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## Model Memory Requirements

The amount of memory required in our current implementation is directly proportional to the number of nodes in our trie. On average a second order model required 238,200 nodes. Since our implementation required 16 bytes per node, the memory required by a third order model should be well under four megabytes. While this model takes almost as much memory as the cache it models, we note that this additional four megabytes seems negligible when compared to the additional 86 megabytes that would be required for an LRU cache to see equivalent performance. It should also be noted that model size is independent of cache size, therefore a 32 megabyte predictive cache would still require less than four megabytes of model space.

Additionally, in our initial implementation we have made no effort to efficiently use memory in our model. We intend to expand on methods used successfully in the compression technique DAFC [13], to limit the number of children that each node in our context model has, and to periodically refresh parts of the set of children by releasing links taken up by less frequently seen children. We expect that this modification will not only significantly reduce the memory requirements of our model, but will also allow it to adapt to patterns of local activity. Limiting the number of children a node can have will also ensure that the time required to update our model and predict new accesses is limited to a constant factor.