Though the various models proposed in the literature for capturing the long-range dependent nature of network traffic are all either exactly or asymptotically second order self-similar, their effect on network performance can be very different. We are thus motivated to characterize the limiting distributions of these models so that they lead to parsimonious modeling and a better understanding of network traffic. In this paper we consider long-range dependent arrival processes based on Markovian arrival and fractional ARIMA processes and show that the suitably scaled distributions of these processes converge to fractional Brownian motion in the sense of finite dimensional distributions. Subsequently, we prove that they also converge weakly to fractional Brownian motion in the space of continuous functions. Thus, the behavior of network elemetns fed with traffic from these models has similar characteristics to those fed with fractional Brownian motion under suitable limiting conditions. Specifically, tails of queues fed with these arrivals have a Weibullian shape in sharp contrast with the exponential tails of conventional queues. Also, the weak convergence results allow us to accurately estiamte the loss probabilities using the expressions for storage models for fractional Browninan motion.
展开▼
