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1 GYROWEB - Dynamic graphs and the web graph Inria Paris-Rocquencourt 2 FT R&D - France Télécom Recherche & Développement 3 LIAFA - Laboratoire d-informatique Algorithmique : Fondements et Applications 4 LIENS - Laboratoire d-informatique de l-école normale supérieure

Abstract : We investigate stratification, an intrinsic property of resource trading in large scale distributed systems. Stratification arose in measurements and analytical studies performed on many different P2P filesharing networks. Stratification is the social trend of collaborating with one-s equal. In this article stratification is shown both formally and trough simulations whenever a global ranking agreement exists: in the extreme case where everyone knows everybody and collaborate with one only peer, the best peer will collaborate with the second, the third with the forth, and so on

. We extend this to peers with multiple connections and partial awareness of other peers. Limited awareness of the system leads to amazing border effects, such as best peers being spoiled by very good peers and bad peers having difficulties to establish collaborations. Our results have a wide application area. As an example we apply them to BitTorrent protocol: they explain the way bandwidth is shared in the post-flash crowd phase; They give insights on the way the number of uploading slots can be tuned; Lastly, they stress out advantages and inconveniences for possible incentive variations.

Autor: Anh-Tuan Gai - Fabien Mathieu - Fabien De Montgolfier - Julien Reynier -



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