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

We suggest the M|G|∞ 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|∞ 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 (see Mathematical Proceedings of the Cambridge Philosophical Society, no.118, p.363-74, 1995). 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|∞ input model is (i) Rayleigh, (ii) gamma, (iii) geometric, (iv) Weibull, (v) log-normal and (vi) Pareto-cases (v) and (vi) have 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