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Shared storage services enjoy wide adoption in commercial clouds. But most systems today provide weak performance isolation and fairness between tenants, if at all. Most approaches to multi-tenant resource allocation are based either on per-VM allocations or hard rate limits that assume uniform workloads to achieve high utilization. Instead, Pisces, our system for shared key-value storage, achieves datacenterwide per-tenant performance isolation and fairness. Pisces achieves per-tenant weighted fair sharing of system resources across the entire shared service, even when partitions belonging to different tenants are co-located and when demand for different partitions is skewed or timevarying. The focus of this paper is to highlight the optimization model that motivates the decomposition of Pisces's fair sharing problem into four complementary mechanisms--- partition placement, weight allocation, replica selection, and weighted fair queuing---that operate on different time-scales to provide system-wide max-min fairness. An evaluation of our Pisces storage prototype achieves nearly ideal (0.98 Min- Max Ratio) fair sharing, strong performance isolation, and robustness to skew and shifts in tenant demand.