  Various methods are proposed in the literature to mitigate the failures in an
infrastructure network. Failure mitigation can be carried out in an active or
passive manner. In active manner, live backups provide the required
reliability. Due to the high cost of active backups, failures can be mitigated
in a reactive manner where mitigation starts when a function fails. In this
paper, network functions are divided into two classes of essential (i.e., core)
functions and additive (i.e., service) functions. Core functions need active
backups and cannot tolerate any failure. However, additive functions do not
require backups and their absence is tolerable in short periods. Maximum
tolerable (function) absence time (TAT) is a measure used for their reliability
level. In our model and within the mitigation process, first, the backup host
to migrate the failed function is selected. Then, the state of the function is
migrated. The process should be carried out in less than TAT. An optimization
problem is formulated investigating cost-effective failure mitigation of
additive functions. The problem is of mixed integer non convex form. To tackle
the computational complexity, it is bisected into two back-to-back
leader-follower parts. The leader selects the migration destinations and the
follower divides network resources among functions for migration. These
problems are both NP-hard. For the leader problem, a central heuristic based on
the Viterbi algorithm suggested. The follower problem is converted into two
convex sub-problems. The validity of the proposed algorithms is proved via
extensive numerical results.
