The rapid growth of the Internet of Healthcare Things (IoHT) has led to challenges in real-time processing, prioritization, and resource allocation of heterogeneous healthcare data. Existing edge-fog-cloud approaches often fail to effectively handle critical medical events and ensure timely interventions. This paper presents a novel IoHT framework that integrates an M/M/C/K priority queue model (M: Markovian arrival/service rates, C: servers, K: capacity) with a three-tier edge-fog-cloud architecture. The proposed approach introduces a dynamic priority assignment mechanism that leverages real-time patient data for swift processing of critical events and an adaptive resource allocation strategy that optimizes performance under varying workloads. Simulations and real-world case studies demonstrate the framework’s superiority, achieving a 30% reduction in average response time for critical events and a 25% improvement in resource utilization compared to state-of-the-art methods. Contributions include: 1) a novel M/M/C/K priority queue model integrated with edge-fog-cloud architecture; 2) dynamic priority assignment and adaptive resource allocation strategies; and 3) comprehensive evaluation through simulations and case studies. By addressing key challenges in IoHT data processing and prioritization, this work enables the development of efficient, responsive, and reliable IoHT systems for timely and personalized healthcare interventions, ultimately improving patient outcomes and quality of care.