Online caching is among the most fundamental and well-studied problems in the area of online algorithms. Innovative algorithmic ideas and analysis -- including potential functions and primal-dual techniques -- give insight into this still-growing area. Here, we introduce a new analysis technique that first uses a potential function to upper bound the cost of an online algorithm and then pairs that with a new dual-fitting strategy to lower bound the cost of an offline optimal algorithm. We apply these techniques to the Caching with Reserves problem recently introduced by Ibrahimpur et al. [10] and give an O(log k)-competitive fractional online algorithm via a marking strategy, where k denotes the size of the cache. We also design a new online rounding algorithm that runs in polynomial time to obtain an O(log k)-competitive randomized integral algorithm. Additionally, we provide a new, simple proof for randomized marking for the classical unweighted paging problem.

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