An adaptive algorithm for computing network s-t reliability with node failures

The survivability of tactical communication networks that are subject to node and link failures can be rated in terms of calculations of network s-t reliability, the probability that a connection exists between a particular pair of nodes (s,t), or the average of such probabilities over the possible pairs of nodes. For networks of realistic size (30 or more nodes), it is well known that the NP nature of the calculations can result in excessive computational times, due to the very large number of combinations of node and link failures. In this paper, a new method for obtaining a fast calculation of this reliability is presented. The method uses the concept of a threshold on link reliability to develop bounds on the s-t reliability, in effect truncating the “Reduction & Partition” algorithm of Deo and Medidi (1992) in order to control the time required for the calculation; that algorithm is capable of handling not only imperfect links (subject to noise and jamming) but also imperfect nodes (subject to physical attack). It is shown that a link reliability can achieve a reasonable tradeoff between bound tightness and the speed of the calculation. Example calculations are given for a tactical area coverage communications network involving 34 nodes