The increased use of micro-services to build web applications has spurred the rapid growth of Function-as-a-Service (FaaS) or serverless computing platforms. While FaaS simplifies provisioning and scaling for application developers, it introduces new challenges in resource management that need to be handled by the cloud provider. Our analysis of popular serverless workloads indicates that schedulers need to handle functions that are very short-lived, have unpredictable arrival patterns, and require expensive setup of sandboxes. The challenge of running a large number of such functions in a multi-tenant cluster makes existing scheduling frameworks unsuitable. We present Archipelago, a platform that enables low latency request execution in a multi-tenant serverless setting. Archipelago views each application as a DAG of functions, and every DAG in associated with a latency deadline. Archipelago achieves its per-DAG request latency goals by: (1) partitioning a given cluster into a number of smaller worker pools, and associating each pool with a semi-global scheduler (SGS), (2) using a latency-aware scheduler within each SGS along with proactive sandbox allocation to reduce overheads, and (3) using a load balancing layer to route requests for different DAGs to the appropriate SGS, and automatically scale the number of SGSs per DAG. Our testbed results show that Archipelago meets the latency deadline for more than 99% of realistic application request workloads, and reduces tail latencies by up to 36X compared to state-of-the-art serverless platforms.