Research Article

Continuum modeling of large networks

  1. Edwin K. P. Chong1,*,
  2. Donald Estep2,
  3. Jan Hannig3

Article first published online: 24 AUG 2007

DOI: 10.1002/jnm.651

Issue

International Journal of Numerical Modelling: Electronic Networks, Devices and Fields

International Journal of Numerical Modelling: Electronic Networks, Devices and Fields

Volume 21, Issue 3, pages 169–186, May/June 2008

Additional Information

How to Cite

Chong, E. K. P., Estep, D. and Hannig, J. (2008), Continuum modeling of large networks. Int. J. Numer. Model., 21: 169–186. doi: 10.1002/jnm.651

Author Information

  1. 1

    Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO 80523, U.S.A.

  2. 2

    Department of Mathematics and Department of Statistics, Colorado State University, Fort Collins, CO 80523, U.S.A.

  3. 3

    Department of Statistics, Colorado State University, Fort Collins, CO 80523, U.S.A.

*Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO 80523, U.S.A.

Publication History

  1. Issue published online: 17 APR 2008
  2. Article first published online: 24 AUG 2007
  3. Manuscript Accepted: 18 JUN 2007
  4. Manuscript Received: 9 MAY 2007

Funded by

  • National Science Foundation. Grant Numbers: ECCS-0700559, DMS-0107832, DGE-0221595003, MSPA-CSE-0434354, DMS-0707037, DMS-0504737
  • Department of Energy. Grant Numbers: DE-FG02-04ER25620, DE-FG02-05ER25699
  • National Aeronautics and Space Administration. Grant Number: NNG04GH63G
  • Sandia Corporation. Grant Number: PO299784

SEARCH

SEARCH BY CITATION

ARTICLE TOOLS

Get PDF (668K)

Keywords:

  • continuum modeling of networks;
  • large network modeling;
  • network optimization;
  • nonlinear parabolic problems;
  • wireless ad hoc networks

Abstract

This paper is concerned with the modeling and simulation of extremely large networks. We derive a time-dependent diffusion–convection partial differential equation, the solution of which captures the global characteristics of a stochastic network model. Continuum modeling provides a powerful way to deal with the number of components in large networks and opens up the use of highly sophisticated mathematical tools such as adaptive finite element methods. This, in turn, makes it possible to carry out—with reasonable computational burden even for very large systems—network performance evaluation and prototyping, network design, systematic parameter studies, and optimization of network characteristics. Copyright © 2007 John Wiley & Sons, Ltd.

Get PDF (668K)