Abstract
Currently there is much interest in networks. This includes queueing network models of manufacturing systems, as well as wired and wireless networks used for communication. At their heart, networks too are just dynamical systems, often stochastic, nonlinear, and distributed. Many of the issues of interest for such systems can be said to be what they have always been for dynamical and controlled dynamical systems — stability, stabilizability, performance analysis, and optimal control. We illustrate this with respect to problems of much contemporary attention, by examining the stability problem for re-entrant lines, and the determination of the information theoretic capacity of wireless networks. We illustrate how the modem emphasis in the former area is on computational proofs of stability, and in the latter area is in the establishment of scaling laws.
This material is based upon work partially supported by USARO under Contract Nos. DAAD19-00-1-0466 and DAAD19-01010-465, DARPA under Contract No. N00014-01-1-0576, AFOSR under Contract No. F49620-02-1-0217, DARPA/AFOSR under Contract No. F49620-02-1-0325, and NSF under Contract No. NSF ANI 02-21357. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the above agencies.
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Kumar, P.R. (2003). The Distributed Nonlinear Stochastic World of Networks. In: Namachchivaya, N.S., Lin, Y.K. (eds) IUTAM Symposium on Nonlinear Stochastic Dynamics. Solid Mechanics and Its Applications, vol 110. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0179-3_17
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DOI: https://doi.org/10.1007/978-94-010-0179-3_17
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