## 4 Analytical Framework for Heterogeneous Service Provisioning
### Algorithms for Rate-Adaptive Provisioning
This results in a complexity of:

\[O(nm). \tag{25}\]

Algorithm 2 traverses each node and evaluates its outgoing links to compute delivery rates, prices, and weights. For each iteration, the computation over all consumers on each link incurs:

\[g_{s}^{t}=\max_{\{i|t\in T_{s,i}\}}g_{s,i}, \tag{17}\]0

leading to a total complexity of:

\[g_{s}^{t}=\max_{\{i|t\in T_{s,i}\}}g_{s,i}, \tag{17}\]1

where \(I\) is the number of iterations until convergence. In practice, \(I\) remains moderate due to the adaptive pricing scheme and ML-based forecasting, which stabilize the convergence process. Algorithm 3 processes each service path to compute the cumulative path price and adapt the delivery rate accordingly. This operation takes:

\[g_{s}^{t}=\max_{\{i|t\in T_{s,i}\}}g_{s,i}, \tag{17}\]2

per iteration, contributing an additional:

\[g_{s}^{t}=\max_{\{i|t\in T_{s,i}\}}g_{s,i}, \tag{17}\]3

to the overall complexity. Combining all phases, the total complexity of the framework is:

\[g_{s}^{t}=\max_{\{i|t\in T_{s,i}\}}g_{s,i}, \tag{17}\]4

Given that \(k\) is typically small relative to \(m\) and \(n\) and that \(I\) remains bounded in realistic deployments, the overall framework is computationally efficient and suitable for large-scale, real-time healthcare networks. The computational demands of ML-RASPF are well within the capabilities of modern edge servers and cloud data centers, enabling real-time deployment in mid- to large-scale smart hospital networks. The proposed analytical framework enables rate-adaptive and latency-aware service provisioning for heterogeneous IoT services in healthcare environments. Through its convex utility formulation, delay penalization model, and integration of predictive and adaptive ML components, the system offers intelligent, dynamic resource allocation while maintaining scalability. The modular algorithmic structure allows for fine-grained control, rapid convergence, and real-time responsiveness, making the framework suitable for mission-critical healthcare applications such as patient monitoring, diagnostics, and emergency services. In summary, ML-RASPF bridges the gap between traditional resource allocation models and the dynamic needs of smart healthcare environments. By combining utility-based optimization, delay sensitivity, and learning-based forecasting and control, the framework ensures robust, real-time service delivery. ## 5 Experimental Evaluation

This section presents the experimental evaluation of the proposed ML-enhanced, rate-adaptive service provisioning framework in a smart healthcare environment. We assess the ML-RASPF's performance in delivering rate-adaptive and latency-sensitive IoT services across a mist-edge-cloud infrastructure. The evaluation focuses on key performance indicators: latency, service delivery rate, energy consumption, bandwidth utilization, and load balancing efficiency. Comparative results are presented against four recent techniques, including JANUS [7], which employs queue management and heuristic coordination, an energy-aware task offloading framework [8] leveraging JAYA-based optimization, and classical scheduling strategies like First-Come-First-Served (FCFS) and Least-Request-First-Served (LRFS). We begin by outlining the experimental setup and the layered simulation architecture used to evaluate ML-RASPF. ### Simulation Setup

To evaluate the proposed framework, we adapt and extend EdgeCloudSim [23], a widely-used simulator for cloud-edge IoT environments. The simulator is customized to model three-tier service delivery (mist, edge, and cloud) and to support service types commonly found in smart healthcare systems. The simulation includes ML components, such as predictive traffic models and adaptive rate control mechanisms that reflect anticipated real-time analytics in actual deployments. We model a healthcare use case involving a network of IoT-enabled hospital zones.