Acyclic discrete phase type distributions: properties and a parameter estimation algorithm

Bobbio, A.; Horváth, András; Scarpa, Marco; Telek, Miklós

doi:10.1016/s0166-5316(03)00044-0

Cited by 109 publications

(76 citation statements)

References 12 publications

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“…Such processes are known as Long-Range Dependent (LRD) processes [1]. This is in contrast to traditional processes used in modeling IP network traffic, all of which include the property that the accumulative functions of their aggregated processes degenerate as the non-overlapping batch size m increasing to infinity, ie, ρ…”

Section: Distinctive Properties Of Long-range Dependent Self-similar mentioning

confidence: 99%

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Advanced Models and Algorithms for Self-Similar IP Network Traffic Simulation and Performance Analysis

Radev¹,

Lokshina²

2010

Journal of Electrical Engineering

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The paper examines self-similar (or fractal) properties of real communication network traffic data over a wide range of time scales. These self-similar properties are very different from the properties of traditional models based on Poisson and Markov-modulated Poisson processes. Advanced fractal models of sequentional generators and fixed-length sequence generators, and efficient algorithms that are used to simulate self-similar behavior of IP network traffic data are developed and applied. Numerical examples are provided; and simulation results are obtained and analyzed.K e y w o r d s: communication networks, IP network traffic, long-range dependent self-similar processes, advanced generators of self-similar teletraffic

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Section: Distinctive Properties Of Long-range Dependent Self-similar mentioning

confidence: 99%

“…We considered the following efficient candidate sequential generators, based on: For the standard Fractal Renewal Process (FRP), inter-event times are independent random variables [1]. The marginal Probability Density Function (PDF) of such a fractal renewal process can be defined as (1),…”

Section: Sequential Generators Of Self-similar Ip Network Trafficmentioning

confidence: 99%

Advanced Models and Algorithms for Self-Similar IP Network Traffic Simulation and Performance Analysis

Radev¹,

Lokshina²

2010

Journal of Electrical Engineering

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“…To overcome these problems the class of PH distributions used for fitting has to be restricted which is in principle possible in the basic EM algorithm by initializing only some elements in the matrix with non-zero values, However, the optimization problem for general PH distributions is too complex to yield satisfactory results if the number of phases is larger than two or three. As shown in several papers [2], [3], [13], [14], the fitting problem becomes much easier if acyclic instead of general phase-type distributions are used, because for this type of distributions a canonical representation exists which reduces the number of free parameters to 2N compared to N 2 + N for the general case, where N is then number of phases [5]. On the other hand, the restriction to acyclic PH distributions does not seem to limit the flexibility of the approach.…”

Section: Introductionmentioning

confidence: 78%

“…Note that each iteration (see steps (2) to (7) in Figure 3) is guaranteed to increase the log-likelihood value and the algorithm is guaranteed to converge to a local maximum of the likelihood function [19]. To check whether convergence is reached, we compute in each iteration either (i) the maximal difference of the values of the parameter vectors of successive iterations,…”

Section: Implementation Issuesmentioning

confidence: 99%

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A Novel Approach for Phase-Type Fitting with the EM Algorithm

Thümmler

Buchholz

Telek

2006

IEEE Trans. Dependable and Secure Comput.

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183

105

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The representation of general distributions or measured data by phase-type distributions is an important and non-trivial task in analytical modeling. Although a large number of different methods for fitting parameters of phase-type distributions to data traces exist, many approaches lack efficiency and numerical stability. In this paper, a novel approach is presented that fits a restricted class of phase-type distributions, namely mixtures of Erlang distributions, to trace data.For the parameter fitting an algorithm of the expectation maximization type is developed. The paper shows that these choices result in a very efficient and numerically stable approach which yields phase-type approximations for a wide range of data traces that are as good or better than approximations computed with other less efficient and less stable fitting methods. To illustrate the effectiveness of the proposed fitting algorithm, we present comparative results for our approach and two other methods using six benchmark traces and two real traffic traces as well as quantitative results from queueing analysis. Keywords:Performance and dependability assessment/analytical and numerical techniques, design of tools for performance/dependability assessment, traffic modeling, hyper-Erlang distributions.

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Improvement of expectation–maximization algorithm for phase‐type distributions with grouped and truncated data

Okamura

Trivedi

2012

Appl Stoch Models Bus & Ind

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This paper proposes an improved expectation–maximization (EM) algorithm for phase‐type (PH) distributions with grouped and truncated data. Olsson (1996) derived an EM algorithm for PH distributions under censored data, and the similar technique can be utilized to the PH fitting even under grouped and truncated data. However, it should be noted that Olsson's algorithm has a drawback in terms of computation speed. Because the time complexity of the algorithm is a cube of number of phases, it does not work well in the case where the number of phases is large. This paper proposes an improvement of the EM algorithm under grouped and truncated observations. By applying a uniformization‐based technique for continuous‐time Markov chains, it is shown that the time complexity of our algorithm can be reduced to the square of number of phases. In particular, when we consider the PH fitting using a canonical form of PH distributions, the time complexity is linear in the number of phases. Copyright © 2012 John Wiley & Sons, Ltd.

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Acyclic discrete phase type distributions: properties and a parameter estimation algorithm

Cited by 109 publications

References 12 publications

Advanced Models and Algorithms for Self-Similar IP Network Traffic Simulation and Performance Analysis

Advanced Models and Algorithms for Self-Similar IP Network Traffic Simulation and Performance Analysis

A Novel Approach for Phase-Type Fitting with the EM Algorithm

Improvement of expectation–maximization algorithm for phase‐type distributions with grouped and truncated data

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