Since emerging edge applications such as Internet of Things (IoT) analytics and augmented reality have tight latency constraints, hardware AI accelerators have been recently proposed to speed up deep neural network (DNN) inference run by these applications. Resource-constrained edge servers and accelerators tend to be multiplexed across multiple IoT applications, introducing the potential for performance interference between latency-sensitive workloads. In this paper, we design analytic models to capture the performance of DNN inference workloads on shared edge accelerators, such as GPU and edgeTPU, under different multiplexing and concurrency behaviors. After validating our models using extensive experiments, we use them to design various cluster resource management algorithms to intelligently manage multiple applications on edge accelerators while respecting their latency constraints. We implement a prototype of our system in Kubernetes and show that our system can host 2.3X more DNN applications in heterogeneous multi-tenant edge clusters with no latency violations when compared to traditional knapsack hosting algorithms.