Academic Journal
A refined mean field approximation of synchronous discrete-time population models
| العنوان: | A refined mean field approximation of synchronous discrete-time population models |
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| المؤلفون: | Gast, Nicolas, Latella, Diego, Massink, Mieke |
| المساهمون: | Performance analysis and optimization of LARge Infrastructures and Systems (POLARIS), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire d'Informatique de Grenoble (LIG), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes 2016-2019 (UGA 2016-2019 )-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes 2016-2019 (UGA 2016-2019 ), CNR Istituto di Scienza e Tecnologie dell’Informazione “A. Faedo” Pisa (CNR, National Research Council of Italy |
| المصدر: | ISSN: 0166-5316 ; Performance Evaluation ; https://inria.hal.science/hal-01845235 ; Performance Evaluation, 2018, pp.1-27. ⟨10.1016/j.peva.2018.05.002⟩. |
| بيانات النشر: | CCSD Elsevier |
| سنة النشر: | 2018 |
| المجموعة: | Université Grenoble Alpes: HAL |
| مصطلحات موضوعية: | Mean field approximation, Discrete time population models, Accuracy of approximation, [INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI], [INFO.INFO-PF]Computer Science [cs]/Performance [cs.PF], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] |
| الوصف: | International audience ; Mean field approximation is a popular method to study the behaviour of stochastic models composed of a large number of interacting objects. When the objects are asynchronous, the mean field approximation of a population model can be expressed as an ordinary differential equation. When the objects are (clock-) synchronous the mean field approximation is a discrete time dynamical system. We focus on the latter.We study the accuracy of mean field approximation when this approximation is a discrete-time dynamical system. We extend a result that was shown for the continuous time case and we prove that expected performance indicators estimated by mean field approximation are $O(1/N)$-accurate. We provide simple expressions to effectively compute the asymptotic error of mean field approximation, for finite time-horizon and steady-state, and we use this computed error to propose what we call a \emph{refined} mean field approximation. We show, by using a few numerical examples, that this technique improves the quality of approximation compared to the classical mean field approximation, especially for relatively small population sizes. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| Relation: | info:eu-repo/semantics/altIdentifier/arxiv/1807.08585; ARXIV: 1807.08585 |
| DOI: | 10.1016/j.peva.2018.05.002 |
| الاتاحة: | https://inria.hal.science/hal-01845235 https://inria.hal.science/hal-01845235v1/document https://inria.hal.science/hal-01845235v1/file/GaLaMa17.pdf https://doi.org/10.1016/j.peva.2018.05.002 |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.995990A9 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1016/j.peva.2018.05.002 |
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