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As artificial intelligence (AI) and machine learning (ML) technologies disrupt a wide range of industries, cloud datacenters face ever-increasing demand in inference workloads. However, conventional CPU-based servers cannot handle excessive computational requirements of deep neural network (DNN) models, while GPU-based servers suffer from huge power consumption and high operating cost. In this paper, we present a scalable systolic-vector architecture that can cope with dynamically changing DNN workloads in cloud datacenters. We first devise a lightweight DNN model description format called unified model format (UMF) that enables general model representation and fast decoding in hardware accelerator. Based on this model format, we propose a heterogeneous architecture that features a load balancer that performs a high-level workload distribution and multiple systolic-vector clusters, in which each cluster consists of a programmable scheduler, throughput-oriented systolic arrays, and function-oriented vector processors. We also propose a heterogeneity-aware scheduling algorithm that enables concurrent execution of multiple DNN workloads while maximizing heterogeneous hardware utilization based on computation and memory access time estimation. Finally, we build an architecture simulation framework based on actual synthesis and place-and-route implementation results and conduct design space exploration for the proposed architecture. As a result, the proposed systolic-vector architecture achieves 10.9x higher throughput performance and 30.17x higher energy efficiency than a compatible GPU on realistic ML workloads. The proposed heterogeneity-aware scheduling algorithm improves the throughput and energy efficiency by 81% and 20%, respectively, compared to a standard round-robin scheduling.