## 2 Related Works  
Many publications in the literature relate to IoT-based e-health patient monitoring systems, their deployment architecture, and performance modeling. [PERSON] et al. [27] proposed a resource preservation net (RPN) framework using Petri nets. The work presents a framework capable of generating non-consumable resource models that are theoretically described and validated. The work aims to measure some performance indicators of an intelligent hospital system with edge and cloud processing components. Among the performance metrics of the study, there is the patient's length of stay (LoS), resources usage rate, and average waiting time. [PERSON] et al. [6] propose analytical models of Petri nets and Reliability Block Diagram (RBD) to assess the availability of an intelligent health monitoring system that depends on edge, fog, and cloud infrastructures. [PERSON] et al. [6] still use a multi-objective optimization algorithm (NSGA-II) to improve system availability, taking into account its cost as a limitation. [PERSON] et al. [28] propose a technological and architectural solution based on Open Source big data technologies to perform realtime data flow analysis on wearable sensors. The architecture proposed by the work comprises four layers: the sensing layer, the preprocessing layer, the cluster processing layer, and the persistence layer. Each layer's performance analysis was performed to gauge each layer's memory and CPU usage. [PERSON] et al. [29] proposed an Edge-Cognitive-Computing-based (ECC-based) smart-healthcare system. The system can monitor and analyze the status of patients using cognitive computing. Furthermore, the system can allocate the use of resources according to the patient's degree of risk. Experiments have shown that the system improves the user experience, optimizes the use of resources, and increases the patient's survival chances in sudden emergencies. [PERSON](a) et al. [30] proposed a high-level model capable of characterizing the behavior of an mHealth system. The objective of the work is to identify the probability of a system message being delivered in a \(t\) time. The paper does not analyze availability, but some parts of the model are characterized as an availability model. [PERSON] et al. [31] propose a patient monitoring architecture using sensors and cloud and fog processing. The work also presents a sensitivity analysis that identifies the components that most impact system availability. [PERSON] et al. [32] also propose a monitoring architecture using cloud and fog. However, [PERSON]. [32] extends the idea of [31] and adds a model that can calculate performance metrics and identify possible bottlenecks in the system. [PERSON] et al. [33] propose models capable of calculating performance and availability metrics in a smart hospitals system. The work presents a performance model capable of calculating Mean Response Time, Resource Utilization, and Discard. The work also presents an availability model and performs a sensitivity analysis on this model. The results show optimal settings for system performance and availability. [PERSON] et al. [34] proposed an intelligent fog computing scheduling model that offers service-provisioning for IoT while reducing the latency. A case study with a critical healthcare application (An electrocardiogram (ECG)) has also been presented. The objective was to optimally schedule the requests of ECG sensors on a fog environment and proficiently handle their demands on existing resources for each fog node. The proposed model was evaluated using the iFogSim toolkit in terms of delay performance metric. The results show that the proposed model performance outperformed the existing approaches. There is a contrast to the related work as seen above. The proposed queueing model analyzes the performance of the health monitoring system considering different contexts, architecture, and workload. There is a consideration of cloud computing conditions and capabilities and cloud resources.