Fluid Models for Content Distribution Systems

Content distribution systems (CDS) such as web caches and file sharing systems are large-scale distributed systems that may serve hundreds of thousands of users. These highly dynamic systems exhibit a very large state space which makes them difficult to analyze with classical tools such as Markovian models or simulation. In this thesis we propose macroscopic fluid models to reduce the complexity of these systems. We show that these simple models provide accurate and insightful results on the performance of CDS. In the first part we propose a generic fluid model for distributed caching systems. The idea is to replace cached documents with fluids that increase with unsatisfied requests. Caches may go up and down according to a birth-death process. We apply this model to study two caching systems: cache clusters and a P2P cooperative cache system called Squirrel. We derive an efficient and accurate expression for their hit probabilities and show how the model identifies the key tradeoffs of these systems. We also propose a multiclass approximation for taking into account document popularity. In the second part of the thesis we consider file sharing systems such as BitTorrent. We propose a two-class fluid model which replaces downloaders with fluids. This simple deterministic model may reflect the problem of service differentiation or bandwidth diversity for instance. We provide a closedform expression of the average download time for each class under the worst-case assumption that users leave the system immediately after completing their download. We also show how to allocate peers bandwidth between classes to achieve service differentiation. te l-0 03 62 75 1, v er si on 1 19 F eb 2 00 9