  We formulate intrusion tolerance for a system with service replicas as a
two-level optimal control problem. On the local level node controllers perform
intrusion recovery, and on the global level a system controller manages the
replication factor. The local and global control problems can be formulated as
classical problems in operations research, namely, the machine replacement
problem and the inventory replenishment problem. Based on this formulation, we
design TOLERANCE, a novel control architecture for intrusion-tolerant systems.
We prove that the optimal control strategies on both levels have threshold
structure and design efficient algorithms for computing them. We implement and
evaluate TOLERANCE in an emulation environment where we run 10 types of network
intrusions. The results show that TOLERANCE can improve service availability
and reduce operational cost compared with state-of-the-art intrusion-tolerant
systems.
