×

Continuum modeling of large networks. (English) Zbl 1138.90342

Summary: 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.

MSC:

90B10 Deterministic network models in operations research
90B15 Stochastic network models in operations research
90B18 Communication networks in operations research
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Gupta, IEEE Transactions on Information Theory IT-46 pp 388– (2000)
[2] Grossglauser, IEEE/ACM Transactions on Networking 10 pp 477– (2002)
[3] Xie, IEEE Transactions on Information Theory 50 pp 748– (2004)
[4] . Throughput-storage tradeoff in ad hoc networks. Proceedings of the 2005 IEEE INFOCOM, Miami, Florida, March 2005.
[5] DASensors and Sensor Networks Program Solicitation NSF 03-512. http://www.nsf.gov/pubs/2003/nsf03512/nsf03512.htm
[6] . Scaling laws for homogeneous sensor networks. Forty-First Annual Allerton Conference on Communication, Control and Computers, Monticello, IL, 2003.
[7] Gamal, IEEE Transactions on Information Theory 51 pp 1229– (2005)
[8] . An Introduction to Optimization (2nd edn). Wiley: New York, NY, 2001. · Zbl 1056.90129
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.