Abstract
We apply mean-field analysis to compute global availability in large networks of generalized SIS and voter models. The main results provide comparison and bounding techniques of the global availability depending on the local degree structure of the networks.
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References
Anderson, H., Britton, T.: Stochastic Epedemic Models and Their Statistical Analysis. Lecture Notes in Statistics. Springer, New York (2000)
Bailey, N.J.: The Mathematical Theory of Infectiuos Diseases and Its Applications. Hafner Press, New York (1975)
Barrat, A., Barthelemy, M., Vespignani, A.: Daynamical Processes on Complex Networks. Cambridge University Press, Cambridge (2008)
Bakhshi, R., Cloth, L., Fokking, W., Haverkoert, B.R.: Mean-field analysis for the evaluation of gossip protocols. In: Proceedings of the Sixth International Conference on Quantitative Evaluation of Systems, pp. 247–256. IEEE Computer Society (2009)
Bakhshi, R., Cloth, L., Fokking, W., Haverkoert, B.R.: Mean-field framework for performance evaluation of push-pull gossip protocols. Performance Analysis 68, 157–179 (2011)
Bakhshi, R., Gavidia, D., Fokking, W., van Steen, M.: An analytical model of information dissemination for a gossip-based protocol. Computer Networks 53, 2288–2303 (2009)
Boudec, J.-Y., McDonald, D., Mundinger, J.: A generic mean field convergence result for systems of interacting objects. In: Proceedings of the Fourth International Conference on Quantitative Evaluation of Systems, pp. 3–15. IEEE Computer Society (2007)
Chakka, R., Mitrani, I.: Approximate solutions for open networks with breakdowns and repairs. In: Kelly, F.P., Zachary, S., Ziedins, I. (eds.) Stochastic Networks, Theory and Applications. Royal Statistical Society Lecture Notes Series, vol. 4, ch. 16, pp. 267–280. Clarendon Press, Oxford (1996)
Daley, D.J., Gani, J.: Epidemic Modelling: An Introduction. Cambridge University Press, Cambridge (2001)
Dorogovtsev, S.N., Mendes, J.F.F.: Evolution of Networks. Oxford University Press, Oxford (2003) (reprint 2004)
Draief, M., Massoulie, L.: Epidemics and Rumours in Complex Networks. London Mathematical Society Lecture Note Series, vol. 369. Cambridge University Press, Cambridge (2010)
Daduna, H., Pestien, V., Ramakrishnan, S.: Throughput limits from the asymptotic profile of cyclic networks with state-dependent service rates. Queueing Systemes and Their Applications 58, 191–219 (2008)
Haverkort, B.R., Marie, R., Rubino, G., Trivedi, K.: Performability Modeling, Technique and Tools. Wiley, New York (2001)
Jackson, M.O.: Social and Economic Networks. Princeton University Press, Princeton (2008)
Jackson, M.O., Rogers, B.W.: Relating network structure to diffusion properties through stochastic dominance. The B.E. Journal of Theoretical Economics 7(1), 1–13 (2007)
Jackson, M.O., Yariv, L.: Diffusion of behavior and equilibrium properties in network games. American Economical Review (Papers and Proceedings) 97, 92–98 (2007)
Lamberson, P.J.: Linking network structure and diffusion through stochastic dominance. In: Complex Adaptive Systems and the Threshold Effects: Views from the Natural and Social Sciences, pp. 76–82. Association for the Advancement of Artificial Intelligence (2009); Papers from the AAAI Fall Symposium: FS-09-03
Liggett, T.M.: Interacting Particle Systems. Grundlehren der mathematischen Wissenschaften, vol. 276. Springer, Berlin (1985)
Lopez-Pintado, D.: Contagion and coordination in random networks. International Journal of Game Theory 34, 371–381 (2006)
Lopez-Pintado, D.: Diffusion in complex social networks. GAMES and Economic Behavior 62, 573–590 (2008)
Müller, A., Stoyan, D., Liggett, T.M.: Comparison Methods for Stochastic Models and Risks. Wiley, Chichester (2002)
Pinski, E., Yemini, Y.: A statistical mechanics of some interconnetion networks. In: Gelenbe, E. (ed.) Performance 1984, pp. 147–158. North-Holland, Amsterdam (1984)
Sauer, C.: Stochastic product form networks with unreliable nodes: Analysis of performance and availability. PhD thesis, University of Hamburg, Department of Mathematics (2006)
Sauer, C., Daduna, H.: Availability formulas and performance measures for separable degradable networks. Economic Quality Control 18, 165–194 (2003)
Wang, Y., Dang, H., Wu, H.: A survey on analytic studies of Delay-Tolerant Mobile Sensor Networks. Wireless Communications and Mobile Computing 7, 1197–1208 (2007)
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Daduna, H., Saul, L.P. (2012). Availability in Large Networks: Global Characteristics from Local Unreliability Properties. In: Schmitt, J.B. (eds) Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance. MMB&DFT 2012. Lecture Notes in Computer Science, vol 7201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28540-0_1
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DOI: https://doi.org/10.1007/978-3-642-28540-0_1
Publisher Name: Springer, Berlin, Heidelberg
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