  In this paper, we design dynamic probabilistic caching for the scenario when
the instantaneous content popularity may vary with time while it is possible to
predict the average content popularity over a time window. Based on the average
content popularity, optimal content caching probabilities can be found, e.g.,
from solving optimization problems, and existing results in the literature can
implement the optimal caching probabilities via static content placement. The
objective of this work is to design dynamic probabilistic caching that: i)
converge (in distribution) to the optimal content caching probabilities under
time-invariant content popularity, and ii) adapt to the time-varying
instantaneous content popularity under time-varying content popularity.
Achieving the above objective requires a novel design of dynamic content
replacement because static caching cannot adapt to varying content popularity
while classic dynamic replacement policies, such as LRU, cannot converge to
target caching probabilities (as they do not exploit any content popularity
information). We model the design of dynamic probabilistic replacement policy
as the problem of finding the state transition probability matrix of a Markov
chain and propose a method to generate and refine the transition probability
matrix. Extensive numerical results are provided to validate the effectiveness
of the proposed design.
