Arm processes and modeling methodology

Melamed, Benjamin

doi:10.1080/15326349908807568

Cited by 8 publications

(5 citation statements)

References 21 publications

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“…Inferred HMPs model the entire network between the source-destination pair, as they can generate sequences whose signatures [10] approximate the probes delay signatures. The model-generated sequences (delays), representing delays applications packets undergo, can ultimately be used to evaluate the applications performance.…”

Section: A Delay-based Hmp Modeling Of Networkmentioning

confidence: 99%

“…To assess the modeling fidelity, model-generated data signatures are contrasted against those of the training data. For the signatures, cumulative distribution function (CDF) and autocorrelation are popular choices in view of their simplicity [10]. CDFs and autocorrelations are compared respectively by Kolmogorov Smirnoff (KS) test-maximum difference-and MSE.…”

Section: B Quantization and Fidelitymentioning

confidence: 99%

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Fine-grained end-to-end network model via vector quantization and hidden Markov processes

Ghorbanzadeh

Chen

Clancy

et al. 2013

2013 IEEE International Conference on Communications (ICC)

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We study and compare modeling an end-to-end network by conventional, bivariate, and exponential observation hidden Markov processes. Furthermore, effects of μ-law, Lindle-Boyde-Gray, and uniform quantization approaches on the modeling granularity is explored. We performed experiments using synthetic representative data from a traffic-modeler autoregressive modular process and the Network Simulator software as well as over-the-Internet experiments with real data to contrast the fidelity produced from each model. Comparing statistical signatures of the model-generated data with those of the training sequence indicates that accompanying Lindle-BoydeGray quantization with conventional or bivariate hidden Markov processes significantly improves the modeling fidelity. I. INTRODUCTIONNetwork simulation, for the purpose of application performance evaluation, using event-driven simulators such as Network Simulator (NS2) [1], Dummynet [2], and NIST [3] Net requires such a multitude of component settings, which makes large-scale networks inconducive to simulation. This has inspired developing simple generic models for networks, regardless of their size and complexity, by means of hidden Markov processes (HMPs) [4] Salamatian et al. [5] use conventional HMPs (CHMPs) [6] for packet loss modeling. Weiwei et al.[4] deploy bivariate HMPs (BHMPs) for delaybased network modeling in that end-to-end delay drastically affects the performance of applications running on the network. Therefore, designing network models based on such delays is insightful to applications performance as HMPgenerated observations represent actual delays the running applications will undergo. Since HMP parameters are the only means of generating the delays, selecting an HMP variation and its precise inference are of high consequence.In this paper, we contrast effectiveness of CHMPs, BHMPs, and exponential observation HMPs (EHMPs) [6] for the delaybased network modeling. CHMPs and BHMPs' requirement for discrete training data incorporates quantization into the modeling procedure. Since the quantized data are the only means of obtaining CHMPs and BHMPs, the quantization quality dramatically affects the modeling fidelity. Weiwei [25] simply deployed uniformly quantized data; however, long tail delay distributions in networks [7] induces a poor discretization for the uniform quantization. Such a choice adversely

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Section: A Delay-based Hmp Modeling Of Networkmentioning

confidence: 99%

Section: B Quantization and Fidelitymentioning

confidence: 99%

Fine-grained end-to-end network model via vector quantization and hidden Markov processes

Ghorbanzadeh

Chen

Clancy

et al. 2013

2013 IEEE International Conference on Communications (ICC)

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“…We mention that in order to fit a general ARM process to a prescribed distribution and autocorrelation function simultaneously, a heuristic search is performed to identify a suitable innovation density that results in a foreground (ARM) sequence that approximates the prescribed autocorrelation, while the prescribed distribution is reproduced exactly by virtue of the inversion method (see Melamed [16] To simplify the discussion, we focus on basic ARM + processes -those with uniform innovations of the form…”

Section: Lemma 1 Guarantees That the Armmentioning

confidence: 99%

“…To fix the ideas, consider the class of so-called ARM + background processes (Jagerman and Melamed [8][9][10]; Melamed [16]) of the form…”

Section: The Notion Of Pseudo-timementioning

confidence: 99%

“…Uniform (0,1) pseudo-random number stream, available on most computers. Examples of such approaches are generation methods based on Transform-Expand-Sample (TES) processes (see Melamed [14]; Jagerman and Melamed [8,9]), and Auto-Regressive Modular (ARM) processes (see Melamed [16]) -a generalization of TES processes, as well as Minification/Maxification methods (see Lewis and McKenzie [7]). This paper is based on ARM processes, to be briefly reviewed in Section 3.…”

Section: Introductionmentioning

confidence: 99%

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Temporal Shaping of Simulated Time Series With Cyclical Sample Paths

Chen

Baveja

Melamed

2017

Prob. Eng. Inf. Sci.

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Temporal shaping of time series is the activity of deriving a time series model with a prescribed marginal distribution and some sample path characteristics. Starting with an empirical sample path, one often computes from it an empirical histogram (a step-function density) and empirical autocorrelation function. The corresponding cumulative distribution function is piecewise linear, and so is the inverse distribution function. The so-called inversion method uses the latter to generate the corresponding distribution from a uniform random variable on [0,1), histograms being a special case. This paper shows how to manipulate the inverse histogram and an underlying marginally uniform process, so as to "shape" the model sample paths in an attempt to match the qualitative nature of the empirical sample paths, while maintaining a guaranteed match of the empirical marginal distribution. It proposes a new approach to temporal shaping of time series and identifies a number of operations on a piecewise-linear inverse histogram function, which leave the marginal distribution invariant. For cyclical processes with a prescribed marginal distribution and a prescribed cycle profile, one can also use these transformations to generate sample paths which "conform" to the profile. This approach also improves the ability to approximate the empirical autocorrelation function.

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ARM Processes and Their Modeling and Forecasting Methodology

Melamed

2010

Handbook of Quantitative Finance and Risk Management

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Arm processes and modeling methodology

Cited by 8 publications

References 21 publications

Fine-grained end-to-end network model via vector quantization and hidden Markov processes

Fine-grained end-to-end network model via vector quantization and hidden Markov processes

Temporal Shaping of Simulated Time Series With Cyclical Sample Paths

ARM Processes and Their Modeling and Forecasting Methodology

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