In high-speed networks based on asynchronous transfer mode (ATM), variable bit rate (VBR) sources generate bursty cell streams which share the link bandwidth wherever multiplexing occurs. In theory, the bandwidth requirement per stream to support a given quality-of-service at a multiplexer should generally decrease as the number of streams increases. In practice, high statistical multiplexing gain is difficult to achieve because good traffic characterizations are usually not available. This paper proposes the use of peakedness-based measures to capture the statistical information from traffic streams needed to determine bandwidth allocations. The standard definition of peakedness applies only to point process models of traffic. Yet fluid models of traffic have certain advantages in terms of tractability. Hence, we introduce a new measure called modified peakedness, which encompasses point process and fluid models under a common framework. We develop some of its properties and specialize it to several common traffic models. Finally, we study the effectiveness of the peakedness/modified peakedness as burstiness measures for real-time traffic.

This paper studies the spectral properties of a class of stochastic sequences generated by basic TES (Transform-Expand-Sample) methods, as well as transformed TES sequences. A TES sequence is obtained as a marginally uniform process from an autoregressive scheme with modulo-1 reduction, followed by additional transformations. We derive formulas for the spectral density function and the spectral distribution function which are suitable for efficient numerical computation. A set of examples is calculated and exhibited for TES processes with uniform and exponential marginals. The results contribute to the understanding of TES sequences as models of autocorrelated sequences, particularly in a Monte Carlo simulation context. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

The sampling theorem is recognized as an interpolation formula. Starting from the Lagrange Polynomial, this theorem is developed under conditions which are of broader applicability than those usually stated. Such a view point indicates the essential unity of temporal and frequency domain application. It will also be shown that the theorem is applicable as an exact interpolation formula throughout the complex plane. The basic theorem is extended to include sampling of the first derivative of the function. The concept of band-limited functions is introduced through use of Fourier-Stieltjes representations. This is then shown to be subsumed under the general class of functions which is considered in connection with the interpolation theorems developed. This approach, as presented, readily leads to the establishment of many sampling theorems. It is hoped that this paper will aid the formulation of particularly applicable sampling theorems for specific problems.