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84
Effective Bandwidths for Multiclass Markov Fluids and Other ATM Sources
, 1993
"... We show the existence of effective bandwidths for multiclass Markov fluids and other types of sources that are used to model ATM traffic. More precisely,we show that when such sources share a buffer with deterministic service rate, a constraint on the tail of the buffer occupancy distribution is a l ..."
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Cited by 187 (14 self)
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We show the existence of effective bandwidths for multiclass Markov fluids and other types of sources that are used to model ATM traffic. More precisely,we show that when such sources share a buffer with deterministic service rate, a constraint on the tail of the buffer occupancy distribution is a linear constraint on the number of sources. That is, for a small loss probability one can assume that each source transmits at a fixed rate called its effective bandwidth. When traffic parameters are known, effective bandwidths can be calculated and may be used to obtain a circuitswitched style call acceptance and routing algorithm for ATM networks. The important feature of the effective bandwidth of a source is that it is a characteristic of that source and the acceptable loss probability only.Thus, the effective bandwidth of a source does not depend on the number of sources sharing the buffer nor on the model parameters of other types of sources sharing the buffer.
Stability, queue length and delay of deterministic and stochastic queueing networks
 IEEE Transactions on Automatic Control
, 1994
"... Motivated by recent development in high speed networks, in this paper we study two types of stability problems: (i) conditions for queueing networks that render bounded queue lengths and bounded delay for customers, and (ii) conditions for queueing networks in which the queue length distribution of ..."
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Cited by 171 (20 self)
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Motivated by recent development in high speed networks, in this paper we study two types of stability problems: (i) conditions for queueing networks that render bounded queue lengths and bounded delay for customers, and (ii) conditions for queueing networks in which the queue length distribution of a queue has an exponential tail with rate `. To answer these two types of stability problems, we introduce two new notions of traffic characterization: minimum envelope rate (MER) and minimum envelope rate with respect to `. Based on these two new notions of traffic characterization, we develop a set of rules for network operations such as superposition, inputoutput relation of a single queue, and routing. Specifically, we show that (i) the MER of a superposition process is less than or equal to the sum of the MER of each process, (ii) a queue is stable in the sense of bounded queue length if the MER of the input traffic is smaller than the capacity, (iii) the MER of a departure process from a stable queue is less than or equal to that of the input process (iv) the MER of a routed process from a departure process is less than or equal to the MER of the departure process multiplied by the MER of the routing process. Similar results hold for MER with respect to ` under a further assumption of independence. These rules provide a natural way to analyze feedforward networks with multiple classes of customers. For single class networks with nonfeedforward routing, we provide a new method to show that similar stability results hold for such networks under the FCFS policy. Moreover, when restricting to the family of twostate Markov modulated arrival processes, the notion of MER with respect to ` is shown to be
A new approach for allocating buffers and bandwidth to heterogeneous, regulated traffic in an ATM node
 IEEE Journal on Selected Areas in Communications
, 1995
"... AbstractA new approach to determining the admissibility of variable bit rate (VBR) traffic in buffered digital networks is developed. In this approach all traffic presented to the network is assumed to have been subjected to leakybucket regulation, and extremal, periodic, onoff regulated traffic ..."
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Cited by 150 (9 self)
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AbstractA new approach to determining the admissibility of variable bit rate (VBR) traffic in buffered digital networks is developed. In this approach all traffic presented to the network is assumed to have been subjected to leakybucket regulation, and extremal, periodic, onoff regulated traffic is considered; the analysis is based on fluid models. Each regulated traffic stream is allocated bandwidth and buffer resources which are independent of other traffic. Bandwidth and buffer allocations are traded off in a manner optimal for an adversarial situation involving minimal knowledge of other traffic. This leads to a singleresource statisticalmultiplexing problem which is solved using techniques previously used for unbuffered traffic. VBR traffic is found to be divisible into two classes, one for which statistical multiplexing is effective and one for which statistical multiplexing is ineffective in the sense that accepting small losses provides no advantage over requiring lossless performance. The boundary of the set of admissible traffic sources is examined, and is found to be sufficiently linear that an effective bandwidth can be meaningfully assigned to each VBR source, so long as only statisticallymultiplexable sources are considered, or only nonstatisticallymultiplexable sources are considered. If these two types of sources are intermixed, then nonlinear interactions occur and fewer sources can be admitted than a linear theory would predict. A qualitative characterization of the nonlinearities is presented. The complete analysis involves conservative approximations; however, admission decisions based on this work are expected to be less overly conservative than decisions based on alternative approaches. I.
Logarithmic Asymptotics For SteadyState Tail Probabilities In A SingleServer Queue
, 1993
"... We consider the standard singleserver queue with unlimited waiting space and the firstin firstout service discipline, but without any explicit independence conditions on the interarrival and service times. We find conditions for the steadystate waitingtime distribution to have smalltail asympt ..."
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Cited by 150 (14 self)
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We consider the standard singleserver queue with unlimited waiting space and the firstin firstout service discipline, but without any explicit independence conditions on the interarrival and service times. We find conditions for the steadystate waitingtime distribution to have smalltail asymptotics of the form x  1 logP(W > x)  q * as x for q * > 0. We require only stationarity of the basic sequence of service times minus interarrival times and a Ga .. rtnerEllis condition for the cumulant generating function of the associated partial sums, i.e., n  1 log Ee qS n y(q) as n , plus regularity conditions on the decay rate function y. The asymptotic decay rate q * is the root of the equation y(q) = 0. This result in turn implies a corresponding asymptotic result for the steadystate workload in a queue with general nondecreasing input. This asymptotic result covers the case of multiple independent sources, so that it provides additional theoretical support for a concept of effective bandwidths for admission control in multiclass queues based on asymptotic decay rates.
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.
Fundamental Bounds and Approximations for ATM Multiplexers with Applications to Video Teleconferencing
, 1995
"... The main contributions of this paper are twofold. First, we prove fundamental, similarly behaving lower and upper bounds, and give an approximation based on the bounds, which is effective for analyzing ATM multiplexers, even when the traffic has many, possibly heterogeneous, sources and their model ..."
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Cited by 105 (12 self)
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The main contributions of this paper are twofold. First, we prove fundamental, similarly behaving lower and upper bounds, and give an approximation based on the bounds, which is effective for analyzing ATM multiplexers, even when the traffic has many, possibly heterogeneous, sources and their models are of high dimension. Second, we apply our analytic approximation to statistical models of video teleconference traffic, obtain the multiplexing system's capacity as determined by the number of admissible sources for given cell loss probability, buffer size and trunk bandwidth, and, finally, compare with results from simulations, which are driven by actual data from coders. The results are surprisingly close. Our bounds are based on Large Deviations theory. The main assumption is that the sources are Markovian and timereversible. Our approximation to the steady state buffer distribution is called "ChernoffDominant Eigenvalue" since one parameter is obtained from Chernoff's theorem and t...
A New Approach to Service Provisioning in ATM Networks
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1993
"... We formulate and solve a problem of allocating resources among competing services differentiated by user traffic characteristics and maximum endtoend delay. The solution leads to an alternative approach to service provisioning in an ATM network, in which the network offers directly for rent its ba ..."
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Cited by 78 (8 self)
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We formulate and solve a problem of allocating resources among competing services differentiated by user traffic characteristics and maximum endtoend delay. The solution leads to an alternative approach to service provisioning in an ATM network, in which the network offers directly for rent its bandwidth and buffers and users purchase freely resources to meet their desired quality. Users make their decisions based on their own traffic parameters and delay requirements and the network sets prices for those resources. The procedure is iterative in that the network periodically adjusts prices based on monitored user demand, and is decentralized in that only local information is needed for individual users to determine resource requests. We derive network's adjustment scheme and users' decision rule and establish their optimality. Since our approach does not require the network to know user traffic and delay parameters, it does not require traffic policing on the part of the network.
Squeezing The Most Out Of ATM
, 1996
"... 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), moderatesize buffers and highly bursty traffic will require that the utilization of the network be ..."
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Cited by 72 (10 self)
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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), moderatesize 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 steadystate 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 effectivebandwidth 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 connectionadmissioncontrol 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 effectivebandwidth approximation is not always conservative. Specifically, for sources less bursty than Poisson, the asymptotic constant grows exponentially in the numbe...
Qualityofservice in packet networks: Basic mechanisms and directions
 COMPUTER NETWORKS
, 1999
"... In this paper, we review the basic mechanisms used in packet networks to support QualityofService QoS guarantees. We outline the various approaches that have been proposed, and discuss some of the tradeoffs they involve. Specifically, the paper starts by introducing the different scheduling and ..."
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Cited by 68 (4 self)
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In this paper, we review the basic mechanisms used in packet networks to support QualityofService QoS guarantees. We outline the various approaches that have been proposed, and discuss some of the tradeoffs they involve. Specifically, the paper starts by introducing the different scheduling and buffer management mechanisms that can be used to provide service differentiation in packet networks. The aim is not to provide an exhaustive review of existing mechanisms, but instead to give the reader a perspective on the range of options available and the associated tradeoff between performance, functionality, and complexity. This is then followed by a discussion on the use of such mechanisms to provide specific endtoend performance guarantees. The emphasis of this second part is on the need for adapting mechanisms to the different environments where they are to be deployed. In particular, fine grain buffer management and scheduling mechanisms may be neither necessary nor cost effective in high speed backbones, where "aggregate" solutions are more appropriate. The paper discusses issues and possible approaches to allow coexistence of different mechanisms in delivering endtoend guarantees.
Call Admission Control Schemes: A Review
"... Over the last few years, a substantial number of call admission control (CAC) schemes have been proposed for ATM networks. In this article, we review the salient features of some of these algorithms. Also, we quantitatively compare the performance of three of these schemes. ..."
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Cited by 62 (1 self)
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Over the last few years, a substantial number of call admission control (CAC) schemes have been proposed for ATM networks. In this article, we review the salient features of some of these algorithms. Also, we quantitatively compare the performance of three of these schemes.