Approximating Extremely Large Networks via Continuum Limits
This paper is concerned with modeling of networks with an extremely large number of components using partial differential equations (PDEs). This modeling method is based on the convergence of a sequence of underlying Markov chains of the network indexed by N, the number of components in the network....
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2013-01-01
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| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/6600754/ |
| _version_ | 1818457924851204096 |
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| author | Yang Zhang Edwin K. P. Chong Jan Hannig Donald Estep |
| author_facet | Yang Zhang Edwin K. P. Chong Jan Hannig Donald Estep |
| author_sort | Yang Zhang |
| collection | DOAJ |
| description | This paper is concerned with modeling of networks with an extremely large number of components using partial differential equations (PDEs). This modeling method is based on the convergence of a sequence of underlying Markov chains of the network indexed by N, the number of components in the network. As N goes to infinity, the sequence converges to a continuum limit, which is the solution of a certain PDE. We provide sufficient conditions for the convergence and characterize the rate of convergence. As an application, we model large wireless sensor networks by PDEs. While traditional Monte Carlo simulation for extremely large networks is practically infeasible, PDEs can be solved with reasonable computation overhead using well-established mathematical tools. |
| first_indexed | 2024-12-14T22:50:18Z |
| format | Article |
| id | doaj.art-b21916dcb2464d8dbe3a925808ea58d1 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-14T22:50:18Z |
| publishDate | 2013-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-b21916dcb2464d8dbe3a925808ea58d12022-12-21T22:44:44ZengIEEEIEEE Access2169-35362013-01-01157759510.1109/ACCESS.2013.22816686600754Approximating Extremely Large Networks via Continuum LimitsYang Zhang0Edwin K. P. Chong1Jan Hannig2Donald Estep3Department of Electrical and Computer Engineering, Colorado State University, Ft. Collins, CO, USADepartment of Electrical and Computer Engineering, Colorado State University, Ft. Collins, CO, USADepartment of Statistics and Operation Research, The University of North Carolina at Chapel Hill, Chapel Hill, NC, USADepartment of Mathematics and Department of Statistics, Colorado State University, Fort Collins, CO, USAThis paper is concerned with modeling of networks with an extremely large number of components using partial differential equations (PDEs). This modeling method is based on the convergence of a sequence of underlying Markov chains of the network indexed by N, the number of components in the network. As N goes to infinity, the sequence converges to a continuum limit, which is the solution of a certain PDE. We provide sufficient conditions for the convergence and characterize the rate of convergence. As an application, we model large wireless sensor networks by PDEs. While traditional Monte Carlo simulation for extremely large networks is practically infeasible, PDEs can be solved with reasonable computation overhead using well-established mathematical tools.https://ieeexplore.ieee.org/document/6600754/Modelingpartial differential equationsMarkov processesnetwork modeling |
| spellingShingle | Yang Zhang Edwin K. P. Chong Jan Hannig Donald Estep Approximating Extremely Large Networks via Continuum Limits IEEE Access Modeling partial differential equations Markov processes network modeling |
| title | Approximating Extremely Large Networks via Continuum Limits |
| title_full | Approximating Extremely Large Networks via Continuum Limits |
| title_fullStr | Approximating Extremely Large Networks via Continuum Limits |
| title_full_unstemmed | Approximating Extremely Large Networks via Continuum Limits |
| title_short | Approximating Extremely Large Networks via Continuum Limits |
| title_sort | approximating extremely large networks via continuum limits |
| topic | Modeling partial differential equations Markov processes network modeling |
| url | https://ieeexplore.ieee.org/document/6600754/ |
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