Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations
We introduce a continuum modeling method to approximate a class of large wireless networks by nonlinear partial differential equations (PDEs). This method is based on the convergence of a sequence of underlying Markov chains of the network indexed by N, the number of nodes in the network. As N goes...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/262581 |
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| _version_ | 1849405506237497344 |
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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 | We introduce a continuum modeling method to approximate a class of large wireless networks by nonlinear partial differential equations (PDEs). This method is based on the convergence of a sequence of underlying Markov chains of the network indexed by N, the number of nodes in the network. As N goes to infinity, the sequence converges to a continuum limit, which is the solution of a certain nonlinear PDE. We first describe PDE models for networks with uniformly located nodes and then generalize to networks with nonuniformly located, and possibly mobile, nodes. Based on the PDE models, we develop a method to control the transmissions in nonuniform networks so that the continuum limit is invariant under perturbations in node locations. This enables the networks to maintain stable global characteristics in the presence of varying node locations. |
| format | Article |
| id | doaj-art-51e7ebd4b89743789148b773bb2b48f0 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-51e7ebd4b89743789148b773bb2b48f02025-08-20T03:36:38ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/262581262581Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential EquationsYang Zhang0Edwin K. P. Chong1Jan Hannig2Donald Estep3Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO 80523-1373, USADepartment of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO 80523-1373, USADepartment of Statistics and Operation Research, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3260, USADepartment of Statistics, Colorado State University, Fort Collins, CO 80523-1373, USAWe introduce a continuum modeling method to approximate a class of large wireless networks by nonlinear partial differential equations (PDEs). This method is based on the convergence of a sequence of underlying Markov chains of the network indexed by N, the number of nodes in the network. As N goes to infinity, the sequence converges to a continuum limit, which is the solution of a certain nonlinear PDE. We first describe PDE models for networks with uniformly located nodes and then generalize to networks with nonuniformly located, and possibly mobile, nodes. Based on the PDE models, we develop a method to control the transmissions in nonuniform networks so that the continuum limit is invariant under perturbations in node locations. This enables the networks to maintain stable global characteristics in the presence of varying node locations.http://dx.doi.org/10.1155/2013/262581 |
| spellingShingle | Yang Zhang Edwin K. P. Chong Jan Hannig Donald Estep Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations Abstract and Applied Analysis |
| title | Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations |
| title_full | Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations |
| title_fullStr | Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations |
| title_full_unstemmed | Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations |
| title_short | Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations |
| title_sort | continuum modeling and control of large nonuniform wireless networks via nonlinear partial differential equations |
| url | http://dx.doi.org/10.1155/2013/262581 |
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