This paper presents a personal view of work to date on effective bandwidths, emphasising the unifying role of the concept: as a summary of the statistical characteristics of sources over different time and space scales; in bounds, limits and approximations for various models of multiplexing under quality of service constraints; and as the basis for simple and robust tariffing and connection acceptance control mechanisms for poorly characterized traffic. The framework assumes only stationarity of sources, and illustrative examples include periodic streams, fractional Brownian input, policed and shaped sources, and deterministic multiplexing.

Information theory has not yet had a direct impact on networking, although there are similarities in concepts and methodologies that have consistently attracted the attention of researchers from both fields. In this paper, we review several topics that are related to communication networks and that have an information theoretic flavor, including multiaccess protocols, timing channels, effective bandwidth of bursty data sources, deterministic constraints on datastreams, queueing theory, and switching networks. Keywords--- Communication networks, multiaccess, effective bandwidth, switching I. INTRODUCTION Information theory is the conscience of the theory of communication; it has defined the "playing field" within which communication systems can be studied and understood. It has provided the spawning grounds for the fields of coding, compression, encryption, detection, and modulation and it has enabled the design and evaluation of systems whose performance is pushing the limits of wha...

This paper describes a framework for admission control for a packet-based network where the decisions are taken by edge devices or end-systems, rather than resources within the network. The decisions are based on the results of probe packets that the end-systems send through the network, and require only that resources apply a mark to packets in a way that is load dependent. One application example is the Internet, where marking information is fed back via an ECN bit, and we show howthis approach allows a rich QoS framework for ows or streams. Our approach allows networks to be explicitly analysed, and consequently engineered.

... In this paper we continue the development of a modelling approach which attempts to integrate these several time-scales, and illustrate its application to the analysis of a family of simple and robust measurement-based admission controls. A subsidiary aim of the paper is to shed light on the relationship between the admission control proposed for ATM networks by Gibbens et al [9] and that proposed for controlled-load Internet services by Floyd [7]. We shall see that their common origin in Chernoff bounds allows the definition of a simple and general family of admission controls, capable of tailoring for several implementation scenarios.

Even though ATM seems to be clearly the wave of the future, one performance analysis indicates that the combination of stringent performance requirements (e.g., 10 - 9 cell blocking probabilities), moderate-size buffers and highly bursty traffic will require that the utilization of the network be quite low. That performance analysis is based on asymptotic decay rates of steady-state distributions used to develop a concept of effective bandwidths for connection admission control. However, we 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-admissioncontrol algorithm using effective bandwidths based solely on tailprobability 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, our analysis indicates that the network actually can support twice as many sources as predicted by the effectivebandwidth approximation. That discrepancy occurs because for a large number of bursty sources the asymptotic constant in the tail probability exponential asymptote is extremely small. That in turn can be explained by the observation that the asymptotic constant decays exponentially in the number of sources when the sources are scaled to keep the total arrival rate fixed. We 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 numbe...

Statistical sharing over several time-scales is a key feature of the Internet, and is likely to be an essential aspect of future ATM networks.

We analyse the queue Q L at a multiplexer with L sources which may display long-range dependence. This includes, for example, sources modelled by fractional Brownian Motion (fBM). The workload processes W due to each source are assumed to have large deviation properties of the form P [W t =a(t) ? x] ß e \Gammav(t)K(x) for appropriate scaling functions a and v, and ratefunction K. Under very general conditions, lim L!1 L \Gamma1 log P [Q L ? Lb] = \GammaI (b) provided the offered load is held constant, where the shape function I is expressed in terms of the cumulant generating functions of the input traffic. For power-law scalings v(t) = t v , a(t) = t a (such as occur in fBM) we analyse the asymptotics of the shape function: lim b!1 b \Gammau=a i I(b) \Gamma ffi b v=a j = u for some exponent u and constant depending on the sources. This demonstrates the economies of scale available through the multiplexing of a large number of such sources, by comparison with ...

This paper describes methods of computing usage charges from simple measurements and relating these to bounds on the effective bandwidth. Thus we show that charging for usage on the basis of effective bandwidths can be well-approximated by charges based on simple measurements. Charging and pricing are essential requirements in the operation of a communication network. They are needed not only to recover costs and make a profit. Even if a generous operator is willing to offer a network for free, there are still compelling reasons to charges for services in order to exercise control. The congestion that has plagued the Internet because it lacks any mechanism for charging and pricing highlights the fact that without charges it is difficult to control congestion or divide network resources amongst users in a workable and stable way. Subject classifications: Communications: measurement-based charging. Of course there are many considerations that influence the prices at which an operator will choose to sell network services. Marketing and regulation are certainly important, but these considerations are not unique to the operation of a communications network. Special considerations do, however, arise from the fact that a broadband communications network is intended simultaneously to carry a wide variety of traffic types. Our conception of a broadband network is that of a collection of resources (links, buffers, switches, etc.) which can be used to provide a wide variety of communications services. These services are distinguished by traffic contracts, which specify parameters to which the traffic must adhere (a maximum peak rate, for example), and the quality of service which the network undertakes to guarantee (typically, cell loss or delay). These concepts are accepted as ...

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