The analytical tool developed by the authors provides a general solution technique for integration of traffic measurement and queueing analysis. The frequency-domain approach is used to combine the advanced techniques in two areas: signal processing and queueing analysis. Essentially, signal processing techniques are used to obtain the steady-state and second-order statistics of a traffic stream. We propose a new programming method for the construction of a special class of Markov chains to statistically match with each given traffic stream (or superposition of heterogeneous traffic streams). The analytical queueing solutions can therefore be obtained by the folding-algorithm based on Markov chain input modeling. Comprehensive numerical examples show the great potential of the statistical-matching and queueing (SMAQ) tool to solve measurement-based traffic management issues.

We study link capacity allocation for a finite buffer system to transmit multimedia traffic. The queueing process is simulated with real video traffic. Two key concepts are explored in this study. First, the link capacity requirement at each node is essentially captured by its low-frequency input traffic (filtered at a properly selected cut-off frequency). Second, the low-frequency traffic stays intact as it travels through a finite-buffer system without significant loss. Hence, one may overlook the queueing process at each node for network-wide traffic flow in the low-frequency band. We propose a simple, effective method for link capacity allocation and network control using on-line observation of traffic flow in the low-frequency band. The study explores a new direction for measurement-based traffic control in high-speed networks.>

Considers a single-server finite-buffer system. Its stationary random input process as characterized by the power spectrum P(/spl omega/) and the input rate steady state distribution f(x). The two functions represent second-order and steady-state input statistics. The authors use the superposition of heterogeneous 2-state Markov chains (MC) for construction of P(/spl omega/) and f(x). The resulting P(/spl omega/) is a monotone function of |/spl omega/|, and f(x) is the convolution of heterogeneous binomial functions. They show how to eliminate the state space explosion in input modeling. Unlike the existing modeling technique which matches the 2-state MC with each individual source, their 2-state MC are built to statistically match with functions P(/spl omega/) and f(x) of the aggregate input. The input state space is then reduced by many orders of magnitude. They examine the maximum throughput of a finite-buffer system to support P(/spl omega/) and f(x) subject to a desired average loss rate L. The numerical study explores a fundamental limit of buffer sizing to the maximum throughput improvement. A simple heuristic formula is developed, which tells quantitatively whether a given finite-buffer system operates in a so-called buffer-noneffective region. The new insight relating link capacity to low frequency input statistics explored in the paper is a fruitful starting point for further research.>

The authors explore a new concept of spectral characterization of wide-band input process in high speed networks. It helps them to localize wide-band sources in a subspace, especially in the low-frequency band, which has a dominant impact on queueing performance. They choose simple periodic-chains for the input rate process construction. Analogous to input functions in signal processing, they use elements of DC, sinusoidal, rectangular pulse, triangle pulse, and their superpositions, to represent various input correlation properties. The corresponding input power spectrum is defined in the discrete-frequency domain. In principle, a continuous spectral function of stationary random input process can be asymptotically approached by its discrete version as one sufficiently reduces the discrete-frequency intervals. An understanding of the queue response to the input spectrum will provide a great deal of knowledge to develop advanced network traffic measurement theory, and help to introduce effective network resource allocation policies. The new relation between queue length and input spectrum is a fruitful starting point for further research.>

Queueing performance in a richer, heterogeneous input environment is studied. A unique way to understand the effect of second- and higher-order input statistics on queues is offered, and new concepts of traffic measurement, network control, and resource allocation are developed for high-speed networks in the frequency domain. The technique applies to the analysis of queue response to the individual effects of input power spectrum, bispectrum, trispectrum, and input-rate steady-state distribution. The study provides clear evidence that of the four input statistics, the input power spectrum is most essential to queueing analysis. Furthermore, input power in the low-frequency band has a dominant impact on queueing performance, whereas high-frequency power to a large extent can be neglected.>

A new concept of spectral characterization of the wideband input process in high-speed networks is examined. The eigenstructure technique, through the modeling of input Markov chains, helps localize wideband sources in a subspace, especially in a low frequency band. Simple periodic chains are used for the construction of the input rate process. The input power spectral distribution is defined in a discrete frequency domain. Each input traffic stream is characterized by an independent Markov modulated Poisson process (MMPP). The underlying Markov chain is used to reflect the time autocorrelation properties of the input process at a macro level. Expressions are derived for correlation and power spectral functions of the MMPP input. A queuing analysis with multiple periodic input functions is described. The queue response to input correlation functions is examined. The advantages of using the spectral domain to analyze and design network control and resource management are discussed.>