Network Cache Design under Stationary Requests: Challenges, Algorithms and Experiments
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The design of caching algorithms to maximize hit probability has been extensively studied. However, the value of high hit probabilities can vary across contents due to differential service requirements. In this paper, we associate each content with a utility, which is a function of the corresponding content hit rate or hit probability. We formulate a cache optimization problem to maximize the sum of utilities over all contents under stationary and ergodic request process, which is non-convex in general. We find that the problem can be reformulated as a convex optimization problem if the inter-request distribution has a non-increasing hazard rate function. We provide explicit optimal solutions for some inter-request distributions, and compare the solutions to the hit-rate based (HRB) and hit-probability based (HPB) problems. We also propose distributed algorithms that not only can adapt to changes in the system with limited information but also provide solutions in a decentralized way. We find that distributed algorithms that solve HRB are more robust than distributed HPB algorithms. Informed by these results, we further propose a lightweight Poisson approximate online algorithm, which is accurate and efficient in achieving exact hit rates and hit probabilities, and also improves the aggregate utilities.
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