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Janus is a system for partitioning the flash storage tier between workloads in a cloud-scale distributed file system with two tiers, flash storage and disk. The file system stores newly created files in the flash tier and moves them to the disk tier using either a First-In-First-Out (FIFO) policy or a Least-Recently-Used (LRU) policy, subject to per-workload allocations. Janus constructs compact metrics of the cacheability of the different workloads, using sampled distributed traces because of the large scale of the system. From these metrics, we formulate and solve an optimization problem to determine the flash allocation to workloads that maximizes the total reads sent to the flash tier, subject to operator-set priorities and bounds on flash write rates. Using measurements from production workloads in multiple data centers using these recommendations, as well as traces of other production workloads, we show that the resulting allocation improves the flash hit rate by 47-76% compared to a unified tier shared by all workloads. Based on these results and an analysis of several thousand production workloads, we conclude that flash storage is a cost-effective complement to disks in data centers.