Abstract
We apply stochastic bounding methods with a partial order on the state space to the analysis of memory overflow in a router. Usually, stochastic bounds are associated to a total order implying useless constraints and decreasing the tightness of bounds. Here we present the basic methodology of sample path comparison with a partial order and some numerical results to show the accuracy of the results. We analyze the probability of a buffer overflow with two types of packets, a Pushout access mechanism and Markov modulated batch arrivals. This problem is strongly related to the memory rejection out a Fiber Delay Loop in an all optical router using deflection routing.
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References
Barth, D., Berthomé, P., Borrero, A., Fourneau, J.M., Laforest, C., Quessette, F., Vial, S.: Performance comparisons of Eulerian routing and deflection routing in a 2d-mesh all optical network. In: European Simulation Multiconference (2001)
Dayar, T., Pekergin, N., Alparslan, D.N.: Componentwise bounds for nearly completely decomposable Markov chains using stochastic comparison and reordering. European Journal of Operational Research 165, 810–825 (2005)
Doisy, M.: Comparison de Processus Markoviens. Ph-D thesis Univ. de Pau (1992)
Fourneau, J.M., Pekergin, N.: An algorithmic approach to stochastic bounds. In: Calzarossa, M.C., Tucci, S. (eds.) Performance 2002. LNCS, vol. 2459, pp. 64–88. Springer, Heidelberg (2002)
Fourneau, J.M., Lecoz, M., Quessette, F.: Algorithms for an irreducible and lumpable strong stochastic bound. Linear Algebra and Applications 386, 167–185 (2004)
Gravey, P., Gosselin, S., Guillemot, C., Chiaroni, D., Le Sauze, N., Jourdan, A., Dotaro, E., Barth, D., Berthomé, P., Laforest, C., Vial, S., Atmaca, T., Hébuterne, G., El Biaze, H., Laalaoua, R., Gangloff, E., Kotuliak, I.: Multiservice optical network: Main concepts and first achievements of the ROM program. Journal of Ligthwave Technology 19, 23–31 (2001)
Massey, W.: Stochastic Ordering for Markov Processes on Partially ordered Spaces. Mathematics of operations Research 12 (1987)
Stoyan, D.: Comparison Methods for Queues and Other Stochastic Models. Wiley, New York (1983)
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Castel-Taleb, H., Fourneau, J.M., Pekergin, N. (2005). Stochastic Bounds on Partial Ordering: Application to Memory Overflows Due to Bursty Arrivals. In: Yolum, p., Güngör, T., Gürgen, F., Özturan, C. (eds) Computer and Information Sciences - ISCIS 2005. ISCIS 2005. Lecture Notes in Computer Science, vol 3733. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11569596_27
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DOI: https://doi.org/10.1007/11569596_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29414-6
Online ISBN: 978-3-540-32085-2
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