IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2013y2013i1n262581.html

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

Author

Listed:
  • Yang Zhang
  • Edwin K. P. Chong
  • Jan Hannig
  • Donald Estep

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.

Suggested Citation

  • Yang Zhang & Edwin K. P. Chong & Jan Hannig & Donald Estep, 2013. "Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:262581
    DOI: 10.1155/2013/262581
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2013/262581
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/262581?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Ji-Huan He, 2012. "Asymptotic Methods for Solitary Solutions and Compactons," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Ji-Huan He, 2012. "Asymptotic Methods for Solitary Solutions and Compactons," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-130, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yang Zhao & Dumitru Baleanu & Mihaela Cristina Baleanu & De-Fu Cheng & Xiao-Jun Yang, 2013. "Mappings for Special Functions on Cantor Sets and Special Integral Transforms via Local Fractional Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Chun-Guang Zhao & Ai-Min Yang & Hossein Jafari & Ahmad Haghbin, 2014. "The Yang‐Laplace Transform for Solving the IVPs with Local Fractional Derivative," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Wei Wei & H. M. Srivastava & Yunyi Zhang & Lei Wang & Peiyi Shen & Jing Zhang, 2014. "A Local Fractional Integral Inequality on Fractal Space Analogous to Anderson’s Inequality," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Mingsheng Hu & Zhijuan Jia & Qiaoling Chen & Suiming Jia, 2014. "Exact Solutions for Nonlinear Wave Equations by the Exp‐Function Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Kai Liu & Ren-Jie Hu & Carlo Cattani & Gong-Nan Xie & Xiao-Jun Yang & Yang Zhao, 2014. "Local Fractional Z‐Transforms with Applications to Signals on Cantor Sets," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    6. Devendra Kumar & Jagdev Singh & A. Kılıçman, 2013. "An Efficient Approach for Fractional Harry Dym Equation by Using Sumudu Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    7. Shu-Li Mei, 2013. "Construction of Target Controllable Image Segmentation Model Based on Homotopy Perturbation Technology," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    8. Ji-Huan He, 2013. "Periodic Solution of the Hematopoiesis Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    9. Zongmin Yue & Xiaoqin Wang & Haifeng Liu, 2013. "Complex Dynamics of a Diffusive Holling‐Tanner Predator‐Prey Model with the Allee Effect," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    10. Jun Zhou, 2013. "Comment on “Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion”," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    11. Li Yao & Yun-Jie Yang & Xing-Wei Zhou, 2013. "A Note on the Semi‐Inverse Method and a Variational Principle for the Generalized KdV‐mKdV Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    12. Fukang Yin & Junqiang Song & Xiaoqun Cao & Fengshun Lu, 2013. "Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    13. Hongliang Liu & Aiguo Xiao & Lihong Su, 2013. "Convergence of Variational Iteration Method for Second‐Order Delay Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    14. Jagdev Singh & Devendra Kumar & A. Kılıçman, 2013. "Homotopy Perturbation Method for Fractional Gas Dynamics Equation Using Sumudu Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    15. Ming-Sheng Hu & Ravi P. Agarwal & Xiao-Jun Yang, 2012. "Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    16. Hong-Zhun Liu, 2013. "A Simplification for Exp‐Function Method When the Balanced Nonlinear Term Is a Certain Product," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    17. Yasir Khan & Zdeněk Šmarda, 2013. "Heat Transfer Analysis on the Hiemenz Flow of a Non‐Newtonian Fluid: A Homotopy Method Solution," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    18. Junqiang Song & Fukang Yin & Xiaoqun Cao & Fengshun Lu, 2013. "Fractional Variational Iteration Method versus Adomian’s Decomposition Method in Some Fractional Partial Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    19. H. M. Srivastava & Alireza Khalili Golmankhaneh & Dumitru Baleanu & Xiao-Jun Yang, 2014. "Local Fractional Sumudu Transform with Application to IVPs on Cantor Sets," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    20. Xiao-Feng Niu & Cai-Li Zhang & Zheng-Biao Li & Yang Zhao, 2014. "Local Fractional Derivative Boundary Value Problems for Tricomi Equation Arising in Fractal Transonic Flow," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:262581. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.