Abstract
Mobility models that have been used in the past to study delay tolerant networks (DTNs) have been either too complex to allow for deriving analytical expressions for performance measures, or have been too simplistic. In this paper we identify several classes of DTNs where the dynamics of the number of nodes that have a copy of some packet can be modeled as branching process with migration. Using recent results on such processes in a random environment, we obtain explicit formulae for the first two moments of the number of copies of a file that is propagated in the DTN, for quite general mobility models. Numerical examples illustrate our approach.
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Adke, S.R., Gadag, V.G.: A new class of branching processes. In: Heyde, C.C. (ed.) Branching Processes: Proceedings of the First World Congress. Springer Lecture Notes, vol. 99, pp. 1–13 (1995)
Albertsen, K.: The Extinction of Families. International Statistical Review/Revue Internationale de Statistique 63(2), 234–239 (1995)
Altman, E.: Competition and cooperation between nodes in Delay Tolerant Networks with Two Hop Routing. In: Proceedings of Netcoop 2009, Eindhoven, The Netherlands (November 2009)
Altman, E., Fiems, D.: Expected waiting time in polling systems with correlated vacations. Queueing Systems 56(3-4), 241–253 (2007)
Athreya, K., Vidyashankar, A.: Branching Processes. In: Maddala, G., Rao, C., Vinod, H. (eds.) Handbook of Statistics, ch. 2, vol. 19. Elsevier Science B.V., Amsterdam (2001)
Bienaymé, I.J.: De la loi de la multiplication et de la durée des familles. Soc. Philomath., Paris Extraits Ser. 5, 37–39 (1845)
Bertoin, J.: Lévy Processes. Cambridge University Press, Cambridge (2002)
Cerf, V., et al.: Delay-tolerant network architecture. IETF RFC 4838
D’Auria, B.: M/M/∞ queues in semi-markovian random environment. Queueing Systems 58(3), 221–237 (2008)
Eliazar, I.: On the discrete-time G/GI/ ∞ queue. Technical report, Holon Institute of Technology (2006)
Fall, K.: A delay-tolerant network architecture for challenged internets. In: Proceedings of SIGCOMM 2003, pp. 27–34 (2003)
Falin, G.: The M/M/∞ queue in a random environment. Queueing Systems 58(1), 65–76 (2008)
Fiems, D., Altman, E.: Markov-modulated stochastic recursive equations with applications to delay-tolerant networks. INRIA Research Report No. 6872 (2009); Submitted to Performance Evaluation
Galton, F.: Problem 4001. Educational Times April 1 (17) (1873)
Galton, F., Watson, H.W.: On the probability of the extinction of the families. J. Royal Antropol. Soc., London 4, 138–144 (1874)
Garetto, M., Giaccone, P., Leonardi, E.: On the effectiveness of the 2-hop routing strategy in mobile ad hoc networks. In: Proceedings of ICC 2007 (2007)
Grishechkin, S.A.: On a relation between processor sharing queues and Crump-Mode-Jagers branching processes. Advances in Applied Probability 24, 653–698 (1992)
Helgason, O., Karlsson, G.: On the effect of cooperation in wireless content distribution. In: Proceedings of WONS 2008 (2008)
Heyde, C.C., Senneta, E.: Studies in the History of Probability and Statistics. XXXI. The simple branching process, a turning point test and a fundamental inequality: A historical note on I. J. Bienaymé, Biometrika 59(3), 680–683 (1972)
Key, E.: Limiting distributions and regeneration times for multitype branching processes with immigration in a random environment. Annals of Probability 15, 344–353 (1987)
Lambert, A.: The genealogy of continuous-state branching processes with immigration. Journal of Probability Theory and Related Fields 122(1), 42–70 (2002)
Le Gall, J.F.: Random trees and spatial branching processes. Maphysto Lecture Notes Series (Univ of Aarhus), vol. 9 (2000)
McNamara, J., Houston, A., Collins, E.: Optimality models in behavioral biology. SIAM Review 43(3), 413–466 (2001)
Núñez Queija, R.: Processor-Sharing Models for Integrated-Services Networks. PhD thesis, Eindhoven University of Technology (2000)
Resing, J.: Polling systems and multi-type branching processes. Queueing Systems 13, 409–426 (1993)
Roitershtein, A.: A note on multitype branching processes with immigration in a random environment. Annals of Probability 35(4), 1573–1592 (2007)
Watson, H.W.: Solution to problem 4001. Educational Times August 1, 115–116 (1873)
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Fiems, D., Altman, E. (2010). Applying Branching Processes to Delay-Tolerant Networks. In: Altman, E., Carrera, I., El-Azouzi, R., Hart, E., Hayel, Y. (eds) Bioinspired Models of Network, Information, and Computing Systems. BIONETICS 2009. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 39. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12808-0_11
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DOI: https://doi.org/10.1007/978-3-642-12808-0_11
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