Optimal policies for control of peers in online multimedia services

In this paper we consider a distributed peer-based system with a centralized controller responsible for managing the peers. For this system customers request large volumes of information such as video clips which instead of retrieving from a centralized repository of a parent organization are obtained from peers that possess the clips. Peers act as servers only for a short duration and therefore the parent organization (i.e. centralized controller) would need to add new peer servers from time to time. This centralized "admission" control of deciding whether or not to admit a customer with a video clip as a peer based on the system state (number of waiting requests and number of existing peers) is the crux of this research. The problem can be posed as a discrete stochastic optimal control and is formulated using a Markov decision process approach with infinite horizon and discounted cost/reward. We show that a stationary threshold policy in terms of the state of the system is optimal. In other words the optimal decision whether or not to accept a customer as a peer server is characterized by a switching curve. In typical Markov decision processes, it is extremely difficult to derive an analytical expression for the switching curve. However, using an asymptotic analysis, by suitably scaling time and states taking fluid limits, we show how this can be done for our problem. In addition, the asymptotic analysis can also be used to show that the switching curve is independent of the model parameters such as customer arrival rate, downloading times and peer-server lifetimes. Several numerical results are presented to support the analytical claims based on asymptotic analysis.