Benjamin Melamed

Traffic modeling for telecommunications networks

As new communications services evolve, professionals must create better models to predict system performance. The article provides an overview of computer simulation modelling for communication networks, as well as some important related modelling issues. It gives an overview of discrete event simulation and singles out two important modelling issues that are germane to extant and emerging networks: traffic modelling and rare event simulation. Monte Carlo computer simulation is used as a performance prediction tool and Markov models are considered.<<ETX>>

Perturbation analysis for online control and optimization of stochastic fluid models

Uses stochastic fluid models (SFMs) for control and optimization (rather than performance analysis) of communication networks, focusing on problems of buffer control. We derive gradient estimators for packet loss and workload related performance metrics with respect to threshold parameters. These estimators are shown to be unbiased and directly observable from a sample path without any knowledge of underlying stochastic characteristics, including traffic and processing rates (i.e., they are nonparametric). This renders them computable in online environments and easily implementable for network management and control. We further demonstrate their use in buffer control problems where our SFM-based estimators are evaluated based on data from an actual system.

Randomization Procedures in the Computation of Cumulative-Time Distributions over Discrete State Markov Processes

This paper proposes a methodology for computing numerical bounds on cumulative-time i.e., the time spent in a specified set of states before entering another specified set of states distributions over discrete state Markov processes. The methodology uses randomization procedures to compute results for appropriately defined transient Markov processes; the transient distribution computed is equivalent to the requisite cumulative-time distribution. A queueing application of the methodology to delay times in queueing networks is outlined and its efficacy is appraised by comparing the results with a sojourn time for a problem with a known distribution.

On arrivals that see time averages

We investigate when Arrivals See Time Averages ASTA in a stochastic model; i.e., when the stationary distribution of an embedded sequence, obtained by observing a continuous-time stochastic process just prior to the points arrivals of an associated point process, coincides with the stationary distribution of the observed process. We also characterize the relation between the two distributions when ASTA does not hold. We introduce a Lack of Bias Assumption LBA which stipulates that, at any time, the conditional intensity of the point process, given the present state of the observed process, be independent of the state of the observed process. We show that LBA, without the Poisson assumption, is necessary and sufficient for ASTA in a stationary process framework. Consequently, LBA covers known examples of non-Poisson ASTA, such as certain flows in open Jackson queueing networks, as well as the familiar Poisson case PASTA. We also establish results to cover the case in which the process is observed just after the points, e.g., when departures see time averages. Finally, we obtain a new proof of the Arrival Theorem for product-form queueing networks.

TES: A Class of Methods for Generating Autocorrelated Uniform Variates

This paper introduces a class of methods called TES (Transform-Expand-Sample) for generating autocorrelated variates with uniform marginals and Markovian structure. TES methods are readily implemented on a computer and have generation complexity comparable to that of the i.i.d. uniform sequence which they transform to an autocorrelated uniform sequence. For any prescribed correlation coefficient ρ, there is a TES method generating a uniform sequence with the 1-lag autocorrelation ρ, and the resultant autocorrelation is monotonic quadratic in two structural TES parameters. A simulation study reveals that TES methods give rise to autocorrelation functions with monotone decreasing as well as oscillating magnitude, bounded by monotone envelopes. The structural parameters were found to control the “amplitude” and “frequency” of the resultant autocorrelation function. A third parameter can be used to transform a TES sequence into more continuous-looking versions and to control the skewness of sample path cycles. INFORMS Journal on Computing , ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

Statistical multiplexing of VBR MPEG compressed video on ATM networks

A variable-bit-rate (VBR) MPEG video compression encoder is introduced, and the performance of a statistically multiplexed asynchronous transfer mode (ATM) network supporting a number of such VBR video sources is evaluated. Bit-rate characteristics obtained from a detailed simulation are provided for a VBR MPEG encoder for CCIR601 video (operating in the 5-10 Mb/s regime) appropriate for medium-quality multimedia or broadcasting applications. The results presented include bit-rate traces and signal-to-noise-ratio data for typical test sequences, along with summary statistics such as the marginal distribution of frame rate. Data from a study of statistical multiplexing on an ATM network are also given. Simulation results for an ATM statistical multiplexer with N>>1 VBR MPEG sources are presented in terms of key performance measures such as cell loss rate and delay versus throughput. The results confirm that ATM channel efficiencies of approximately 80-90% can be obtained at reasonable cell loss rate and delay levels.<<ETX>>

The transition and autocorrelation structure of tes processes

TES (Transform-Expand-Sample) is a versatile class of stochastic sequences which can capture arbitrary marginals and a wide variety of sample path behavior and autocorrelation functions. In TES, the initial variate is uniform on [0,1) and the next variate is obtained recursively by taking the fractional part (i.e., modulo-1 reduction) of a linear autoregressive scheme. We show how this class gives rise to uniform Markovian sequences in a general and natural way, by observing that marginal uniformity is closed under modulo-1 addition of an independent variate with arbitrary distribution. We derive the transition function of TES sequences and the autocovariance function of transformed TES sequences using Fourier and Laplace Transform methods. The autocovariance formulas are amenable to fast and accurate calculation and provide the theoretical basis for a computer-based methodology of heuristic TES modeling of empirical data. A companion paper contains various examples which show the efficacy of the TES appr...

An Overview of Tes Processes and Modeling Methodology

TES (Transform-Expand-Sample) is a versatile methodology for modeling stationary time series with general marginal distributions and a broad range of dependence structures. From the viewpoint of Monte Carlo simulation, TES constitutes a new and flexible input analysis approach whose principal merit is its potential ability to simultaneously capture first-order and second-order statistics of empirical time series. That is, TES is designed to fit an arbitrary empirical marginal distribution (histogram), and to simultaneously approximate the leading empirical autocorrelations. This paper is a tutorial introduction to the theory of TES processes and to the modeling methodology based on it. It employs a didactic approach which relies heavily on visual intuition as a means of conveying key ideas and an aid in building deep understanding of TES. This approach is in line with practical TES modeling which itself is based on visual interaction under software support. The interaction takes on the form of a heuristic search in a large parameter space, and it currently relies on visual feedback supplied by computer graphics. The tutorial is structured around an illustrative example both to clarify the modeling methodology and to exemplify its efficacy.

Online IPA Gradient Estimators in Stochastic Continuous Fluid Models

This paper applies infinitesimal perturbation analysis (IPA) to loss-related and workload-related metrics in a class of stochastic flow models (SFM). It derives closed-form formulas for the gradient estimators of these metrics with respect to various parameters of interest, such as buffer size, service rate, and inflow rate. The IPA estimators derived are simple and fast to compute, and are further shown to be unbiased and nonparametric, in the sense that they can be computed directly from the observed data without any knowledge of the underlying probability law. These properties hold out the promise of utilizing IPA gradient estimates as ingredients of online management and control of telecommunications networks. While this paper considers single-node SFMs, the analysis method developed is amenable to extensions to networks of SFM nodes with more general topologies.

Capturing human intelligence in the net

112 August 2000/Vol. 43, No. 8 COMMUNICATIONS OF THE ACM As a resource the Web is amazing and bewildering, and, at times, infuriating. All of us have, at one time or another, followed a seemingly endless loop, hopefully clicking one more time in a quest for some specific information. Many of us were also not the first person ever to be frustrated searching for that particular information. But the Web does not (yet) learn from other people’s mistakes. In that sense, we who use it are not even as clever as ants in the kitchen, who always leave chemical trails for their nestmates when they find something good to eat. Pursuing the ant metaphor, we imagine a user community operating in asynchronous collaboration mode, where information trails from user quests for information on the Internet are left behind for any community member to follow. The goal is to post and share communal knowledge: as community members engage in individual information quests, they make a small extra CapturingHUMAN INTELLIGENCE in the Net Paul B. Kantor, Endre Boros, Benjamin Melamed, Vladimir MeÑkov, Bracha Shapira, and David J. Neu