M|G|∞ input processes: a versatile class of models for network traffic

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Abstract
We suggest the M|G|\infty input process as a viable model for network traffic due to its versatility and tractability. We characterize the process as short or long--range dependent by means of a simple test. To gauge its performance, we study the large buffer asymptotics of a multiplexer driven by an M|G|\infty input process. The decay rate of the tail probabilities for the buffer content (in steady--state) is investigated using large deviations techniques suggested by Duffield and O'Connell. We show that the selection of the appropriate large deviations scaling is related to the forward recurrence time of the service time distribution, and a closed--form expression is derived for the corresponding generalized limiting log--moment generating function associated with the input process. We apply our results to cases where the service time distribution in the M|G|\infty input model is (i) Rayleigh (ii) Gamma (iii) Geometric (iv) Weibull (v) Log--normal and (vi) Pareto -- cases (v) and (vi) have recently been found adequate for modeling packet traffic streams in certain networking applications. Finally, we comment on the insufficiency of the short-- vs. long--range dependence characterization of an input process as a means to accurately describe the corresponding buffer dynamics.

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