# End-to-End Service Availability in Heterogeneous Multi-Tier Cloud-Fog-Edge Networks
## 2 Related Works
The authors of [26] analyzed a multi-tier cobalt supply chain case for electric vehicles to demonstrate the challenges of achieving transparency for sustainability in complex, multi-tier supply chains, finding that the existing literature had oversimplified operationalizing transparency in multi-tier, sustainable supply chain management. The study compared supply chain maps before and after an auditing and mapping project to outline how focal companies could increase multi-tier supply chain transparency. The authors of [27] surveyed and classified edge computing architectures for IoT according to factors like data placement, orchestration, security, and big data capabilities, comparing architectures with various features, limitations, and solutions while also mapping architectures to IoT models and recommending edge computing usage scenarios for IoT applications. The survey in [28] comprehensively analyzed time-sensitive applications in fog computing, categorizing surveyed articles and discussing concepts of real-time and near real-time systems to understand the applications being implemented and how their temporal requirements are addressed. The two-tier computation offloading strategy for multi-user, multi-MEC servers in 5G heterogeneous networks was investigated in [29], with the authors proposing an efficient particle swarm optimization algorithm to minimize mobile device computing overhead, including completion time and energy consumption. The simulation results showed that the algorithm reduced overhead and guaranteed convergence compared to baselines. A distributed, multi-tier, emergency alert system using IoT sensors for real-time, georeferenced critical event detection in smart cities was proposed in [30], which delivered configurable emergency alarms based on detected events, area risk levels, and temporal data to enable flexible and modular perceptions of emergencies. Implementation on open-source platforms and real-time visualization demonstrated a useful application of the system as a supporting service for adaptive, IoT-based, emergency-aware, smart city applications. The authors of [31] defined and formulated the problem of enabling smart neighborhoods in the context of smart grids through an extensive literature review on fog computing, smart grids, microgrids, and their challenges, identifying fog computing as a promising solution to provide ultra-low latency and reliable, secure, cost-effective power to smart grids serving smart neighborhoods. Potential solutions and the integration of challenges were discussed without rigorous analysis. In some specific case studies, e.g., unique geographical terrains and densely packed urban settings, conventional three-tier systems occasionally fall short. These gaps in service birthed need for more granulated multi-tier systems, such as those employing aircraft and drones [32] or satellites in the space segment [33; 34]. These innovations aimed to ensure consistent quality of service (QoS) and enhance the reliability of networks, irrespective of the operational environment. Prior works on availability modeling in multi-tier networks have limitations in several areas, which this research aims to address, including:  
* Most existing analytical models focus on reliability within isolated tiers rather than end-to-end availability across systems. For example, the authors of [2; 3; 4; 12; 13; 14] assessed the reliability of individual cloud, edge, or fog tiers but did not study overall system availability. This fails to account for cascading failures between interdependent layers. * Simulation-based techniques like those in [8; 9; 10] provide high fidelity but lack the generalizability of closed-form mathematical models. They also incur high computational overhead. * Approaches such as those in [7; 8; 9] tend to study cloud, fog, and edge in separation rather than as integrated systems spanning all layers.