Multiscale Queuing Analysis of Long-Range-Dependent Network Traffic
Ribeiro, Vinay Joseph
Riedi, Rudolf H.
Baraniuk, Richard G.
queuing; wavelets; multiscale; multifractals; networks; traffic
This paper develops a novel approach to queuing analysis tailor-made for multiscale long-range-dependent (LRD) traffic models. We review two such traffic models, the wavelet-domain independent Gaussian model (WIG) and the multifractal wavelet model (MWM). The WIG model is a recent generalization of the ubiquitous fractional Brownian motion process. Both models are based on a multiscale binary tree structure that captures the correlation structure of traffic and hence its LRD. Due to its additive nature, the WIG is inherently Gaussian, while the multiplicative MWM is non-Gaussian. The MWM is set within the framework of multifractals, which provide natural tools to measure the multiscale statistical properties of traffic loads, in particular their burstiness. Our queuing analysis leverages the tree structure of the models and provides a simple closed-form approximation to the tail queue probability for any given queue size. This makes the WIG and MWM suitable for numerous practical applications, including congestion control, admission control, and cross-traffic estimation. The queuing analysis reveals that the marginal distribution and, in particular, the large values of traffic at different time scales strongly affect queuing. This implies that merely modeling the traffic variance at multiple time scales, or equivalently, the second-order correlation structure, can be insufficient for capturing the queuing behavior of real traffic. We confirm these analytical findings by comparing the queuing behavior of WIG and MWM traffic through simulations.