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Notes on Effective Bandwidths
, 1996
"... 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 unde ..."
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Cited by 132 (4 self)
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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.
Large Deviations, the Shape of the Loss Curve, and Economies of Scale in Large Multiplexers
, 1995
"... We analyse the queue Q L at a multiplexer with L inputs. We obtain a large deviation result, namely that 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 ..."
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Cited by 114 (11 self)
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We analyse the queue Q L at a multiplexer with L inputs. We obtain a large deviation result, namely that 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. This provides an improvement on the usual effective bandwidth approximation P[Q L ? b] e \Gammaffib , replacing it with P[Q L ? b] e \GammaLI(b=L) . The difference I(b) \Gamma ffi b determines the economies of scale which are to be obtained in large multiplexers. If the limit = \Gamma lim t!1 t t (ffi) exists (here t is the finite time cumulant of the workload process) then lim b!1 (I(b) \Gamma ffi b) = . We apply this idea to a number of examples of arrivals processes: heterogeneous superpositions, Gaussian processes, Markovian additive processes and Poisson processes. We obtain expressions for in these cases. is zero for independent arrivals, but positive for arrivals with positive correlations. Thus economies of scale are obtainable for highly bursty traffic expected in ATM multiplexing.
Effective bandwidths: call admission, traffic policing, and filtering for atm networks, Queueing Systems 20
, 1995
"... In this paper we review and extend the e ective bandwidth results of Kelly [28], and Kesidis, Walrand and Chang [29, 6]. These results provide a framework for call admission schemes which are sensitive to constraints on the mean delay or the tail distribution of the workload in bu ered queues. We pr ..."
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Cited by 61 (8 self)
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In this paper we review and extend the e ective bandwidth results of Kelly [28], and Kesidis, Walrand and Chang [29, 6]. These results provide a framework for call admission schemes which are sensitive to constraints on the mean delay or the tail distribution of the workload in bu ered queues. We present results which are valid for a wide variety of tra c streams and discuss their applicability for tra c management inATM networks. We discuss the impact of tra c policing schemes, such as thresholding and ltering, on the e ective bandwidth of sources. Finally we discuss e ective bandwidth results for Brownian tra c models for which explicit results reveal the interaction arising in nite bu ers. Short title: E ective Bandwidths
Resource Management in WideArea ATM Networks using Effective Bandwidths
 IEEE J. SELECT. AREAS COMMUN
, 1995
"... This paper is principally concerned with resource allocation for connections tolerating statistical qualityof service (QoS) guarantees in a public widearea ATM network. Our aim is to sketch a framework, based on effective bandwidths, for call admission schemes that are sensitivetoindividual QoS r ..."
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Cited by 60 (3 self)
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This paper is principally concerned with resource allocation for connections tolerating statistical qualityof service (QoS) guarantees in a public widearea ATM network. Our aim is to sketch a framework, based on effective bandwidths, for call admission schemes that are sensitivetoindividual QoS requirements and account for statistical multiplexing. We begin by describing recent results approximating the effective bandwidth required by heterogeneous streams sharing buffered links, including results for the packetized generalized processor sharing service discipline. Extensions to networks follow via the concept of decoupling bandwidths  motivated by a study of the inputoutput properties of queues. Based on these results we claim that networks with sufficient routing diversity will inherently satisfy nodal decoupling. We then discuss online methods for estimating the effective bandwidth of a connection. Using this type of traffic monitoring we propose an approach to usage parameter ...
Analysis, Approximations and Admission Control of a MultiService Multiplexing System with Priorities
 In Proc. IEEE INFOCOM '95
, 1995
"... We consider an ATM system with an architecture which is designed to accommodate users with very different quality of service requirements. In the base case with only two services, sources which require low loss belong to a High Priority class, and share a FCFS buffer, which has priority access to th ..."
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Cited by 53 (3 self)
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We consider an ATM system with an architecture which is designed to accommodate users with very different quality of service requirements. In the base case with only two services, sources which require low loss belong to a High Priority class, and share a FCFS buffer, which has priority access to the trunk. A Low Priority class of sources with typically less stringent requirements on loss have a separate FCFS buffer, which receives the timevarying, residual bandwidth, if any, of the trunk. By administering admission control and restricting the combination of sources to an admissible set, the service guarantees for both classes may be satisfied. The sources are bursty and stochastic fluid models are used to handle burstscale congestion effects. Our contributions are: (i) we develop simple, fast and robust analytic approximations for the queue distributions in the two buffers; (ii) for admission control, we calculate the admissible set by using our analytic approximations and find that...
Entropy Of ATM Traffic Streams: A Tool For Estimating QoS Parameters
, 1995
"... this paper, we are concerned with the components of cellloss and celldelay which are attributable to a single buffer of finite size. The QoS parameters we are concerned with are: ..."
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Cited by 37 (5 self)
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this paper, we are concerned with the components of cellloss and celldelay which are attributable to a single buffer of finite size. The QoS parameters we are concerned with are:
The Output of a Switch, Or, Effective Bandwidths for Networks
 Queueing Systems
, 1999
"... Consider a switch which queues traffic from many independent input flows. We show that in the large deviations limiting regime in which the number of inputs increases and the service rate and buffer size are increased in proportion, the statistical characteristics of a flow are essentially uncha ..."
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Cited by 35 (2 self)
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Consider a switch which queues traffic from many independent input flows. We show that in the large deviations limiting regime in which the number of inputs increases and the service rate and buffer size are increased in proportion, the statistical characteristics of a flow are essentially unchanged by passage through the switch. This significantly simplifies the analysis of networks of switches. It means that each traffic flow in a network can be assigned an effective bandwidth, independent of the other flows, and the behaviour of any switch in the network depends only on the effective bandwidths of the flows using it. Keywords. Effective bandwidths, feedforward networks, large deviations, decoupling bandwidths, output of a switch, many sources. 1 Introduction A switch is a device that routes traffic. A switch has several input flows of traffic, each of which is routed to a specified destination; and inside the switch, work from all of the inputs is queued together. Switch...
Large Deviations and the Generalized Processor Sharing Scheduling: Upper and Lower Bounds  Part I: TwoQueue Systems
 Queueing Systems
, 1995
"... We prove asymptotic upper and lower bounds on the asymptotic decay rate of persession queue length tail distributions for a single constant service rate server queue shared by multiple sessions with the generalized processor sharing (GPS) scheduling discipline. The simpler case of a GPS system with ..."
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Cited by 31 (1 self)
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We prove asymptotic upper and lower bounds on the asymptotic decay rate of persession queue length tail distributions for a single constant service rate server queue shared by multiple sessions with the generalized processor sharing (GPS) scheduling discipline. The simpler case of a GPS system with only two queues needs special attention, as under this case, it is shown that the upper bounds and lower bounds match, thus yielding exact bounds. This result is established in this part (Part I) of the paper. The general case is much more complicated, and is treated separately in Part II of the paper [42], where tight upper and lower bound results are proved by examining the dynamics of bandwidth sharing nature of GPS scheduling. The proofs use samplepath large deviation principle and are based on some recent large deviation results for a single queue with a constant service rate server. These results have implications in call admission control for highspeed communication networks. 1 Int...
Stochastic Modeling Of Traffic Processes
 Frontiers in Queueing: Models, Methods and Problems
, 1996
"... 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, nota ..."
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Cited by 30 (0 self)
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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...
On the Relevance of Time Scales in Performance Oriented Traffic Characterizations
 In Proc. IEEE INFOCOM
, 1996
"... 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" app ..."
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Cited by 28 (2 self)
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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 highspeed 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...