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Serverless computing is a rapidly growing paradigm that easily harnesses the power of the cloud. With serverless computing, developers simply provide an event-driven function to cloud providers, and the provider seamlessly scales function invocations to meet demands as event-triggers occur. As current and future serverless offerings support a wide variety of serverless applications, effective techniques to manage serverless workloads becomes an important issue. This work examines current management and scheduling practices in cloud providers, uncovering many issues including inflated application run times, function drops, inefficient allocations, and other undocumented and unexpected behavior. To fix these issues, a new quality-of-service function scheduling and allocation framework, called Sequoia, is designed. Sequoia allows developers or administrators to easily def ne how serverless functions and applications should be deployed, capped, prioritized, or altered based on easily configured, flexible policies. Results with controlled and realistic workloads show Sequoia seamlessly adapts to policies, eliminates mid-chain drops, reduces queuing times by up to 6.4X, enforces tight chain-level fairness, and improves run-time performance up to 25X.