Multiscale Queuing Analysis of Long-Range-Dependent Network Traffic
Vinay Ribeiro (vinay@rice.edu)
Electrical and Computer Engineering, Rice University
Rudolf Riedi (riedi@rice.edu)
Electrical and Computer Engineering, Rice University
Matthew Crouse (mcrouse@ece.rice.edu)
Electrical and Computer Engineering, Rice University
Richard Baraniuk (richb@rice.edu)
Electrical and Computer Engineering, Rice University
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.