Subnetworks Reliability Analysis of Complete Transposition Networks

Characterization of matroidal connectivity of regular networks

Multistage Interconnection Networks (MINs) are a cost-effective idea for connection between different nodes in multi-processor systems. In the meantime, understanding the impact of increasing the number of stages (i.e. a famous method for improving fault tolerance) on the reliability of these networks is essential. Last studies on this challenging issue, revealed that adding one switching stage to MINs is preferable to two in terms of reliability. However, there were some non-negligible gaps in previous researches: (i) The probability of failure for terminal nodes was not considered in the calculation of reliability. (ii) Numerical results were only based on the small size of the network, i.e. 8 × 8. (iii) Reliability analyses were time-independent. (iv) The lack of some important parameters such as the mean time to failure and availability was noticeable. Therefore, this paper will take a more comprehensive analysis of reliability to meet the above specifications.

The vertex (edge) connectivity has been regularly used to measure the fault tolerance and reliability of interconnection networks, while it has defects in the assumption that all neighbors of one node will fail concurrently. To overcome this deficiency, some new generalizations of traditional connectivity have been suggested to quantize the size or the number of the connected components of the survival graph. The [Formula: see text]-component (edge) connectivity, one generalization of vertex (edge) connectivity, has been proposed to characterize the vulnerability of multiprocessor systems based on the number of components of the survival graph. In this paper, we determine the [Formula: see text]-component (edge) connectivity of a family of networks, called the round matching composition networks [Formula: see text], which are a class of networks composed of [Formula: see text] ([Formula: see text]) clusters with the same order, linked by [Formula: see text] perfect matchings. By exploring the combinatorial properties and fault-tolerance of [Formula: see text], we establish the [Formula: see text]-component (edge) connectivity [Formula: see text] for [Formula: see text] and [Formula: see text], [Formula: see text] and [Formula: see text] for [Formula: see text].

Reliability of interconnection networks is important to design multiprocessor systems. The extra edge connectivity and component edge connectivity are two parameters for the reliability evaluation. The [Formula: see text]-extra edge connectivity [Formula: see text] is the cardinality of the minimum extra edge cut [Formula: see text] such that [Formula: see text] is not connected and each component of [Formula: see text] has at least [Formula: see text] vertices. The [Formula: see text]-component edge connectivity [Formula: see text] of a graph [Formula: see text] is the minimum edge number of a set [Formula: see text] such that [Formula: see text] is not connected and [Formula: see text] has at least [Formula: see text] components. In this paper, we find the relation of extra edge connectivity and component edge connectivity for regular networks. As an application, we determine the component edge connectivity of BC networks, [Formula: see text]-ary [Formula: see text]-cubes, enhanced hypercubes.

Reliability evaluation of half hypercube networks

Bijective connection (BC) networks, including a family of interconnection networks of multiprocessor systems, have been studied extensively due to its desirable properties, such as lower diameter, high reliability, and diagnosability. To meet the demand of processing integrating tasks with large-scale and complex architectures, it is significant to explore alternative interconnection networks for multiprocessor configuration. To this end, we propose a novel framework called hyper bijective connection network (HBC network) as an extension of BC networks, which allows to study the properties of other potential interconnection networks in unity rather than in individual. We prove that when n ≥ 3, m ≥ 2, every n-dimensional HBC network H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> (m) has (edge) connectivity m + n - 2, super connectivity 2n + m - 4, and super edge-connectivity 2n + 2m - 6, and is super-connected and super-edge-connected. These results indicate the high reliability of HBC networks. Moreover, we analyze three classic diagnos abilities of a HBC network, including tp-, t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> /t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -, and t/k-diagnosability. We show that when n ≥ 3 and m ≥ 2, an n-dimensional HBC network H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> (m) is (m + n - 2)-diagnosable, (2n + m - 4)/(2n + m - 4)-diagnosable, and t(m, n, k)/k-diagnosable, where 0 ≤ k ≤ m + n - 2 and t(m, n, k) = (k + 1)n + (m - 2) - ((k + 1)(k + 2)/2) + 1. Besides, it is shown that the corresponding properties for BC networks can be derived naturally as special cases of that for HBC networks.

Structure and substructure connectivity of divide-and-swap cube

The generalized 3-connectivity of two kinds of regular networks

Structure connectivity and substructure connectivity of split-star networks

Multi-processor systems need interconnection networks (INs) in order to make the connection among the processors, memory modules, and nodes. Bus interconnection network is the simplest and least expensive one among all the INs. Therefore, bus network is easily understood and preferred by manufactures for implementation. However, a bus network is inherently a non-fault tolerant and blocking network. To cope with these problems, a solution is to use several buses in parallel on a network. Based on this idea, various schemes can be designed for a bus network: (1) Multiple-bus with full bus-memory connection, (2) Multiple-bus with single bus-memory connection, (3) Multiple-bus with partial bus-memory connection, and (4) Multiple-bus with class-based memory connection. On the other hand, a metric for the efficiency of fault-tolerant systems is its reliability. Although, there is no detailed analysis of the reliability of bus-based networks, this paper presents accurate and complete reliability analysis of bus-based networks to achieve these aims: (1) Determining the most efficient design of bus-based networks in terms of reliability, cost-effectiveness, and blocking issues, (2) Providing new methods for evaluating the performance of bus-based networks.

With the rapid increase of the number of processors in multiprocessor systems and the fast expansion of interconnection networks, the reliability of interconnection network is facing severe challenges, where the fast recognition of fault processors is crucial. In practice, most of the processor failures are intermittent faults. In this article, we first determine the intermittent fault diagnosability <inline-formula><tex-math notation="LaTeX">$t_{I}^{PMC}(S_{n}^{2})$</tex-math></inline-formula> of <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> -dimensional split-star network <inline-formula><tex-math notation="LaTeX">$S_{n}^{2}$</tex-math></inline-formula> under the PMC model. In addition, we propose a fast intermittent fault probabilistic diagnosis algorithm FIFPDPMC to identify the nodes with intermittent fault in the <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> -dimensional split-star network <inline-formula><tex-math notation="LaTeX">$S_{n}^{2}$</tex-math></inline-formula> under the PMC model, and we calculated the time complexity of the algorithm FIFPDPMC. Then we implement the algorithm FIFPDPMC in the IoT-based wireless sensor network (IoTWSN) and a randomly generated network (RGN) under different number of nodes with intermittent fault, and we evaluate the performance and efficiency of the algorithm FIFPDPMC in terms of accuracy, precision, recall (TPR), F1, G-mean, FPR, TNR and FNR. Experimental results show that, as the number of stages of executing the algorithm FIFPDPMC increases, the number of nodes with intermittent fault being diagnosed by the algorithm FIFPDPMC increases, which implies that the algorithm FIFPDPMC has good performance and efficiency in both IoTWSN and RGN.

An interconnection network can be modelled as a connected graph [Formula: see text]. The reliability of interconnection networks is critical for multiprocessor systems. Several conditional edge-connectivities have been introduced in the past for accurately reflecting various realistic network situations, with the [Formula: see text]-extra edge-connectivity being one such conditional edge-connectivity. The [Formula: see text]-extra edge-connectivity of [Formula: see text], denoted by [Formula: see text], is the minimum cardinality of faulty edges whose deletion disconnects the graph [Formula: see text] with each resulting component containing at least [Formula: see text] processors. In general, for a connected graph [Formula: see text], determining whether the graph exists an [Formula: see text]-extra edge-cut is [Formula: see text]-hard. The folded-crossed hypercube [Formula: see text] is a variation of the crossed hypercube [Formula: see text] with [Formula: see text] processors. In this paper, after excavating the layer structure of folded-crossed hypercube, we investigate some recursive properties of [Formula: see text], based on some recursive properties, an effective [Formula: see text] algorithm of [Formula: see text]-extra edge-connectivity of folded-crossed hypercube is designed, which can determine the exact value and the [Formula: see text]-optimality of [Formula: see text] for each positive integer [Formula: see text]. Our results solve this problem thoroughly.

Classical connectivity is a vital metric to assess the reliability of interconnection networks, while it has defects in the defective assumption that all neighbours of one node may fail concurrently. To overcome this deficiency, many new generalizations of traditional connectivity, such as g-component (edge) connectivity, restricted (edge) connectivity, g-extra (edge) connectivity and so on, have been suggested. For any positive integer a, the a-regular edge connectivity of a connected graph G is the minimum cardinality of an edge cut, whose deletion disconnects G so that each component is a a-regular graph. In this work, we investigate the a-regular edge connectivity of some regular networks, which provides a novel idea for further exploring the reliability of networks. Finally, simulations are carried out to compare the a-regular connectivity with other types of connectivity in some regular networks. The comparison results imply that the a-regular edge connectivity has its superiority.

Multistage interconnection networks are used as a medium for interconnecting processors and memories in multiprocessor systems. Multistage interconnection networks are an effective substitute for crossbar switches, used in telephone network systems and parallel computers, due to their low cost, better performance and easy maintainability. In this paper, we propose new fault-tolerant hybrid multistage interconnection networks obtained from shuffle exchange gamma interconnection network (SEGIN) and logical neighborhood network named as shuffle exchange gamma logical neighborhood interconnection network (SEGLNIN). We evaluated the performance of SEGLNIN in terms of disjoint paths, reliability and hardware cost and compared it with some well-known MINs like shuffle exchange network (SEN), shuffle exchange network with one extra stage (SEN +) and shuffle exchange network with two extra stages (SEN + 2), SEGIN-1, and SEGIN-2. The results illustrate that the performance of the proposed SEGLNIN is better than that of the compared networks in terms of reliability and disjoint paths.

Interconnection network has been an active research area for parallel and distributed computer systems. The diagnosability is one of the important issues in the reliability of interconnection networks. In this paper, a novel idea on system diagnosis called local diagnosability is presented. The concept of local diagnosability is strongly related to the traditional global one. For this local sense, the status of every particular processor can be correctly identified. A sufficient condition is also proposed to determine the local diagnosability of a given processor. Following this local sense, we prove that the diagnosability of an n-dimensional hypercube-like network HL(subscript n) is n for n≥5, and show that in HL(subscript n) with up to n-2 faulty links, the local diagnosability of each processor equals to the connection links incident with it.