Matching marginal moments and lag autocorrelations with MAPs

Horväth, Gábor

doi:10.4108/icst.valuetools.2013.254368

Cited by 4 publications

(3 citation statements)

References 17 publications

(28 reference statements)

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“…Our sequence has however such a lag-1 auto-correlation that cannot be realized with only 2 states. In [19] a method was proposed that creates a MAP with any 3 inter-arrival time moments and lag-1 auto-correlation. This method, implemented in the BuTools package, provides the following 6-state MAP: As opposed to the approach used in Sect.…”

Section: Markovian Arrival Processesmentioning

confidence: 99%

Petri Nets Validation of Markovian Models of Emergency Department Arrivals

Ballarini

Duma

Horváth

et al. 2020

Application and Theory of Petri Nets and Concurrency

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Modeling of hospital's Emergency Departments (ED) is vital for optimisation of health services offered to patients that shows up at an ED requiring treatments with different level of emergency. In this paper we present a modeling study whose contribution is twofold: first, based on a dataset relative to the ED of an Italian hospital, we derive different kinds of Markovian models capable to reproduce, at different extents, the statistical character of dataset arrivals; second, we validate the derived arrivals model by interfacing it with a Petri net model of the services an ED patient undergoes. The empirical assessment of a few key performance indicators allowed us to validate some of the derived arrival process model, thus confirming that they can be used for predicting the performance of an ED.

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Section: Markovian Arrival Processesmentioning

confidence: 99%

Petri Nets Validation of Markovian Models of Emergency Department Arrivals

Ballarini

Duma

Horváth

et al. 2020

Application and Theory of Petri Nets and Concurrency

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“…2.3 can be used to fit a MAP into interevent data. In this study, we use the simplest fitting method among the available methods, which fits a MAP with the same first-two moments and first-lag autocorrelation to inter-event data (Horváth 2013). We adopt such a M AP to demonstrate the potential of employing MAPs in estimating the optimal base-stock level by using shop-floor inter-event data.…”

Section: Setting the Base-stock Level By Using Shop-floor Datamentioning

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 method for creating an order-2 MAP from 3 moments and 1 correlation parameter published in [5] is implemented by the MAP2FromMoments function. The only flexible matching procedure (that can adjust the order of the result automatically, based on the input parameters) is MAPFromFewMomentsAnd-Correlations, that implements [9].…”

Section: Tools For Mapsmentioning

confidence: 99%

BuTools 2: a Rich Toolbox for Markovian Performance Evaluation

Horväth

Telek

2017

Proceedings of the 10th EAI International Conference on Performance Evaluation Methodologies and Tools

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BuTools 2 is collection of computational methods that are useful for Markovian and non-Markovian matrix analytic performance analysis. It consists of various packages. There are packages to obtain, analyze, transform and minimize discrete and continuous time phase-type (PH) distributions and Markovian arrival processes (MAP); to fit empirical measurement data and to evaluate the result; to solve many performance measures of various Markovian queueing systems; and to solve block-structured Markov chains. All three major mathematical frameworks are supported: BuTools is released for MATLAB, Mathematica and NumPy/IPython as well, with the same features, with the same call interfaces. Every function is documented, the documentation is supplemented by many examples and the related citations. BuTools uses the state-of-the art algorithms and apart of the basic functionalities it contains several unique, difficult to implement procedures as well. of contributors include: Levente Bodrog, Peter Buchholz, Armin Heindl, András Horváth, István Kolossváry, András ACM ISBN 978-1-4503-2138-9.

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Matching marginal moments and lag autocorrelations with MAPs

Cited by 4 publications

References 17 publications

Petri Nets Validation of Markovian Models of Emergency Department Arrivals

Petri Nets Validation of Markovian Models of Emergency Department Arrivals

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

BuTools 2: a Rich Toolbox for Markovian Performance Evaluation

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