Continuum modeling of large networks

Authors:
Edwin K. P. Chong;Donald Estep;Jan Hannig
Affiliations:
Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO 80523, U.S.A.;Department of Mathematics and Department of Statistics, Colorado State University, Fort Collins, CO 80523, U.S.A.;Department of Statistics, Colorado State University, Fort Collins, CO 80523, U.S.A.
Venue:
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Year:
2008

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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.