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In a hierarchically-structured cloud/edge/device computing environment, workload allocation can greatly affect the overall system performance. This paper deals with AI-oriented medical workload generated in emergency rooms (ER) or intensive care units (ICU) in metropolitan areas. The goal is to optimize AI-workload allocation to cloud clusters, edge servers, and end devices so that minimum response time can be achieved in life-saving emergency applications. In particular, we developed a new workload allocation method for the AI workload in distributed cloud/edge/device computing systems. An efficient scheduling and allocation strategy is developed in order to reduce the overall response time to satisfy multi-patient demands. We apply several ICU AI workloads from a comprehensive edge computing benchmark Edge AIBench. The healthcare AI applications involved are short-of-breath alerts, patient phenotype classification, and life-death threats. Our experimental results demonstrate the high efficiency and effectiveness in real-life health-care and emergency applications.