation methods based on the results of the analysis. The actual arrival process is approximated by an (M+1)-state MMDP in the first method and by a two-state MMDP in the second. The major advantages of both methods are simplicity, computational efficiency, and numerical stability. The most attractive feature of the second method is that the cell loss probability can be expressed in closed form. Numerical and simulation results show that the first method is sufficiently accurate for all cases in which burst-level congestion is the main contributing factor to cell loss, while the dosed-form formula is sufficiently accurate for applications where the average burst length is large (such as large file transfers, image retrievals, etc.)