  Caching systems have long been crucial for improving the performance of a
wide variety of network and web based online applications. In such systems,
end-to-end application performance heavily depends on the fraction of objects
transferred from the cache, also known as the cache hit probability. Many
caching policies have been proposed and implemented to improve the hit
probability. In this work, we propose a new method to compute an upper bound on
hit probability for all non-anticipative caching policies, i.e., for policies
that have no knowledge of future requests. Our key insight is to order the
objects according to the ratio of their Hazard Rate (HR) function values to
their sizes and place in the cache the objects with the largest ratios till the
cache capacity is exhausted. Under some statistical assumptions, we prove that
our proposed HR to size ratio based ordering model computes the maximum
achievable hit probability and serves as an upper bound for all
non-anticipative caching policies. We derive closed form expressions for the
upper bound under some specific object request arrival processes. We also
provide simulation results to validate its correctness and to compare it to the
state-of-the-art upper bounds. We find it to be tighter than state-of-the-art
upper bounds for a variety of object request arrival processes.
