A robustness measure for hypercube networks

This paper addresses a constrained two-terminal reliability measure referred to as Distance Reliability (DR) between two nodes s and t of Hamming distance H(s,t). in hypercube networks (B_n). The shortest distance restriction guarantees optimal communication delay between processors and high link/node utilization across the network. Moreover, it provides a measure for the robustness of the network. In particular, when H(s,t)=n in B_n, DR will yield the probability of degradation in the diameter, a concept which directly relates to fault-diameter. The paper proposes two schemes to evaluate DR in B_n. The first scheme uses a combinatorial approach by limiting the number of faulty components to (2H(s,t)-2), while the second outlines paths of length H(s,t) and, then, generates a recursive closed-form solution to compute DR. The theoretical results have been verified by simulation. The discrepancy between the theoretical and simulation results is in most cases below 1% and in the worst case 4.6%