  Caching is an effective mechanism for reducing bandwidth usage and
alleviating server load. However, the use of caching entails a compromise
between content freshness and refresh cost. An excessive refresh allows a high
degree of content freshness at a greater cost of system resource. Conversely, a
deficient refresh inhibits content freshness but saves the cost of resource
usages. To address the freshness-cost problem, we formulate the refresh
scheduling problem with a generic cost model and use this cost model to
determine an optimal refresh frequency that gives the best tradeoff between
refresh cost and content freshness. We prove the existence and uniqueness of an
optimal refresh frequency under the assumptions that the arrival of content
update is Poisson and the age-related cost monotonically increases with
decreasing freshness. In addition, we provide an analytic comparison of system
performance under fixed refresh scheduling and random refresh scheduling,
showing that with the same average refresh frequency two refresh schedulings
are mathematically equivalent in terms of the long-run average cost.
