Optimal policy for batch operations: backup, checkpointing, reorganization, and updating

Many database maintenance operations are performed periodically in batches, even in real-time systems. The purpose of this paper is to present a general model for determining the optimal frequency of these batch operations. Specifically, optimal backup, checkpointing, batch updating, and reorganization policies are derived. The approach used exploits inventory parallels, by seeking the optimal number of items --- rather than a time interval --- to trigger a batch. The Renewal Reward Theorem is used to find the average long run costs for backup, recovery, and item storage, per unit time, which is then minimized to find the optimal backup policy. This approach permits far less restrictive assumptions about the update arrival process than did previous models, as well as inclusion of storage costs for the updates. The optimal checkpointing, batch updating, and reorganization policies are shown to be special cases of this optimal backup policy. The derivation of previous results as special cases of this model, and an example, demonstrate the generality of the methodology developed.