Abstract
In this chapter, we use an asymptotic analysis similar to the sphere-packing argument in the proof of Shannon’s channel capacity theorem to derive optimal provisioning requirements for networks with both static and dynamic provisioning. We consider an N-user shared-link model where W s wavelengths are statically assigned to each user, and a common pool of W d wavelengths are available to all users. We derive the minimum values of W s and W d required to achieve asymptotically non-blocking performance as the number of users N becomes large. We also show that it is always optimal to statically provision at least enough wavelengths to support the mean of the traffic.
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Notes
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Portions reprinted, with permission, from “A Geometric Approach to Capacity Provisioning in WDM Networks with Dynamic Traffic”, 40th Annual Conference on Information Sciences and Systems. ©2006 IEEE.
References
R. Ramaswami and K. N. Sivarajan, Optical Networks: A Practical Perspective, Morgan Kaufmann, 1998.
L. Li and A. K. Somani, “Dynamic wavelength routing using congestion and neighborhood information,” IEEE/ACM Trans. Networking, vol. 7, pp. 779–786, October 1999.
A. Birman, “Computing approximate blocking probabilities for a class of all-optical networks,” IEEE J. Select. Areas Commun., vol. 14, no. 5, pp. 852–857, June 1996.
O. Gerstel, G. Sasaki, S. Kutten, and R. Ramaswami, “Worst-case analysis of dyanmic wavelength allocation in optical networks,” IEEE/ACM Trans. Networking, vol. 7, pp. 833–845, December 1999.
T. Cover and J. Thomas, Elements of Information Theory, Wiley-Interscience, 1991.
R. Guerin and L. Y.-C. Lien, “Overflow analysis for finite waiting-room systems,” IEEE Trans. Commun., vol. 38, pp. 1569–1577, September 1990.
R. I. Wilkinson, “Theories of toll traffic engineering in the U.S.A.,” Bell Syst. Tech. J., vol. 35, pp. 412–514, March 1956.
R. B. Cooper, Introduction to Queueing Theory, 2nd Ed., North Holland, New York, 1981.
D. A. Garbin M. J. Fischer and G. W. Swinsky, “An enhanced extension to wilkinson’s equivalent random technique with application to traffic engineering,” IEEE Trans. Commun., vol. 32, pp. 1–4, January 1984.
A. A. Fredericks, “Congestion in blocking systems - a simple approximation technique,” Bell Syst. Tech. J., vol. 59, pp. 805–827, July-August 1980.
Acknowledgement
This work was supported in part by NSF grants ANI-0073730, ANI-0335217, and CNS-0626781.
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Chen, LW., Modiano, E. (2010). Geometric Capacity Provisioning for Wavelength-Switched WDM Networks. In: Cormode, G., Thottan, M. (eds) Algorithms for Next Generation Networks. Computer Communications and Networks. Springer, London. https://doi.org/10.1007/978-1-84882-765-3_3
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DOI: https://doi.org/10.1007/978-1-84882-765-3_3
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