Fig. 2

Expected time to failure (ETTF) under attack. In each sub-figure, each point (a marker along a dashed line) indicates the ETTF (the position in the vertical axis) of a specific intrusion-tolerant system 〈n,f〉, with n being the total number of nodes and f being the threshold of tolerated intrusions. The marker represents the reference system 〈1,0〉. Each other type of marker (, ■, , , ) represents a specific functional relation between n and f (as detailed in the auxiliary box in the upper area of each sub-figure). The vertical axis (labeled ETTF) actually measures the ratio μ_n,f/μ_1,0, between the ETTF of the respective 〈n,f〉 system and the ETTF of 〈1,0〉. For λ=1, it follows that μ_1,0=1/λ=1, so the ratio is indeed the ETTF of 〈n,f〉. The horizontal dashed line, starting to the right of marker , highlights the threshold between desirable and undesirable ETTF. The value to the right of each curve, and prefixed with a small arrow, indicates the limit ETTF as f→∞