Characterizing failure duration in 2-terminal network problems

To characterize the "reliability" or "robustness" of a network, more information is required than simply the system failure rate. In particular the length of the downtimes can be of great relevance. Hence, in this paper we present two methods for computing the system downtime distribution in 2-terminal network problems. The first method is an importance sampling simulation which allows simulations to capture the tail of the distribution with much greater precision than simple Monte Carlo methods. Hence the statistics of unusually long failures can be investigated by simulation. The second method is an approximate analytical method whereby system failures due to 1 or 2 or • • • or N component failures are characterized exactly. The error in using N = 2 and neglecting greater than three simultaneous component failures is shown to be negligible in many cases of interest. This method can be extended to handle N > 2 component failures but the resulting calculations escalate rather quickly and are omitted here. This technique makes it possible to provide approximate failure time distributions very rapidly for arbitrary networks.