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40
The Importance of LongRange Dependence of VBR Video Traffic in ATM Traffic Engineering: Myths and Realities
 IN PROC. ACM SIGCOMM '96
, 1996
"... There has been a growing concern about the potential impact of longterm correlations (secondorder statistic) in variablebitrate (VBR) video traffic on ATM buffer dimensioning. Previous studies have shown that video traffic exhibits longrange dependence (LRD) (Hurst parameter large than 0.5). We ..."
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Cited by 116 (9 self)
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There has been a growing concern about the potential impact of longterm correlations (secondorder statistic) in variablebitrate (VBR) video traffic on ATM buffer dimensioning. Previous studies have shown that video traffic exhibits longrange dependence (LRD) (Hurst parameter large than 0.5). We investigate the practical implications of LRD in the context of realistic ATM traffic engineering by studying ATM multiplexers of VBR video sources over a range of desirable cell loss rates and buffer sizes (maximum delays). Using results based on large deviations theory, we introduce the notion of Critical Time Scale (CTS). For a given buffer size, link capacity, and the marginal distribution of frame size, the CTS of a VBR video source is defined as the number of frame correlations that contribute to the cell loss rate. In other words, secondorder behavior at the time scale beyond the CTS does not significantly affect the network performance. We show that whether the video source model i...
Distributed connection acceptance control for a connectionless network
, 1999
"... We describe how a packet network with a simple pricing mechanism and no connection acceptance control may be used to carry a telephonylike service with low packet loss and some call blocking. The packet network uses packet marking to indicate congestion and endsystems are charged a fixed small amou ..."
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Cited by 104 (1 self)
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We describe how a packet network with a simple pricing mechanism and no connection acceptance control may be used to carry a telephonylike service with low packet loss and some call blocking. The packet network uses packet marking to indicate congestion and endsystems are charged a fixed small amount per mark received. The endsystems are thus provided with the information and the incentive to use the packet network efficiently. We demonstrate that algorithms embedded in the endsystems are able to synthesize a telephonylike service by blocking calls at times when the load in the packet network is high. 1.
Point Process Approaches for Modeling and Analysis of SelfSimilar Traffic: Part II  Applications
, 1997
"... In previous work [24], Fractal Point Processes (FPPs) have been proposed as novel tools for understanding, modeling and analyzing diverse types of selfsimilar traffic behavior. We apply the FPP models in the context of network traffic modeling and performance analysis. Two qualitatively different f ..."
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Cited by 50 (8 self)
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In previous work [24], Fractal Point Processes (FPPs) have been proposed as novel tools for understanding, modeling and analyzing diverse types of selfsimilar traffic behavior. We apply the FPP models in the context of network traffic modeling and performance analysis. Two qualitatively different fractal data sets (Bellcore Ethernet traces) are characterized by FPP models. Comparison of modeldriven and tracedriven queueing simulation results show that the matched models yield close agreement with the traces over a wide range of system parameters. We also show that under suitable conditions, the FPP models yield Gaussian processes. Queueing simulation shows that the FPP models can be computationally efficient alternatives for generating fractional Gaussian noise processes. Finally, we divide fractal traffic into two types, applicationlevel fractal traffic and networklevel fractal traffic, and argue that each type has radically different implications for the design and control of fut...
A Poisson Limit for Buffer Overflow Probabilities
 in Proceedings of IEEE INFOCOM
, 2002
"... Abstract — A key criterion in the design of highspeed networks is the probability that the buffer content exceeds a given threshold. We consider Ò independent identical traffic sources modelled as point processes, which are fed into a link with speed proportional to Ò. Under fairly general assumpti ..."
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Cited by 39 (1 self)
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Abstract — A key criterion in the design of highspeed networks is the probability that the buffer content exceeds a given threshold. We consider Ò independent identical traffic sources modelled as point processes, which are fed into a link with speed proportional to Ò. Under fairly general assumptions on the input processes we show that the steady state probability of the buffer content exceeding a threshold � � tends to the corresponding probability assuming Poisson input processes. We verify the assumptions for a large class of longrange dependent sources commonly used to model data traffic. Our results show that with superposition, significant multiplexing gains can be achieved for even smaller buffers than suggested by previous results, which consider Ç Ò buffer size. Moreover, simulations show that for realistic values of the exceedance probability and moderate utilisations, convergence to the Poisson limit takes place at reasonable values of the number of sources superposed. This is particularly relevant for highspeed networks in which the cost of highspeed memory is significant. Keywords—Longrange dependence, overflow probability, Poisson limit, heavy tails, point processes, multiplexing.
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...
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...
Optimal Trajectory to Overflow in a Queue Fed By a Large Number of Sources
 Queueing Systems
, 1998
"... We analyse the deviant behavior of a queue fed by a large number of traffic streams. In particular, we explicitly give the most likely trajectory (or `optimal path') to buffer overflow, by applying large deviations techniques. This is done for a broad class of sources, consisting of Markov fluid sou ..."
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Cited by 16 (8 self)
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We analyse the deviant behavior of a queue fed by a large number of traffic streams. In particular, we explicitly give the most likely trajectory (or `optimal path') to buffer overflow, by applying large deviations techniques. This is done for a broad class of sources, consisting of Markov fluid sources and periodic sources. Apart from a number of ramifications of this result, we present guidelines for the numerical evaluation of the optimal path.
Multiplexing Regulated Traffic Streams: Design and Performance
, 2001
"... The main network solutions for supporting QoS rely on traffic policing (conditioning, shaping). In particular, for IP networks the IETF has developed Intserv (individual flows regulated) and Diffserv (only aggregates regulated). The regulator proposed could be based on the (dual) leakybucket mechan ..."
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Cited by 13 (0 self)
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The main network solutions for supporting QoS rely on traffic policing (conditioning, shaping). In particular, for IP networks the IETF has developed Intserv (individual flows regulated) and Diffserv (only aggregates regulated). The regulator proposed could be based on the (dual) leakybucket mechanism. This explains the interest in network element performance (loss, delay) for leakybucket regulated traffic. This paper describes a novel approach to the above problem. Explicitly using the correlation structure of the sources' traffic, we derive approximations for both small and large buffers. Importantly, for small (large) buffers the shortterm (longterm) correlations are dominant. The large buffer result decomposes the traffic stream in a stream of constant rate and a periodic impulse stream, allowing direct application of the Brownian bridge approximation. Combining the small and large buffer results by a concave majorization, we propose a simple, fast and accurate technique to statistically multiplex homogeneous regulated sources. To address heterogeneous inputs, we present similarly efficient techniques to evaluate the performance of multiple classes of traffic, each with distinct characteristics and QoS requirements. These techniques, applicable under more general conditions, are based on optimal resource (bandwidth and buffer) partitioning. They can also be directly applied to set GPS (Generalized Processor Sharing) weights and buffer thresholds in a shared resource system.
Simplification of Network Analysis in LargeBandwidth Systems
, 2003
"... In this paper, we show that significant simplicities can arise in the analysis of a network when link capacities are large enough to carry many flows. In particular, we prove that, when an upstream queue serves a large number of regulated traffic sources, the queuelength of the downstream queue con ..."
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Cited by 11 (0 self)
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In this paper, we show that significant simplicities can arise in the analysis of a network when link capacities are large enough to carry many flows. In particular, we prove that, when an upstream queue serves a large number of regulated traffic sources, the queuelength of the downstream queue converges almost surely to the queuelength of a simplified queueing system (single queue) obtained by removing the upstream queue. We provide similar results (convergence of the queuelength in distribution) for general (including nonregulated) traffic arrivals. In both cases, the convergence of the overflow probability is uniform and at least exponentially fast. Through an extensive numerical investigation, we demonstrate several aspects and implications of our results in simplifying network analysis.
Exact overflow asymptotics for queues with many Gaussian inputs
 J. Appl. Probab
, 2002
"... In this paper we consider a queue fed by a large number n of independent continuoustime Gaussian processes with stationary increments. After scaling the buffer exceedance threshold B and the (constant) service capacity C bythenumber of sources (i.e., B nb and C nc), we present asymptotically e ..."
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Cited by 9 (4 self)
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In this paper we consider a queue fed by a large number n of independent continuoustime Gaussian processes with stationary increments. After scaling the buffer exceedance threshold B and the (constant) service capacity C bythenumber of sources (i.e., B nb and C nc), we present asymptotically exact results for the probability that the buffer threshold is exceeded. We both consider the stationary overflow probability, and the (transient) probabilityofoverflow at a finite time horizon T . We give detailed results on the practically important cases in which the inputs are fractional Brownian motion processes or integrated Gaussian processes.