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The design of caching algorithms to maximize hit probability has beenextensively studied. In this paper, we associate each content with a utility,which is a function of either the corresponding content hit rate or hitprobability. We formulate a cache optimization problem to maximize the sum ofutilities over all contents under stationary and ergodic request processes.This problem is non-convex in general but we reformulate it as a convexoptimization problem when the inter-request time (irt) distribution has anon-increasing hazard rate function. We provide explicit optimal solutions forsome irt distributions, and compare the solutions of the hit-rate based (HRB)and hit-probability based (HPB) problems. We formulate a reverse engineeringbased dual implementation of LRU under stationary arrivals. We also proposedecentralized algorithms that can be implemented using limited information anduse a discrete time Lyapunov technique (DTLT) to correctly characterize theirstability. We find that decentralized algorithms that solve HRB are more robustthan decentralized HPB algorithms. Informed by these results, we furtherpropose lightweight Poisson approximate decentralized and online algorithmsthat are accurate and efficient in achieving optimal hit rates and hitprobabilities.

Network Cache Design under Stationary Requests: Exact Analysis and Poisson Approximation