The Population Dynamics of File-Sharing Peer-to-Peer Networks

Abstract

Recently  peer-to-peer  file-sharing applications  have  shown  an  extreme  popularity  and the  workload  generated  to  the  Internet  has  been dominated  by  the  traffic  coming  from  these applications.  In  this  paper  we  develop  a  simple  but effective  mathematical  model  to  capture  the  file population  dynamics  of  such  systems.  Our  modeling framework  is  based  on  the  theory  of  branching processes. We describe analytically the behavior of the proposed  model.  The  precise  characterization  of  the necessary  and  sufficient  conditions  of  population extinction  or  explosion  is  given  based  on  the  system parameters.  We  also  present  the  expected  ratio  of active,  passive  and  dead  peers  for  the  long-term regime.  We  validate  and  demonstrate  our  results  in several  simulation  studies.  Based  on  our  results  we propose  a  number  of  engineering  guidelines  to  the design and control of file-sharing P2P systems.