Keep-Alive Caching for the Hawkes process

TL;DR

This paper introduces a caching model for serverless computing that balances cache retention costs and miss costs, deriving optimal and near-optimal policies for Hawkes processes and validating them with simulations and real data.

Contribution

It develops a novel caching framework for non-fixed size caches, providing a closed-form solution for Hawkes processes and practical policies that perform near-optimally.

Findings

Optimal policies outperform heuristic approaches.

Near-optimal policies achieve performance close to the optimal.

Simulation and real data validate the effectiveness of the proposed policies.

Abstract

We study the design of caching policies in applications such as serverless computing where there is not a fixed size cache to be filled, but rather there is a cost associated with the time an item stays in the cache. We present a model for such caching policies which captures the trade-off between this cost and the cost of cache misses. We characterize optimal caching policies in general and apply this characterization by deriving a closed form for Hawkes processes. Since optimal policies for Hawkes processes depend on the history of arrivals, we also develop history-independent policies which achieve near-optimal average performance. We evaluate the performances of the optimal policy and approximate polices using simulations and a data trace of Azure Functions, Microsoft's FaaS (Function as a Service) platform for serverless computing.