Results 1  10
of
28
Effective bandwidth of general markovian traffic sources and admission control of high speed networks
 IEEE/ACM Trans. Netw
, 1993
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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 220 (15 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.
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 143 (21 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.
Queue Response to Input Correlation Functions: Continuous Spectral Analysis
 IEEE/ACM Trans. Networking
, 1993
"... This paper, together with [1] and [2], opens a new window for the study of queueing performance in a richer, heterogeneous input environment. It offers a unique way to understand the effect of second and higherorder input statistics on queues, and develops new concepts of traffic measurement, netw ..."
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Cited by 126 (28 self)
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This paper, together with [1] and [2], opens a new window for the study of queueing performance in a richer, heterogeneous input environment. It offers a unique way to understand the effect of second and higherorder input statistics on queues, and develops new concepts of traffic measurement, network control and resource allocation for high speed networks in the frequency domain. The technique developed in this paper applies to the analysis of queue response to the individual effects of input power spectrum, bispectrum, trispectrum, and input rate steady state distribution. Our study provides clear evidence that of the four input statistics, the input power spectrum is most essential to queueing analysis. Furthermore, input power in the lowfrequency band has a dominant impact on queueing performance, whereas highfrequency power to a large extent can be neglected. The research reported here was supported by NSF under grant NCR9015757 and by Texas Advanced Research Program under gr...
Exponential approximations for tail probabilities in queues, I: waiting times
 Oper. Res
, 1995
"... In this paper, we focus on simple exponential approximations for steadystate tail probabilities in G/GI/1 queues based on largetime asymptotics. We relate the largetime asymptotics for the steadystate waiting time, sojourn time and workload. We evaluate the exponential approximations based on th ..."
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Cited by 50 (20 self)
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In this paper, we focus on simple exponential approximations for steadystate tail probabilities in G/GI/1 queues based on largetime asymptotics. We relate the largetime asymptotics for the steadystate waiting time, sojourn time and workload. We evaluate the exponential approximations based on the exact asymptotic parameters and their approximations by making comparisons with exact numerical results for BMAP/GI/1 queues. Numerical examples show that the exponential approximations are remarkably accurate at the 90 th percentile and beyond. Key words: queues; approximations; asymptotics; tail probabilities; sojourn time and workload.
Statistical Properties of a NearOptimal MeasurementBased CAC Algorithm
, 1997
"... Our algorithm, called Mosquito, allows sources to be ignorant of their statistics but offers nearoptimal utilisation of the network. Our approach is based on Large Deviation Theory: the large deviation ratefunction (entropy) of bursty ATM traffic can be estimated from measurements of traffic act ..."
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Cited by 18 (1 self)
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Our algorithm, called Mosquito, allows sources to be ignorant of their statistics but offers nearoptimal utilisation of the network. Our approach is based on Large Deviation Theory: the large deviation ratefunction (entropy) of bursty ATM traffic can be estimated from measurements of traffic activity. The entropy can be used to determine the bandwidth requirement of the traffic. In this paper, we explain the basic ideas behind the algorithm and describe its implementation. We present some results of a statistical investigation of the performance of the Mosquito CAC algorithm comparing it with that of various modifications of the algorithm.
On input state space reduction and buffer noneffective region
 in Proc. IEEE INFOCOM
, 1994
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Second Order Effect of Binary Sources on Characteristics of Queue and Loss Rate
 In Proc. IEEE In,f.com
, 1993
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Diffusion approximation modeling for Markov modulated bursty traffic and its applications to bandwidth allocation in ATM networks
 IEEE J. Sel. Areas Commun
, 1998
"... Abstract—We consider a statistical multiplexer model, in which each of K sources is a Markov modulated rate process (MMRP). This formulation allows a more general source model than the well studied “on–off ” source model in characterizing variable bit rate (VBR) sources such as compressed video. In ..."
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Cited by 10 (0 self)
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Abstract—We consider a statistical multiplexer model, in which each of K sources is a Markov modulated rate process (MMRP). This formulation allows a more general source model than the well studied “on–off ” source model in characterizing variable bit rate (VBR) sources such as compressed video. In our model we allow an arbitrary distribution for the duration of each of M states (or levels) that the source can take on. We formulate Markov modulated sources as a closed queueing network with M infiniteserver nodes. By extending our earlier results [17] we introduce an Mdimensional diffusion process to approximate the aggregate traffic of such Markov modulated sources. Under a set of reasonable assumptions we then show that this diffusion process can be expressed as an Mdimensional Ornstein–Uhlenbeck (O–U) process. The queueing behavior of buffer content is analyzed by applying a diffusion process approximation to the aggregate arrival process. We show some numerical examples which illustrate typical sample paths, and autocorrelation functions of the aggregate traffic and its diffusion process representation. Simulation results validate our proposed approximation model, showing good fits for distributions and autocorrelation functions of the aggregate rate process and the asymptotic queueing behaviors. We also discuss how the analytical formulas derived from the diffusion approximation can be applied to compute equivalent bandwidth for realtime call admission controls, and how the model can be modified to characterize traffic sources with longrange dependence. I.
Analysis of a Correlated Queue in a Communication System
 IN PROC. INFOCOM'93
, 1993
"... In this paper we study a family of queues where the service time B n of customer n depends on the interarrival time I n between customers n \Gamma 1 and n. In particular, we focus on dependencies that arise naturally in the context of communication systems, where the finite speed of the communicatio ..."
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Cited by 8 (2 self)
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In this paper we study a family of queues where the service time B n of customer n depends on the interarrival time I n between customers n \Gamma 1 and n. In particular, we focus on dependencies that arise naturally in the context of communication systems, where the finite speed of the communication links constrains the amount of data that can be received in a given time interval. Specifically, we study queues where the random variables I n and B n exhibit some form of proportionality relation. Such dependencies can have significant impact on system performance and it is, therefore, critical to develop tractable models that account for them. The paper starts with the simple case of a deterministic proportionality relation between the service time of a customer and its preceding interarrival time. This is then extended to allow for the addition of an independent, generally distributed overhead to the service time of each customer. Next, we consider several models that capture the ONO...