Modelling TTL-based Internet Caches

This paper presents a way of modeling the hit rates of caches that use a time-to-live (TTL)-based consistency policy. TTL-based consistency, as exemplified by DNS and Web caches, is a policy in which a data item, once retrieved, remains valid for a period known as the “time-to-live”. Cache systems using large TTL periods are known to have high hit rates and scale well, but the effects of using shorter TTL periods are not well understood. We model hit rate as a function of request arrival times and the choice of TTL, enabling us to better understand cache behavior for shorter TTL periods. Our formula for the hit rate is closed form and relies upon a simplifying assumption about the inter-arrival times of requests for the data item in question: that these requests can be modeled as a sequence of independent and identically distributed random variables. Analyzing extensive DNS traces, we find that the results of the formula match observed statistics surprisingly well; in particular, the analysis is able to adequately explain the somewhat counterintuitive empirical finding of Jung et al. [1] that the cache hit rate for DNS accesses rapidly increases as a function of TTL, exceeding 80% for a TTL of 15 minutes.