Subgraph reliability of the cactus-based networks

Multiprocessor systems play a significance role in big data processing. As the probability of presence of processor failures in a multiprocessor system raises with the increase of the system, the effect of processor failure is worthy of quantifying. The subsystem reliability of a multiprocessor system is the probability that a fault-free subsystem of a certain size still operate with the arise of individual faults. In this work, we establish the subsystem reliability for the cactus-based networks, one class of newly proposed Cayley graphs generated by transpositions. More specifically, we employ the probabilistic fault model and the Principle of Inclusion-Exclusion to establish approximation and upper bound on the subsystem reliability by taking into account the intersection of no more than three subsystems. Numerical simulations show that the upper bound derived this way are close to approximation of the accurate subsystem reliability.