David M. Lucantoni

A Markov Modulated Characterization of Packetized Voice and Data Traffic and Related Statistical Multiplexer Performance

We study the performance of a statistical multiplexer whose inputs consist of a superposition of packetized voice sources and data. The performance analysis predicts voice packet delay distributions, which usually have a stringent requirement, as well as data packet delay distributions. The superposition is approximated by a correlated Markov modulated Poisson process (MMPP), which is chosen such that several of its statistical characteristics identically match those of the superposition. Matrix analytic methods are then used to evaluate system performance measures. In particular, we obtain moments of voice and data delay distributions and queue length distributions. We also obtain Laplace-Stieitjes transforms of the voice and data packet delay distributions, which are numerically inverted to evaluate tails of delay distributions. It is shown how the matrix analytic methodology can incorporate practical system considerations such as finite buffers and a class of overload control mechanisms discussed in the literature. Comparisons with simulation show the methods to be accurate. The numerical results for the tails of the voice packet delay distribution show the dramatic effect of traffic variability and correlations on performance.

New results on the single server queue with a batch markovian arrival process

The versatile Markovian point process was introduced by M. F. Neuts in 1979. This is a rich class of point processes whichcontains many familiar arrival process as very special cases. Recently, the Batch Markovian Arrival Process, a class of point processes which was subsequently shown to be equivalent to Neuts’ point process, has been studied using a more transparent notation. Recent results in the matrix-analytic approach to queueing theory have substantially reduced the computational complexity of the algorithmic solution of single server queues with a general Markovian arrival process. We generalize these results to the single server queue with the batch arrival process and emphasize the resulting simplifications. Algorithms for the special cases of the PH/G/l and MMPP/G/1 queues are highlighted as these models are receiving renewed attention in the literature and the new algorithms proposed here are simpler than existing ones. In particular, the PH/G/1 queue has additional structure which further enh...

Squeezing the Most Out of ATM

Although ATM seems to be the wave of the future, one analysis requires that the utilization of the network be quite low. That analysis is based on asymptotic decay rates of steady-state distributions used to develop a concept of effective bandwidths for connection admission control. The present authors have developed an exact numerical algorithm that shows that the effective-bandwidth approximation can overestimate the target small blocking probabilities by several orders of magnitude when there are many sources that are more bursty than Poisson. The bad news is that the appealing simple connection admission control algorithm using effective bandwidths based solely on tail-probability asymptotic decay rates may actually not be as effective as many have hoped. The good news is that the statistical multiplexing gain on ATM networks may actually be higher than some have feared. For one example, thought to be realistic, the analysis indicates that the network actually can support twice as many sources as predicted by the effective-bandwidth approximation. The authors also show that the effective bandwidth approximation is not always conservative. Specifically, for sources less bursty than Poisson, the asymptotic constant grows exponentially in the number of sources (when they are scaled as above) and the effective-bandwidth approximation can greatly underestimate the target blocking probabilities. Finally, they develop new approximations that work much better than the pure effective-bandwidth approximation.

The BMAP/G/1 QUEUE: A Tutorial

We present an overview of recent results related to the single server queue with general independent and identically distributed service times and a batch Markovian arrival process (BMAP). The BMAP encompasses a wide range of arrival processes and yet, mathematically, the BMAP/G/1 model is a relatively simple matrix generalization of the M/G/1 queue. Stationary and transient distributions for the queue length and waiting time distributions are presented. We discuss numerical algorithms for computing these quantities, which exploit both matrix analytic results and numerical transform inversion. Two-dimensional transform inversion is used for the transient results.

Methods for performance evaluation of VBR video traffic models

Models for predicting the performance of multiplexed variable bit rate video sources are important for engineering a network. However, models of a single source are also important for parameter negotiations and call admittance algorithms. In this paper we propose to model a single video source as a Markov renewal process whose states represent different bit rates. We also propose two novel goodness-of-fit metrics which are directly related to the specific performance aspects that we want to predict from the model. The first is a leaky bucket contour plot which can be used to quantify the burstiness of any traffic type. The second measure applies only to video traffic and measures how well the model can predict the compressed video quality. >

Meeting the challenge: congestion and flow control strategies for broadband information transport

Determining approaches to congestion and flow control, especially real-time components in an overall strategy, is recognized as one of the fundamental challenges facing broadband packet-based information transport, e.g. in the case of B-ISDN/ATM (broadband integrated services digital network/asynchronous transfer mode). Basic issues underlying this subject are summarized and a particular approach to achieving a broadband congestion-, flow-, and error control architecture, based on a core congestion-control strategy called bandwidth management, is described. The modular and layered nature of this control architecture is described and shown to lend itself to a structured approach to characterizing the control architecture performance.<<ETX>>

Modeling multiple IP traffic streams with rate limits

We start with the premise, and provide evidence that it is valid, that a Markov-modulated Poisson process (MMPP) is a good model for Internet traffic at the packet/byte level. We present an algorithm to estimate the parameters and size of a discrete MMPP (D-MMPP) from a data trace. This algorithm requires only two passes through the data. In tandem-network queueing models, the input to a downstream queue is the output from an upstream queue, so the arrival rate is limited by the rate of the upstream queue. We show how to modify the MMPP describing the arrivals to the upstream queue to approximate this effect. To extend this idea to networks that are not tandem, we show how to approximate the superposition of MMPPs without encountering the state-space explosion that occurs in exact computations.Numerical examples that demonstrate the accuracy of these methods are given. We also present a method to convert our estimated D-MMPP to a continuous-time MMPP, which is used as the arrival process in a matrix-analytic queueing model.

The transient BMAP/G/l queue

We derive the two-dimensional transforms of the transient workload and queue-length distributions in the single-server queue with general service times and a batch Markovian arrival process (BMAP). This arrival process includes the familiar phase-type renewal process and the Markov modulated Poisson process as special cases, as well as superpositions of these processes, and allows correlated interarrival times and batch sizes. Numerical results are obtained via two-dimensional transform inversion algorithms based on the Fourier-series method. From the numerical examples we see that predictions of system performance based on transient and stationary performance measures can be quite different

Bandwidth management: A congestion control strategy for broadband packet networks — characterizing the throughput-burstiness filter

Abstract A congestion/flow/error control architecture for broadband packet networks, based on a “core” network congestion control strategy called Bandwidth Management (BWM), is described. Associated with this control architecture is a set of traffic/performance analysis modules for quantitatively assessing the overall control performance. A particular module, that quantitatively characterizes a “throughput-burstiness filter” associated with BWM, is studied through an analytically tractable traffic model, and results of analysis of this model are used to illustrate the operation of the BWM controls.

Some steady-state distributions for the MAP /SM /1 queue

A detailed discussion of the stationary distributions of the classical descriptors of the MAP/SM/l queue with group arrivals is presented. As that model generalizes a large number of single server queueing models, the paper contains a unified mathematical treatment and generalization of many classical results