Abstract
In this paper we present an approach to compute the invariant vector of the N + 1 state Markov chain P presented in (Rogiest et al., Lecture Notes in Computer Science, NET-COOP 2007 Special Issue, pp. 4465:185-194) to determine the loss rate of an FDL buffer consisting of N lines, by solving a related Hessenberg system (i.e., a Markov chain skip-free in one direction). This system is obtained by inserting additional time instants in the sample paths of P and allows us to compute the loss rate for various FDL lengths by solving a single system. This is shown to be especially effective in reducing the computation time of the heuristic LRA algorithm presented in (Lambert et al., Proc. NAEC 2005, pp. 545-555) to optimize the FDL lengths, where improvements of several orders of magnitude can be realized.
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Almeida, R.C., Pelegrini, J.U., Waldman, H.: A generic-traffic optical buffer modeling for asynchronous optical switching networks. Communications Letters, IEEE 9(2), 175–177 (2005)
Callegati, F.: Optical buffers for variable length packet switching. IEEE Communications Letters 4, 292–294 (2000)
Chlamtac, et al.: CORD: Contention resolution by delay lines. IEEE Journal on Selected Areas in Communications 14, 1014–1029 (1996)
Haas, Z.: The staggering switch: An electronically controlled optical packet switch. Journal on Lightwave Technology 11, 925–936 (1993)
Hong, D., Poppe, F., Reynier, J., Bacelli, F., Petit, G.: The impact of burstification on TCP throughput in optical burst switching networks. In: Proc. of the 18th International Teletraffic Congress (ITC), Berlin, Germany (September 2003)
Van Houdt, B., Laevens, K., Lambert, J., Blondia, C., Bruneel, H.: Channel utilization and loss rate in a single-wavelength fibre delay line (FDL) buffer. In: Proceedings of IEEE Globecom 2004, paper OC05-07, Dallas, USA (November 2004)
Hunter, D., Andonovic, I.: Approaches to optical Internet packet switching. IEEE Communications Magazine 38(9), 116–120 (2000)
Hunter, D., Cornwell, W.D., Gilfedder, T.H., Franzen, A., Andonovic, I.: SLOB: A switch with large optical buffers for packet switching. IEEE/OSA Journal on Lightwave Technology 16, 1725–1736 (1998)
Laevens, K., Bruneel, H.: Analysis of a single wavelength optical buffer. In: Proceedings of Infocom, San Francisco (April 2003)
Lambert, J., Van Houdt, B., Blondia, C.: Single-wavelength optical buffers: non-equidistant structures and preventive drop mechanisms. In: Proceedings of NAEC 2005, Riva del Garda, pp. 545–555 (2005)
Qiao, J., Yoo, M.: Optical burst switching: A new paradigm for an optical Internet. Journal on High-Speed Networks 8, 69–84 (1999)
Rogiest, W., Fiems, D., Laevens, K., Bruneel, H.: Tracing an optical buffer’s performance: An effective approach. In: Chahed, T., Tuffin, B. (eds.) NET-COOP 2007. LNCS, vol. 4465, pp. 185–194. Springer, Heidelberg (2007)
Turner, J.: Terabit burst switching. Journal on High-Speed Networks 8, 3–16 (1999)
Xiong, Y., Vandenhoute, M., Chankaya, H.: Control architecture in optical burst-switched WDM-networks. IEEE Journal on Selected Areas in Communications 18, 1838–1851 (2000)
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Lambert, J., Rogiest, W., Van Houdt, B., Fiems, D., Blondia, C., Bruneel, H. (2008). A Hessenberg Markov Chain for Fast Fibre Delay Line Length Optimization. In: Al-Begain, K., Heindl, A., Telek, M. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2008. Lecture Notes in Computer Science, vol 5055. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68982-9_8
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DOI: https://doi.org/10.1007/978-3-540-68982-9_8
Publisher Name: Springer, Berlin, Heidelberg
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