  Several real-time delay-sensitive applications pose varying degrees of
freshness demands on the requested content. The performance of cache
replacement policies that are agnostic to these demands is likely to be
sub-optimal. Motivated by this concern, in this paper, we study caching
policies under a request arrival process which incorporates user freshness
demands. We consider the performance metric to be the steady-state cache hit
probability. We first provide a universal upper bound on the performance of any
caching policy. We then analytically obtain the content-wise hit-rates for the
Least Popular (LP) policy and provide sufficient conditions for the asymptotic
optimality of cache performance under this policy. Next, we obtain an accurate
approximation for the LRU hit-rates in the regime of large content population.
To this end, we map the characteristic time of a content in the LRU policy to
the classical Coupon Collector's Problem and show that it sharply concentrates
around its mean. Further, we develop modified versions of these policies which
eject cache redundancies present in the form of stale contents. Finally, we
propose a new policy which outperforms the above policies by explicitly using
freshness specifications of user requests to prioritize among the cached
contents. We corroborate our analytical insights with extensive simulations.
