Analysis of Unavailability in Middleboxes With Multiple Backup Servers Under Shared Protection

Middlebox functions, implemented as software on general-purpose servers via network function virtualization, require reliable protection mechanisms to ensure service continuity. Assessing the unavailability of these functions is critical, as failures can lead to significant service disruptions. However, existing analytical models primarily assume that a function is protected by at most one or two backup servers, limiting their applicability in scenarios requiring higher resilience. To address this limitation, this paper proposes an analytical model for evaluating the unavailability of middlebox functions under a multiple-backup shared protection strategy, where multiple backup servers protect one or more functions. Our model allows each function to be protected by multiple backup servers, ensuring availability while ensuring that each backup server can simultaneously recover at most one function. Utilizing a Markov chain, we analyze state transitions and establish equilibrium-state equations, providing an analytical foundation for evaluating the performance of the multiple-backup shared protection strategy. Numerical results demonstrate that this strategy significantly enhances availability, reducing unavailability by up to 72.3% compared to the single-backup shared protection strategy in the scenarios examined. Our study provides a detailed analysis of backup allocation strategies, focusing on their impact on function availability and offering more profound insights into their effectiveness through theoretical properties and performance comparisons with existing strategies. Our evaluation reveals that the multiple-backup shared protection strategy reduces unavailability by up to 64.8% compared to the single-backup shared protection strategy in the examined allocation cases.