“…Let Q f,m,1:T = (q f,m,1 , ..., q f,m,T ) be a set of samples of the popularity of file f ∈ F , where q f,m,t shows the number of requests for file f submitted to SBS m at time j = 1, ..., T . Assume that the popularity is 8 It is worth noting that in some previous works, for example, in [27] and [24], the authors assume the following: Every SBS observes the cache hits, i.e., the number of requests for the files in the cache, whereas the number of cache drops, i.e., the number of requests for the files that do not belong to the cache, is not observable. However, such an assumption is unnecessary in many cases, where the users submit the requests for files to the corresponding SBS, while not knowing the cache status of the SBS.…”