## 1 Introduction  
The proliferation of Internet of Things (IoT) devices has accelerated rapidly in recent years, with projections estimating nearly 125 billion devices by 2032 [1]. This exponential growth, coupled with advancements in quantum computing and the increasing convergence of IoT and artificial intelligence (AI), is expected to generate unprecedented volumes of heterogeneous data. One of the most impactful domains leveraging IoT is smart healthcare, where intelligent systems support personalized care, continuous monitoring, and timely interventions. In such environments, connected medical devices and wearables operate autonomously to facilitate real-time data exchange and decision making. Unlike traditional session-based models, IoT communication is inherently content-centric, where devices request and consume data or services directly from the network without persistent connectivity to specific service hosts [2]. Latency-sensitive and compute-intensive healthcare use cases, such as remote diagnostics, real-time monitoring, and emergency response, can benefit significantly from IoT's sensing capabilities and intelligent service provisioning [3]. However, the explosive growth in IoT-enabled healthcare services introduces major challenges in ensuring timely, scalable, and efficient resource provisioning. This calls for advanced, machine learning (ML)-based frameworks capable of adaptive and optimized service delivery tailored to the unique demands of smart healthcare systems. The emerging vision of the Internet of Services emphasizes the need to collect, analyze, and respond to data in a personalized and context-aware manner [4], which poses serious challenges in smart healthcare environments due to the limited capacity of IoT devices such as wearables and monitoring sensors [3]. Although cloud computing has traditionally addressed scalability through centralized processing, its high end-to-end latency and privacy concerns make it unsuitable for delay-critical applications such as real-time patient monitoring, emergency alerts, or AR-assisted diagnostics [5]. Edge computing offers a partial solution by enabling local analytics and stream mining closer to the data source, but alone it cannot meet the demands of heterogeneous services with fluctuating latency and throughput needs. To address these gaps, mist computing further reduces delay through lightweight, near-device processing, enabling context-aware responsiveness in mobile and critical care scenarios [6]. The motivation of this work is best illustrated through a realistic smart hospital scenario where multiple IoT-enabled services operate simultaneously across a mist-edge-cloud infrastructure. Consider a situation where three services are concurrently active: (i) an ECG streams continuous cardiac data to an edge server, requiring ultra-low transmission latency (e.g., \(<\)100 ms) and a steady delivery rate of 3 Mbps [3]; (ii) a public health display delivers real-time video content in a hospital lobby, requiring a delivery rate of over 10 Mbps with moderate latency tolerance [7]; and (iii) a diagnostic kiosk fetches on-demand lab records via a hospital portal, tolerating up to 500 ms delay but needing consistent delivery around 5 Mbps [8]. These services traverse network links with constrained bandwidth. For example, an inter-zone edge-to-cloud link with a capacity of 15 Mbps may concurrently serve both ECG and video streams. If both are routed to the central cloud, the compounded queuing delay and transmission overhead can cause the ECG stream to exceed its 100 ms threshold, potentially compromising patient safety. In contrast, intelligent routing through edge nodes with local decision-making can meet the latency requirements while relieving bandwidth stress on core cloud links. However, most existing service provisioning methods handle such workloads using static scheduling or heuristic policies [9; 10].