History has demonstrated that healthcare and medical systems play a crucial role in enforcing the development of science and technology. Humans have been seeing an explosive growth of e-health applications, where cloud computing has dominated e-healthcare systems and all domains in the past decades. However, one primary barrier to cloud-based e-health systems is their high response time. In emergencies, data aggregation and handling and decision-making regarding treatment need to be performed in seconds and directly affect the life of patients. These issues relate to resource constraints, such as medical equipment, ambulances, medical staff, medical facilities, and other conditions. To address these problems, computing architectures have been introduced, such as edge, fog, and cloud computing methods. In this work, we propose an all-in-one computing framework based on combining different computing solutions in real-time smart healthcare domains. Then, considering the efficiency of the proposed solution by the queue network model tool, we give recommendations for the optimal network infrastructure deployment depending on the scale-patients of hospitals. We believe that the results of this work will play an important role in the network infrastructure optimization of medical facilities while ensuring the provision of real-time healthcare services.