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A centrallimittheorembased approach for analyzing queue behavior in highspeed networks
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1998
"... In this paper, we study P(Q > x), the tail of the steadystate queue length distribution at a highspeed multiplexer. In particular, we focus on the case when the aggregate traffic to the multiplexer can be characterized by a stationary Gaussian process. We provide two asymptotic upper bounds for ..."
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In this paper, we study P(Q > x), the tail of the steadystate queue length distribution at a highspeed multiplexer. In particular, we focus on the case when the aggregate traffic to the multiplexer can be characterized by a stationary Gaussian process. We provide two asymptotic upper bounds for the tail probability and an asymptotic result that emphasizes the importance of the dominant time scale and the maximum variance. One of our bounds is in a singleexponential form and can be used to calculate an upper bound to the asymptotic constant. However, we show that this bound, being of a singleexponential form, may not accurately capture the tail probability. Our asymptotic result on the importance of the maximum variance and our extensive numerical study on a known lower bound motivate the development of our second asymptotic upper bound. This bound is expressed in terms of the maximum variance of a Gaussian process, and enables the accurate estimation of the tail probability over a wide range of queue lengths. We apply our results to Gaussian as well as multiplexed nonGaussian input sources, and validate their performance via simulations. Wherever possible, we have conducted our simulation study using importance sampling in order to improve its reliability and to effectively capture rare events. Our analytical study is based on extreme value theory, and therefore different from the approaches using traditional Markovian and Large Deviations techniques.
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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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 birthdeath fluid queues
, 1996
"... Abstract We present a survey of techniques for analysing the performance of a reservoir which receives and releases fluid at rates which are determined by the state of a background birthdeath process. The reservoir is assumed to be in nitely large, but the state space of the modulating birthdeath ..."
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Abstract We present a survey of techniques for analysing the performance of a reservoir which receives and releases fluid at rates which are determined by the state of a background birthdeath process. The reservoir is assumed to be in nitely large, but the state space of the modulating birthdeath process may be nite or innite.
A diffusion approximation analysis of an ATM statistical multiplexer with multiple types of traffic, Part I: Equilibrium state solutions
 in Proc. 1993 IEEE International Conference on Communications
, 1993
"... We introduce a multidimensional diffusion model to characterize the "onoff " sources behavior in an ATM statistical multiplexer, where multiple types of traffic are concentrated. Under a reasonable set of assumptions, this diffusion process can then be approximated by a multidimensiona ..."
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Cited by 5 (1 self)
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We introduce a multidimensional diffusion model to characterize the "onoff " sources behavior in an ATM statistical multiplexer, where multiple types of traffic are concentrated. Under a reasonable set of assumptions, this diffusion process can then be approximated by a multidimensional OrnsteinUhlenbeck process, which is a Gaussian Markov process. The packet arrival process is shown to be a Gaussian (but not Markov) process, and this process determines the statistical behavior of the buffer content. We then derive an expression for the joint probability distribution of the buffer content and "onoff " sources in the equilibrium state. The final solution form is given in terms of the eigenfunctions of Weber's equation. Some numerical case is compared with the solution method developed by Kosten [1984]. In a companion paper (Ren and Kobayashi [1992b]), we shall derive the timedependent solution of the diffusion approximation model. 1
INVESTIGATION OF DELAY JITTER OF HETEROGENEOUS TRAFFIC IN BROADBAND NETWORKS
, 2006
"... There is a great demand for wired and wireless network architectures to support a variety of applications with very high speed communication. Nowadays, the pace of our business and social lives has created a great demand for not only instant transferring and accessing various kinds of data by a clic ..."
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There is a great demand for wired and wireless network architectures to support a variety of applications with very high speed communication. Nowadays, the pace of our business and social lives has created a great demand for not only instant transferring and accessing various kinds of data by a click on the mouse (i.e. digitized voice and video, file transfers, ecommerce, transactions, email, telnet, web browsing and multicast), but also for reliable and better quality of Internet service. As a result, quality of service (QoS) currently becomes an issue of concern for wide area network (WAN) telecommunications providers or backbone carriers. For instance, what is the required bandwidth for the local area network (LAN) or wide area network (WAN) to provide sufficient capacity for video transferring with desired minimum level jitter? A critical challenge for both wired and wireless networking vendors and carrier companies is to be able to accurately estimate the quality of service (QoS) that will be provided based on the network architecture, router/switch topology, and protocol applied. The variation in QoS performance based on the priority assignment is of significant importance, due to the fact that the differentiated services (DiffServ) capable networks
©2008 INFORMS ResourceSharing Queueing Systems with FluidFlow Traffic
"... doi 10.1287/opre.1070.0483 ..."
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Advances in Applied Probability (March 1999) ON THE SUPREMUM DISTRIBUTION OF INTEGRATED STATIONARY GAUS SIAN PROCESSES WITH NEGATIVE LINEAR DRIFT
"... In this paper we study the supremum distribution of a class of Gaussian processes having stationary increments and negative drift using key results from Extreme Value Theory. We focus on deriving an asymptotic upper bound to the tail of the supremum distribution of such processes. Our bound is valid ..."
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In this paper we study the supremum distribution of a class of Gaussian processes having stationary increments and negative drift using key results from Extreme Value Theory. We focus on deriving an asymptotic upper bound to the tail of the supremum distribution of such processes. Our bound is valid for both discrete and continuoustime processes. We discuss the importance of the bound, its applicability to queueing problems, and show numerical examples to illustrate
On the Suprema Distribution of Gaussian Processes with Stationary Increment and Drift
, 1997
"... This document has been made available through Purdue ePubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for additional information. ..."
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This document has been made available through Purdue ePubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for additional information.