Distributed deep neural network (DDNN) training constitutes an increasingly important workload that frequently runs in the cloud. Larger DNN models and faster compute engines are shifting DDNN training bottlenecks from computation to communication. This paper characterizes DDNN training to precisely pinpoint these bottlenecks. We found that timely training requires high performance parameter servers (PSs) with optimized network stacks and gradient processing pipelines, as well as server and network hardware with balanced computation and communication resources. We therefore propose PHub, a high performance multi-tenant, rack-scale PS design. PHub co-designs the PS software and hardware to accelerate rack-level and hierarchical cross-rack parameter exchange, with an API compatible with many DDNN training frameworks. PHub provides a performance improvement of up to 2.7x compared to state-of-the-art cloud-based distributed training techniques for image classification workloads, with 25% better throughput per dollar.