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

Journal Article · Tue Jan 01 00:00:00 EST 2013 · Abstract and Applied Analysis

DOI:https://doi.org/10.1155/2013/262581· OSTI ID:1227756

Zhang, Yang  ^[1]; Chong, Edwin K. P. ^[1]; Hannig, Jan ^[2]; Estep, Donald  ^[3]

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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

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.

• Sponsoring Organization: USDOE
• Grant/Contract Number: FG02-04ER25620; FG02-05ER25699; FC02-07ER54909; SC0001724; SC0005304; INL00120133
• OSTI ID: 1227756
• Journal Information: Abstract and Applied Analysis, Journal Name: Abstract and Applied Analysis Vol. 2013; ISSN 1085-3375
• Publisher: Hindawi Publishing Corporation
• Country of Publication: Country unknown/Code not available
• Language: English