# End-to-End Service Availability in Heterogeneous Multi-Tier Cloud-Fog-Edge Networks
## 2 Related Works
* A few models, like the ones in [25; 26; 30], consider complex multi-level architectures beyond basic three-tier topologies but the end-to-end availability of the service provided by all layers was not analyzed. * There is limited guidance for setting availability requirements during the design process based on user needs, as seen in previous works like [12; 13; 14]. Our proposed modeling methodology attempts to overcome these gaps by:  
* Leveraging Markov chains to create an analytical model of availability spanning edge, fog, and cloud tiers;
* Accounting for inter-tier dependencies and cascading failures in an integrated system-level model;
* Providing a flexible approach adaptable to different multi-tier architectures, including sublayers;
* Enabling quantitative availability target setting based on user specifications;
* Striking a balance between model simplicity, mathematical tractability, and practical fidelity. This work aims to develop an analytical technique for availability modeling in complex, heterogeneous communication networks by considering end-to-end system availability across interconnected tiers. The motivation behind this study is twofold. Firstly, there is a necessity to formulate a structured methodology that gauges the availability of these multi-level systems. Such a methodology would allow stakeholders to predict, assess, and optimize their networks based on robust mathematical foundations. Secondly, in an era in which data-driven decisions reign supreme, having a model that can guide the design, implementation, and maintenance of future network architectures is invaluable. While existing works have made valuable contributions to availability modeling in multi-tier networks, the proposed Markov-based methodology offers several advantages:  
* Compared to purely analytical models like those in [12; 13; 14], the proposed approach better handles cascading failures between interdependent tiers. The Markov chain captures state transitions across layers. * Unlike purely simulation-based techniques in [15; 16], the proposed methodology provides a generalizable mathematical model with lower computational overhead. The Markov model enables broader insights. * In contrast to methods focusing only on specific tiers, like edge [27] or fog [28], the proposed unified Markov approach models the entire multi-tier topology. This enables assessing end-to-end availability. * The proposed model is adaptable to complex multi-level architectures beyond basic three-tier systems, which most works were limited to studying, as in [32; 33; 34]. The proposed Markov approach scales to any topology. * The methodology enables quantitative availability target setting during design, which most of the literature lacks. This ties modeling to user requirements. * Compared to reliability-focused models like in [18; 19; 20], the proposed approach emphasizes measuring availability, which directly relates to service uptime guarantees. While no single method will excel in all aspects, the proposed Markov modeling approach balances generality, mathematical tractability, design insight, and focuses on end-to-end availability across complex multi-tier systems. By leveraging Markov chains, it provides a flexible and practical methodology for availability analysis in emerging heterogeneous networks.