Asymptotics of Replication and Matching in Large Caching Systems

We consider a generic model of distributed caching systems, where the cache servers are constrained by two main resources: memory size and bandwidth. Content distribution networks (CDNs) providing video contents and peer-to-peer video-on-demand services are a few examples of such systems. The throughput of these systems crucially depends on how these resources are managed, i.e., how contents are replicated across servers and how requests of specific contents are matched to servers storing the contents. In this paper, we formulate the problem of computing the replication policy and the matching policy, which jointly maximizes the throughput of the caching system. It is shown that computing the optimal replication policy for a given finite system is an NP-hard problem. A greedy replication scheme is then proposed and is shown to achieve a constant factor approximation guarantee when combined with the optimal matching policy. We note that the optimal matching policy has the problem of interruption in service of the ongoing requests due to re-assignment or repacking of the existing requests. To avoid this problem, we propose a simple randomized online matching scheme and analyze its performance in conjunction with the proposed replication scheme. We consider a limiting regime, where the number of servers is large and the arrival rates of the contents are scaled proportionally, and show that the proposed policies achieve asymptotic optimality. Extensive simulation results are presented to evaluate the performance of different policies and study the behavior of the caching system under different service time distributions of the requests.