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Caches are a fundamental component of latency-sensitive computer systems.Recent work of [ASWB20] has initiated the study of delayed hits: a phenomenonin caches that occurs when the latency between the cache and backing store ismuch larger than the time between new requests. We present two results for thedelayed hits caching model.  (1) Competitive ratio lower bound. We prove that the competitive ratio of thealgorithm in [ASWB20], and more generally of any deterministic online algorithmfor delayed hits, is at least Omega(kZ), where k is the cache size and Z is thedelay parameter.  (2) Antimonotonicity of the delayed hits latency. Antimonotonicity is anaturally desirable property of cache latency: having a cache hit instead of acache miss should result in lower overall latency. We prove that the latency ofthe delayed hits model is not antimonotone by exhibiting a scenario wherehaving a cache hit instead of a miss results in an increase in overall latency.We additionally present a modification of the delayed hits model that makes thelatency antimonotone.

Lower Bounds for Caching with Delayed Hits