The stable configuration in acyclic preference-based systems
  Acyclic preferences recently appeared as an elegant way to model many distributed systems. An acyclic instance admits a unique stable configuration, which can reveal the performance of the system. In this paper, we give the statistical properties of the stable configuration for three classes of acyclic preferences: node-based preferences, distance-based preferences, and random acyclic systems. Using random overlay graphs, we prove using mean-field and fluid-limit techniques that these systems have an asymptotically continuous independent rank distribution for a proper scaling, and the analytical solution is compared to simulations. These results provide a theoretical ground for validating the performance of bandwidth-based or proximity-based unstructured systems. 
Fabien Mathieu (INRIA Rocquencourt, FT R&D, INRIA Rocquencourt),   Gheorghe Postelnicu, Julien Reynier (INRIA Rocquencourt)