A key problem for modern network designers is to characterize /model the "bursty" traffic arising in broadband networks with a view on predicting and guaranteeing performance. In this paper we attempt to unify several approaches ranging from histogram/interval based methods to "frequency domain" approaches by further investigating the asymptotic behavior of a multiplexer carrying a large number of streams. This analysis reveals the salient traffic /performance relationships which should guide us in selecting successful methods for traffic management and network dimensioning. 1 Introduction Efficient methods for congestion control in high-speed communication networks will be based on reasonable characterizations for traffic flows and time scale decompositions of the network dynamics. With a view on resolving the question of admission control, including bandwidth allocation and routing, as well as other traffic management activities, researchers have developed several approaches to mod...

Modern telecommunications networks are being designed to accomodate a heterogenous mix of traffic classes ranging from traditional telephone calls to video and data services. Thus, traffic models are of crucial importance to the engineering and performance analysis of telecommunications system, notably congestion and overload controls and capacity estimation. This chapter surveys teletraffic models, addressing both theoretical and computational aspects. It first surveys the main classes of teletraffic models commonly used in teletraffic modeling, and then proceeds to survey traffic methods for computing statistics relevant to the engineering a teletraffic network. 1 INTRODUCTION Traffic is the driving force of telecommunications systems, representing customers making phone calls, transferring data files and other electronic information, or more recently, transmitting compressed video frames to a display device. The most common modeling context is queueing; traffic is offered to a qu...

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At a buffered switch in an ATM (asynchronous transfer mode) network it is important to know what combinations of different types of traffic can be carried simultaneously without risking more than a very small probability of overflowing the buffer. We show that a simple and serviceable measure of effective bandwidths may be computed for stationary traffic sources. For large buffers the effective bandwidth of a source is a function only of its mean rate, index of dispersion and the size of the buffer. Keywords: communications, effective bandwidths, large deviations, stationary processes 1 Effective bandwidths The traffic in an ATM network is packaged in cells and carried over links between switches in the network. Traffic sources are bursty and so for periods of time cells may arrive at a switch faster than they can be switched to output links. For this reason, switches are buffered and the problem is to know how much total total traffic can be carried while keeping the probability of b...

Modern communication networks are able to respond to randomly uctuating demands and failures by allowing bu ers to ll, by rerouting tra c and by reallocating resources. They are able to do this so well that, in many respects, largescale networks appear as coherent, almost intelligent, organisms. The design and control of such networks present challenges of a mathematical, engineering and economic nature. In this lecture I describe some of the models that have proved useful in the analysis of stability, statistical sharing and pricing, in systems ranging from the telephone networks of today to the information superhighways of tomorrow.

The theory of large deviations provides a simple unified basis for statistical mechanics, information theory and queueing theory. The objective of this paper is to use large deviation theory and the Laplace method of integration to provide an simple intuitive overview of the recently developed theory of effective bandwidth for high speed digital networks, especially ATM networks. This includes (i) identification of the appropriate energy function, entropy function and effective bandwidth function of a source, (ii) the calculus of the effective bandwidth functions, (iii) bandwidth allocation and buffer management, (iv) traffic descriptors, and (v) envelope processes and conjugate processes for fast simulations and bounds.

Following our work described in Part I of this paper that modeled various correlation structures of Gaussian traffic in wavelet domain, we extend our previous models to heterogeneous network traffic with either a non-Gaussian distribution or a periodic structure. To include a non-Gaussian distribution, we first investigate what higher-order statistics are pertinent by exploring a relationship between time-scale analysis of wavelets and cumulative traffic. We then develop a novel algorithm in the wavelet domain to capture the important statistics. By utilizing local properties of wavelet basis in both space and time, we further extend such wavelet models to periodic MPEG traffic. As wavelets provide a natural fit to higher-order statistics as well as localized spatial and temporal dependence of periodic traffic at different time scales, the resulting wavelet models for both non-Gaussian and periodic traffic are simple and accurate with the lowest computational complexity attainable. 1 I...

In this paper, we study discrete-time priority queueing systems fed by a large number of arrival streams. We first provide bounds on the actual delay asymptote in terms of the virtual delay asymptote. Then, under suitable assumptions on the arrival process to the queue, we show that these asymptotes are the same. As an application of this result, we then consider a priority queueing system with two queues. Using the earlier result, we derive an upper bound on the tail probability of the delay. Under certain assumptions on the rate function of the arrival process, we show that the upper bound is tight. We then consider a system with Markovian arrivals and numerically evaluate the delay tail probability and validate these results with simulations.

We consider a single class, acyclic network of G/G/1 queues. We impose some mild assumptions on the service and external arrival processes and we characterize the large deviations behaviour of all the processes resulting from various operations in the network. For the network model that we are considering, these operations are passing-through-asingle -server-queue (the process resulting from this operation being the departure process), superposition of independent processes, and deterministic splitting of a process to a number of processes. We also characterize the large deviations behaviour of the waiting time and the queue length observed by a typical customer in a single server queue. We prove that the assumptions imposed on the external arrival processes are preserved by these operations, and we show how to inductively apply these results to obtain the large deviations behaviour of the waiting time and the queue length in all the queues of the network. Our results indicate how thes...

We consider the problem of Quality of Service (QoS) provisioning in modern highspeed, multimedia, communication networks. We quantify QoS by the probabilities of loss and excessive delay of an arbitrary packet, and introduce the model of a multiclass node (switch) which provides network access to users that may belong to multiple service classes. We treat such a node as a stochastic system which we analyze and control. In particular, we develop an analytical approach to estimate both the delay and the buffer overflow probability per service class, based on ideas from large deviations and optimal control. We exploit these performance analysis results by devising a call admission control algorithm which can provide per class QoS guarantees. We compare the proposed approach to alternative worst-case and effective bandwidth-based schemes and argue that it leads to increased efficiency. Finally, we discuss extensions to the network case in order to provide end-to-end QoS guarantees. Key w...