Shared Backup Resource Assignment for Middleboxes Considering Server Capability

This paper presents two strategies to obtain an assignment of backup servers to network functions of middleboxes when each backup server can recover a half of the functions which it protects at the same time. In the previous work, there are approaches to obtain an assignment only when each backup server protects two functions and recovers one of them at the same time. Therefore, we present two strategies to expand the cases where an assignment can be obtained by utilizing the previous approaches. The basic ideas of our two strategies are dividing each server into a set of small servers that protects two functions and recovers one of them at the same time, obtaining an assignment with them, and combining them. In the process of obtaining an assignment with our presented two strategies, there is a constraint to avoid impairing the capabilities of backup servers. Our two strategies incorporate this constraint before and after obtaining an assignment with the divided small servers, respectively. We define six survival probabilities regarding our two strategies and analyze their relationships. Then, we derive two theorems to consider when our strategy can obtain an assignment that satisfies the constraint. Based on the theorems, we analyze properties of our strategies and the relationship between the different survival probabilities. Numerical results show that one of our strategies provides the higher survival probability than the other one for all the settings that we examine.