BuTools 2: a Rich Toolbox for Markovian Performance Evaluation

Horväth, Gábor; Telek, Miklós

doi:10.4108/eai.25-10-2016.2266400

Cited by 26 publications

(22 citation statements)

References 16 publications

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“…Fitting functions are supplied to help the user parameterize such processes in terms of phase-type distributions. In LINE 2.0.0, the QBD solver implementation depends on the BUTools library [5].…”

Section: Solution Methodsmentioning

confidence: 99%

Automated Multi-paradigm Analysis of Extended and Layered Queueing Models with LINE

Casale

2019

Companion of the 2019 ACM/SPEC International Conference on Performance Engineering

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LINE is an open source MATLAB library for performance and reliability analysis of systems that can be modeled by means of queueing theory. Recently, a new major release of the tool (version 2.0.0) has introduced several novel features, which are the focus of this demonstration. These include, among others, an object-oriented modeling language aligned with the abstraction of the Java Modelling Tools (JMT) simulator and a set of native solvers based on state-of-the-art analytical and simulation-based solution paradigms. CCS CONCEPTS • Mathematics of computing → Queueing theory; • Computing methodologies → Modeling and simulation;

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Section: Solution Methodsmentioning

confidence: 99%

Automated Multi-paradigm Analysis of Extended and Layered Queueing Models with LINE

Casale

2019

Companion of the 2019 ACM/SPEC International Conference on Performance Engineering

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“…We use processing, cycle, and inter-arrival time data of different equipments collected from shop-floor. We use the methods implemented in Bause et al (2010), and Horváth and Telek (2017) in fitting MAP. The goodness-of-fit of these methods have been investigated thoroughly in the telecommunications literature (Kriege and Buchholz 2010) for processes with positive autocorrelations.…”

Section: Performance Of Map-fitting Methodsmentioning

confidence: 99%

“…We employ a PH distribution with the same first-two moments ( PH 2 ) to model the arrival process by means of it's first-two moments. We employ the method presented in Horváth and Telek (2017) to generate a PH distribution with the first-two moments of the correlated arrival process. We employ the queue length distribution of the PH 2 /M/1 to calculate the base-stock level of the system.…”

Section: Performance Of Renewal Approximations In Estimating Correlatmentioning

confidence: 99%

Modelling and analysis of the impact of correlated inter-event data on production control using Markovian arrival processes

Dizbin

Tan

2018

Flex Serv Manuf J

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Empirical studies show that the inter-event times of a production system are correlated. However, most of the analytical studies for the analysis and control of production systems ignore correlation. In this study, we show that real-time data collected from a manufacturing system can be used to build a Markovian arrival processes (MAP) model that captures correlation in inter-event times. The obtained MAP model can then be used to control production in an effective way. We first present a comprehensive review on MAP modeling and MAP fitting methods applicable to manufacturing systems. Then we present results on the effectiveness of these fitting methods and discuss how the collected inter-event data can be used to represent the flow dynamics of a production system accurately. In order to study the impact of capturing the flow dynamics accurately on the performance of a production control system, we analyze a manufacturing system that is controlled by using a basestock policy. We study the impact of correlation in inter-event times on the optimal base-stock level of the system numerically by employing the structural properties of the MAP. We show that ignoring correlated arrival or service process can lead to overestimation of the optimal base-stock level for negatively correlated processes, and underestimation for the positively correlated processes. We conclude that MAPs can be used to develop data-driven models and control manufacturing systems more effectively by using shop-floor inter-event data.

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“…The generalized linear chain trick (GLCT) [51] extends this technique to allow modellers to assume these passage times follow a much broader family of distributions that includes the phase-type family of distributions [15,44,46,66,91]. These real-valued, matrix exponential distributions on [0, ∞) are the family of all possible hitting time (or absorption time) distributions for finite-state, absorbing, continuous time Markov chains (CTMCs).…”

Section: Introductionmentioning

confidence: 99%

Building mean field ODE models using the generalized linear chain trick & Markov chain theory

Hurtado

Richards

2021

Journal of Biological Dynamics

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The well known linear chain trick (LCT) allows modellers to derive mean field ODEs that assume gamma (Erlang) distributed passage times, by transitioning individuals sequentially through a chain of sub-states. The time spent in these sub-states is the sum of k exponentially distributed random variables, and is thus gamma distributed. The generalized linear chain trick (GLCT) extends this technique to the broader phase-type family of distributions, which includes exponential, Erlang, hypoexponential, and Coxian distributions. Phase-type distributions are the family of matrix exponential distributions on [0, ∞) that represent the absorption time distributions for finite-state, continuous time Markov chains (CTMCs). Here we review CTMCs and phase-type distributions, then illustrate how to use the GLCT to efficiently build ODE models from underlying stochastic model assumptions. We introduce two novel model families by using the GLCT to generalize the Rosenzweig-MacArthur predator-prey model, and the SEIR model. We illustrate the kinds of complexity that can be captured by such models through multiple examples. We also show the benefits of using a GLCT-based model formulation to speed up the computation of numerical solutions to such models. These results highlight the intuitive nature, and utility, of using the GLCT to derive ODE models from first principles.

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BuTools 2: a Rich Toolbox for Markovian Performance Evaluation

Cited by 26 publications

References 16 publications

Automated Multi-paradigm Analysis of Extended and Layered Queueing Models with LINE

Automated Multi-paradigm Analysis of Extended and Layered Queueing Models with LINE

Modelling and analysis of the impact of correlated inter-event data on production control using Markovian arrival processes

Building mean field ODE models using the generalized linear chain trick & Markov chain theory

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