As the scale of multiprocessor systems increases, so do the requirements for system reliability and security. Modeling how processors and links are connected in a multiprocessor system through a network topology (or graph) is an effective means to study the reliability of the system. Connectivity, one of the important concepts in graph theory, can be used as an indicator of multiprocessor system’s reliability. However, as classical connectivity is not well suited for practical applications, the concept of$g$-extra connectivity has been proposed to more accurately characterize system’s reliability. The exchanged crossed cube, an innovative network topology derived from the classical hypercube, achieves not only a smaller diameter (improving information transmission efficiency) but also fewer connecting edges (reducing hardware costs when scaling the network). In this article, we derive the$g$-extra connectivity of the exchanged crossed cube and comparatively analyze its advantages in reliability evaluation through simulations.

Abstract For the multiprocessor systems modeled by interconnection networks, one of the important properties is the characterization of fault tolerability. Connectivity, as an important parameter to evaluate fault tolerability, has witnessed research achievements. To make the evaluation more practical, conditional connectivity has been promisingly proposed. As one kind of conditional connectivity, $h$-restricted connectivity of a connected graph $G$, denoted by $\kappa ^h (G)$, is defined as the cardinality of the minimum vertex cut set $F$ such that $\delta (G-F)\geq h$. In this paper, we establish a universally $h$-restricted connectivity for a class of hypercube-based compound networks, in which the well-known networks, such as hierarchical cubic network $HCN(n, n)$ and its generalization complete cubic network $CCN(n)$, are involved.

As the size and complexity of a multiprocessor system increases, reliability evaluation becomes an important issue. The performability of a multiprocessor system heavily depends on the application program and the underlying architecture. In multitasking multiprocessor system, the problem of dynamically assigning a given dimensional subsystem to a special task is considered as a reallocation in the presence of node and/or link failures. This paper takes the generalization of star graph, (n, k)-star graph, as an empirical object. In order to measure the reliability of (n, k)star graph, the analytical model introduces mean time to failure (MTTF) to show the time that the appearance of a certain number of faulty Sn-1,k-1costs. The higher the MTTF, the better the robustness. So, the way to evaluate the robustness of an (n, k)-star is to count how much the MTTF is. In fact, an (n, k)-star can be partitioned along any dimension (except the first one) with corresponding identification code. So, we will explore the reliability of (n, k)-star graph when it is partitioned along any dimension (except the first one) under node and/or link fault model. Comparisons among the simulation results under two partitioning models reveal that the MTTF is higher under liberal partition model, which better reflect the steady state of an interconnection network that can persist when the network is destroyed.

As the cardinality of multiprocessor systems grows, the probability of arising malfunctioning or failing processors in the system is bound to increase. It is then of both practical and theoretical importance to know the reliability of the system as a whole. One metric for a system's overall reliability is the measurement of the collective effect of its subsystems becoming faulty. However, a challenge of this approach is that the subsystems often interact with each other in a complex manner, making the analysis difficult. Wu and Latifi (Int. Sci., vol. 178, pp. 2337-2348, Oct. 2008) proposed two schemes to evaluate the system reliability of the Star graph network under a probabilistic fault model. The first scheme computes the combinatorial probability of subgraphs to obtain an upper-bound on the reliability by considering the intersection of no more than three subgraphs. The second scheme computes an approximate combinatorial probability by completely neglecting the intersection among subgraphs. Recently, Lin et al. have applied this approach to investigate the reliability of the multiprocessor system based on the arrangement graph (IEEE Trans. Rel., vol. 62, no. 2, pp. 807-818, Jun. 2015). In this paper, we extend the above approach by computing both upper- and lower-bounds and considering the difference of the two, to establish the reliability of the (n, k) -Star graph, another extensively studied interconnection network for multiprocessor systems. More specifically, we compute a lower-bound and an upper-bound on the reliability by taking into account the intersection of no more than four or three subgraphs, respectively. The empirical study shows that the upper- and lower-bounds are both very close to the approximate results. Especially, the lower the single-node reliability goes, the closer the approximate reliability is to both lower- and upper-bounds.