Prefix caching has significant benefits in media delivery systems in terms of reduced startup latency and network traffic. However, with the conventional admission control model, prefix caching may incur some performance penalty. When the media server is heavily loaded and has to deny the client request finally, forwarding a large number of initial frames from proxy to clients can result in dramatic waste of critical network resource. An ideal solution to this problem is to let proxy servers perform the admission control on behalf of the media servers. In this paper, we present a distributed admission control policy. We consider an aggressive disk bandwidth allocation scheme where an agent may, with a certain probability, admit a new request when the current bandwidth used at the agent has reached its limit. We formulate the problem as a min-max optimization problem and provide a MINMAX algorithm to find the solutions. The effectiveness of our algorithm is demonstrated through simulation studies.