Evaluating Robustness of Subnetworks for the Split-Star Network

The robustness of subnetworks for the interconnection network of a computer system is an important consideration for the system performance. It can be measured by the extent to which subnetworks can stay fault-free when faults are present in the system. In this paper, we evaluate the subnetwork robustness for the n-dimensional split-star network S_n². Let S²_n-m, 1≤ m≤ n-3, be a subnetwork of S_n², and let p be the node reliability, the probability that a single node remains fault-free. We determine two values that reflect how robust S²_n-m subnetworks are, from two perspectives. We first establish the upper/lower bounds for F_m(S_n²), the minimum number of faulty nodes to make all S²_n-m subnetworks faulty. Then, we determine the subnetwork reliability, denoted by R_m(S_n²,p), which is the probability that at least one fault-free S_n-m² subnetwork exists in S_n², given the node reliability p. The upper/lower bounds and an approximation expression for R_m(S_n²,p) are obtained. We also propose a simulation method to estimate R_m(S_n²,p). The experimental results show that a) when p is relatively low, R_m(S_n²,p) can be approximated by the mean value of its upper and lower bounds, or the estimation value by the approximation expression; b) when p is high, Rm(S_n²,p) can be more accurately estimated by our simulation method.