Title :
M|G|∞ input processes: a versatile class of models for network traffic
Author :
Parulekar, Minothi ; Makowski, Armand M.
Author_Institution :
Dept. of Electr. Eng. & Syst. Res. Center, Maryland Univ., College Park, MD, USA
Abstract :
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
Keywords :
Weibull distribution; buffer storage; correlation methods; gamma distribution; log normal distribution; packet switching; queueing theory; telecommunication networks; telecommunication traffic; M|G|∞ input processes; Pareto distribution; Rayleigh distribution; Weibull distribution; buffer dynamics; closed-form expression; correlation properties; decay rate; forward recurrence time; gamma distribution; generalized limiting log-moment generating function; geometric distribution; large buffer asymptotics; large deviations scaling; large deviations techniques; log-normal distribution; long-range dependent process; multiplexer; network traffic; packet traffic streams; performance; service time distribution; short-range dependent process; steady state buffer content; tail probabilities; Closed-form solution; Educational institutions; Multiplexing; Predictive models; Solid modeling; Steady-state; Tail; Telecommunication traffic; Testing; Traffic control;
Conference_Titel :
INFOCOM '97. Sixteenth Annual Joint Conference of the IEEE Computer and Communications Societies. Driving the Information Revolution., Proceedings IEEE
Conference_Location :
Kobe
Print_ISBN :
0-8186-7780-5
DOI :
10.1109/INFCOM.1997.644490