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60
A Benchmark for PH Estimation Algorithms: Results for AcyclicPH
, 1994
"... Distribution functions that can be expressed as exponential polynomials have useful computational properties in applied stochastic modeling and have gained widespread acceptance in recent years. Nevertheless, the implementation of ecient numerical procedures for estimating the distribution parameter ..."
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Cited by 25 (14 self)
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Distribution functions that can be expressed as exponential polynomials have useful computational properties in applied stochastic modeling and have gained widespread acceptance in recent years. Nevertheless, the implementation of ecient numerical procedures for estimating the distribution parameters remains an open problem that limits the use of this class of distributions in applications. The diculty of the tting problem is largely related to the nonlinearity of the model and to the number of the parameters to be estimated. Many attempts have been presented in the literature. However, the lack of accepted and standardized test examples makes it dicult to establish a comparative merit among the various approaches. This paper proposes a benchmark based on the workshop on Fitting phase type distributions, organized by S. Asmussen in February 1991. It also presents the results obtained by applying the Maximum Likelihood (ML) estimation procedure to the canonical representation of Acyc...
Modeling and Analysis of PowerTail Distributions via Classical Teletraffic Methods
, 2000
"... e of exponentials The research was performed while this author was a Ph.D student at the Technion  Israel Institute of Technology This work was supported by the Israel Science Foundation administrated by the Academy of Science and Humanities 2 Starobinski and Sidi / Modeling and Analysis of ..."
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Cited by 14 (2 self)
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e of exponentials The research was performed while this author was a Ph.D student at the Technion  Israel Institute of Technology This work was supported by the Israel Science Foundation administrated by the Academy of Science and Humanities 2 Starobinski and Sidi / Modeling and Analysis of PowerTail Distributions 1. Introduction Recent studies have revealed that network trac exhibits burstiness over multiple time scales [15,22]. In many circumstances, powertail probability distributions have been found appropriate for capturing this salient feature (see [19] and references therein). A random variable X has a powertail distribution if its complementary cumulative distribution function (ccdf) F (t) satises F (t) = PrfX > tg ct as t !
Asymptotic behavior of total times for jobs that must start over if a failure occurs
, 2007
"... Many processes must complete in the presence of failures. Different systems respond to task failure in different ways. The system may resume a failed task from the failure point (or a saved checkpoint shortly before the failure point), it may give up on the task and select a replacement task from th ..."
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Cited by 13 (0 self)
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Many processes must complete in the presence of failures. Different systems respond to task failure in different ways. The system may resume a failed task from the failure point (or a saved checkpoint shortly before the failure point), it may give up on the task and select a replacement task from the ready queue, or it may restart the task. The behavior of systems under the first two scenarios is well documented, but the third (RESTART) has resisted detailed analysis. In this paper we derive tight asymptotic relations between the distribution of task times without failures to the total time when including failures, for any failure distribution. In particular, we show that if the task time distribution has an unbounded support then the total time distribution H is always heavytailed. Asymptotic expressions are given for the tail of H in various scenarios. The key ingredients of the analysis are the Cramér–Lundberg asymptotics for geometric sums and integral asymptotics, that in some cases are obtained via Tauberian theorems and in some cases by barehand calculations. Key words CramérLundberg approximation, failure recovery, geometric sums, heavy tails, logarithmic asymptotics, mixture distribution, power tail, RESTART, Tauberian theorem
Impact of aggregated, selfsimilar ON/OFF traffic on delay in stationary queueing models
 Proceedings of SPIE, Performance and Control of Network Systems III
, 1999
"... The impact of the now widely acknowledged selfsimilar property of network traffic on cell delay in a single server queueing model is investigated. The analytic traffic model, called NBurst, uses the superposition of N independent cell streams of ON/OFF type with PowerTail distributed ON periods. ..."
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Cited by 12 (5 self)
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The impact of the now widely acknowledged selfsimilar property of network traffic on cell delay in a single server queueing model is investigated. The analytic traffic model, called NBurst, uses the superposition of N independent cell streams of ON/OFF type with PowerTail distributed ON periods. Delay for such arrival processes is mainly caused by oversaturation periods, which occur when too many sources are in their ONstate. The duration of these oversaturation periods is shown to have a PowerTail distribution, whose exponent fi is in most scenarios different from the tail exponent of the individual ONperiod. Conditions on the model parameters, for which the mean and higher moments of the delay distribution become infinite, are investigated. Since these conditions depend on traffic parameters as well as on network parameters, careful network design can alleviate the performance impact of such selfsimilar traffic. Furthermore, in real networks, a Maximum Burst Size (MBS) leads...
Telecommunication Traffic, Queueing Models, and Subexponential Distributions
, 1999
"... This article reviews various models within the queueing framework which have been suggested for teletraffic data. Such models aim to capture certain stylised features of the data, such as variability of arrival rates, heavytailedness of on and offperiods and longrange dependence in teletraffic t ..."
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Cited by 11 (0 self)
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This article reviews various models within the queueing framework which have been suggested for teletraffic data. Such models aim to capture certain stylised features of the data, such as variability of arrival rates, heavytailedness of on and offperiods and longrange dependence in teletraffic transmission. Subexponential distributions constitute a large class of heavytailed distributions, and we investigate their (sometimes disastrous) influence within teletraffic models. We demonstrate some of the above effects in an explorative data analysis of Munich Universities' intranet data.
Performance Analysis of a Digital Link with Heterogeneous Multislot Traffic
 IEEE Trans. on Comm
, 1995
"... We present a unified model to compute various performance measures when Poissonian and nonPoissonian (renewal) multislot traffic streams are offered to a digital link in a (double) loss system. We represent the nonPoissonian arrival process by a matrixexponential distribution, requiring only tha ..."
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Cited by 10 (8 self)
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We present a unified model to compute various performance measures when Poissonian and nonPoissonian (renewal) multislot traffic streams are offered to a digital link in a (double) loss system. We represent the nonPoissonian arrival process by a matrixexponential distribution, requiring only that the interarrival distribution has a rational Laplace transform. Several distributions are considered as the nonPoissonian traffic. The resulting model uses matrix algebraic techniques only,thus not requiring any complex and/or tedious transform techniques. We also incorporate various control policies in our modeling framework using acceptance functions. Through our computational studies, we conclude that the second and the third moments of the nonPoissonian traffic have significant impact on various performance measures.
Behavior of TCPlike elastic traffic at a buffered bottleneck router
, 2001
"... A major challenge in traffic modeling and performance analysis for the Transmission Control Protocol (TCP) stems from the fact that the incoming traffic is not independent of the congestion level in the network. This paper investigates a queueing model where the traffic essentially shows ON/OFF char ..."
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Cited by 10 (0 self)
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A major challenge in traffic modeling and performance analysis for the Transmission Control Protocol (TCP) stems from the fact that the incoming traffic is not independent of the congestion level in the network. This paper investigates a queueing model where the traffic essentially shows ON/OFF characteristics, i.e. the number of active TCP connections of finite (probabilistic) duration varies as described by a stochastic process. The essential behavior of TCPlike flowcontrol mechanisms is captured in the analytic model by the feature that the packetrate of active connections can be throttled in order to avoid that the overall packetstream exceeds the outputbandwidth of the bottleneck router. By appropriate adjustment of the connection duration, the number of packets in the connections remains unaffected. However, since TCP reacts to existing congestion, the throttling mechanism is only activated when the bufferoccupancy at the bottleneck router exceeds a certain threshold. The impact of such a flowcontrol mechanism on the characteristics of the incoming traffic as well as on the performance behavior at the bottleneck router is discussed and illustrated by numerical results of the analytic model. In particular, the use of (truncated) PowerTail distributions for the ON periods leads to conclusions about the behavior of longrange dependent traffic under the influence of TCP's flowcontrol mechanism. Keywords TCP flowcontrol, ON/OFF models, Markov Modulated Poisson Processes, LongRange Dependence, Truncated PowerTail Distributions I.
Characterizing the BMAP/MAP/1 departure process via the ETAQA truncation
, 2005
"... We propose a family of finite approximations for the departure process of a BMAP/MAP/1 queue. The departure process approximations are derived via an exact aggregate solution technique (called ETAQA) applied to M/G/1type Markov processes. The proposed approximations are indexed by a parameter n (n> ..."
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Cited by 9 (6 self)
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We propose a family of finite approximations for the departure process of a BMAP/MAP/1 queue. The departure process approximations are derived via an exact aggregate solution technique (called ETAQA) applied to M/G/1type Markov processes. The proposed approximations are indexed by a parameter n (n> 1), which determines the size of the output model as n + 1 block levels of the M/G/1type process. This output approximation preserves exactly the marginal distribution of the true departure process and the lag correlations of the interdeparture times up to lag n − 2. Experimental results support the applicability of the proposed approximation in trafficbased decomposition of queueing networks.
On the Performance of Parallel Computers: Order Statistics and Amdahl's Law
 International Journal of Computers and Their Applications
, 1995
"... this paper, we will give a short review of Amdahl's law, and order statistics, and provide some examples of what realistic speedups to expect. In particular, we will look at Uniform, Exponential, and Powertail distributions in detail. Then we will examine the much more difficult problem where the n ..."
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Cited by 8 (6 self)
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this paper, we will give a short review of Amdahl's law, and order statistics, and provide some examples of what realistic speedups to expect. In particular, we will look at Uniform, Exponential, and Powertail distributions in detail. Then we will examine the much more difficult problem where the number of tasks exceeds the number of processors. In this case the tasks must queue up for service. This is equivalent to Mean time to drain of a G/C queue with no new arrivals, and in Reliability Theory, to Mean time to failure, with hot and cold backup. We will also present some examples of this. We also give a description of how to treat jobs where the tasks come from different distributions, and show how longest task time can be computed if the distributions are all exponential (but with different parameters). In this case, if k exceeds C,
Performance Results For Analytic Models Of Traffic In Telecommunication Systems, Based On Multiple ONOFF Sources With SelfSimilar Behavior
 Elsevier Science B.V
, 1999
"... this paper is the introduction of a broad class of models, called NBurst, that has the A major part of this research was funded by Deutsche Telekom AG. ..."
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Cited by 8 (6 self)
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this paper is the introduction of a broad class of models, called NBurst, that has the A major part of this research was funded by Deutsche Telekom AG.