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Title: Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations

Abstract

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.

Authors:
ORCiD logo [1];  [1];  [2]; ORCiD logo [3]
  1. Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO 80523-1373, USA
  2. Department of Statistics and Operation Research, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3260, USA
  3. Department of Statistics, Colorado State University, Fort Collins, CO 80523-1373, USA
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1227756
Grant/Contract Number:  
FG02-04ER25620; FG02-05ER25699; FC02-07ER54909; SC0001724; SC0005304; INL00120133
Resource Type:
Journal Article: Published Article
Journal Name:
Abstract and Applied Analysis
Additional Journal Information:
Journal Name: Abstract and Applied Analysis Journal Volume: 2013; Journal ID: ISSN 1085-3375
Publisher:
Hindawi Publishing Corporation
Country of Publication:
Country unknown/Code not available
Language:
English

Citation Formats

Zhang, Yang, Chong, Edwin K. P., Hannig, Jan, and Estep, Donald. Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations. Country unknown/Code not available: N. p., 2013. Web. doi:10.1155/2013/262581.
Zhang, Yang, Chong, Edwin K. P., Hannig, Jan, & Estep, Donald. Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations. Country unknown/Code not available. https://doi.org/10.1155/2013/262581
Zhang, Yang, Chong, Edwin K. P., Hannig, Jan, and Estep, Donald. 2013. "Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations". Country unknown/Code not available. https://doi.org/10.1155/2013/262581.
@article{osti_1227756,
title = {Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations},
author = {Zhang, Yang and Chong, Edwin K. P. and Hannig, Jan and Estep, Donald},
abstractNote = {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.},
doi = {10.1155/2013/262581},
url = {https://www.osti.gov/biblio/1227756}, journal = {Abstract and Applied Analysis},
issn = {1085-3375},
number = ,
volume = 2013,
place = {Country unknown/Code not available},
year = {Tue Jan 01 00:00:00 EST 2013},
month = {Tue Jan 01 00:00:00 EST 2013}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at https://doi.org/10.1155/2013/262581

Citation Metrics:
Cited by: 2 works
Citation information provided by
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