Metaverse as-a-Service (MaaS) enables Metaverse tenants to execute their APPlications (MetaAPP) by allocating Metaverse resources in the form of Metaverse service functions (MSF). Usually, each MSF is deployed in a virtual machine (VM) for better resiliency and security. However, these MSFs along with VMs and virtual machine monitors (VMM) running them may encounter software aging after prolonged continuous operation. Then, there is a decrease in MetaAPP dependability, namely, the dependability of the MSF chain (MSFC), consisting of MSFs allocated to MetaAPP. This paper aims to investigate the impact of both software aging and rejuvenation techniques on MetaAPP dependability in the scenarios, where both active components (MSF, VM and VMM) and their backup components are subject to software aging. We develop a hierarchical model to capture behaviors of aging, failure, and recovery by applying Semi-Markov process and reliability block diagram. Numerical analysis and simulation experiments are conducted to evaluate the approximation accuracy of the proposed model and dependability metrics. We then identify the key parameters for improving the MetaAPP/MSFC dependability through sensitivity analysis. The investigation is also made about the influence of various parameters on MetaAPP/MSFC dependability.

翻译：元宇宙即服务（MaaS）通过以元宇宙服务功能（MSF）形式分配元宇宙资源，使元宇宙租户能够执行其应用程序（MetaAPP）。通常，每个MSF部署在虚拟机（VM）中，以增强弹性和安全性。然而，这些MSF及其运行的虚拟机与虚拟机监视器（VMM）在长时间连续运行后可能遭遇软件老化。进而导致MetaAPP可靠性下降，即由分配给MetaAPP的MSF所构成的MSF链（MSFC）的可靠性降低。本文旨在研究在活动组件（MSF、VM和VMM）及其备份组件均受软件老化影响的情况下，软件老化与恢复技术对MetaAPP可靠性的影响。我们采用半马尔可夫过程与可靠性框图，构建了一个层次化模型来刻画老化、故障与恢复行为。通过数值分析与仿真实验，评估了所提模型的近似精度及可靠性指标。进而通过敏感性分析识别出提升MetaAPP/MSFC可靠性的关键参数，并探讨了不同参数对MetaAPP/MSFC可靠性的影响。