Evaluation and comparison of cell loss and delay models for ATM multiplexers

Among several models that are available to represent the aggregate cell flow generated by on–off sources at an ATM multiplexer (either at an access or a switching node), the Interrupted Bernoulli Process (IBP) is characterized by particular simplicity and analytical tractability. The superposition of sources individually modeled as an IBP, whose cells enter a common buffer, is considered in this paper. The main goal is to compute approximations of two basic Quality of Service (QoS) indicators, namely, cell loss rate, whose analytical computation has been already presented in previous works, and the rate of cells exceeding a specified delay, whose presentation constitutes the theoretical novelty of the paper. Analytical expressions of these two quantities are given for homogeneous sources, i.e., possessing the same statistical parameters and QoS requirements. The analytical formulation is carefully evaluated by comparing the results obtained with others presented in the literature and with simulation results; in the latter, the actual cell arrival process is generated by means of a Markov Modulated Deterministic Process (MMDP) model of the on–off sources. Several comparisons are performed for different offered loads and by varying the buffer length, which show the effectiveness and the limits of the technique under investigation.

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