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.

翻译：我们研究在无服务器计算等应用场景中的缓存策略设计问题。此类场景下，缓存并非拥有固定容量，而是与项目在缓存中驻留的时间存在关联成本。我们提出一种能够刻画缓存成本与缓存未命中成本之间权衡关系的缓存策略模型。我们刻画了一般情形下的最优缓存策略，并通过推导霍克斯过程的闭式解来应用该刻画结果。由于霍克斯过程的最优策略依赖于到达历史记录，我们还开发了能够实现接近最优平均性能的历史无关策略。我们通过模拟实验以及微软FaaS（函数即服务）无服务器计算平台Azure Functions的数据轨迹，评估了最优策略与近似策略的性能表现。