PMC Model Research Articles

Connectivity and diagnosability of the complete Josephus cube networks under h-extra fault-tolerant model

The h-extra connectivity and the h-extra diagnosability are key parameters for evaluating the reliability and fault-tolerance of the interconnection networks of the multiprocessor systems, and play an important role in designing and maintaining interconnection networks. Recently, various self-diagnostic models have emerged to assess the fault-tolerance in interconnection networks. These interconnection networks are typically expressed by a connected graph G(V,E). For a non-complete graph G and h≥0, the h-extra cut signifies a vertex subset R of G, whose removal results in G−R disconnected, with each remaining component containing at least h+1 vertices. And the h-extra connectivity of G is defined as the minimum cardinality of all h-extra cuts of G. The h-extra diagnosability for a graph G denotes the maximum number of detectable faulty vertices when focusing on these h-extra faulty sets only. The complete Josephus cube CJCn, a variant of Qn, exhibits superior properties compared to hypercube Qn, and also boasts higher connectivity. In this study, with the help of the exact value of the h-extra connectivity of CJCn, the explicit expression of h-extra diagnosability of CJCn under both the PMC model for n≥5 and 1≤h≤⌊n−32⌋ and the MM* model for n≥5 and 2≤h≤⌊n−32⌋ are identified to share the same value (h+1)n−(h−12)+1.

Non-inclusive g-extra diagnosability of interconnection networks under PMC model

System level fault diagnosis theory is of great weight in the design and maintenance of multiprocessor systems. In this paper, we propose a novel kind of diagnosability, called non-inclusive g-extra diagnosability, that requires all faulty sets to be non-inclusive and every connected fault-free subgraph has at least g+1 vertices. Furthermore, we determine the non-inclusive g-extra diagnosability of a class of graphs under PMC model. As applications, the non-inclusive g-extra diagnosability of (n,k)-star graph Sn,k, data center networks DCell (Dk,n), BCDC (Bn) and BCube (BCn,k) under PMC model are determined successively.

The cyclic diagnosability of balanced hypercubes under the PMC and MM⁎ model

In 2023, Zhang et al. proposed a novel diagnostic parameter, namely the cyclic diagnosability and explored the cyclic diagnosability of Qn. In this paper, the cyclic diagnosability of BHn is determined under the PMC model and the MM⁎ model.

An expandable and cost-effective data center network

With the rapid growth of data volume, the escalating complexity of data businesses, and the increasing reliance on the Internet for daily life and production, the scale of data centers is constantly expanding. The data center network (DCN) is a bridge connecting large-scale servers in data centers for large-scale distributed computing. How to build a DCN structure that is flexible and cost-effective, while maintaining its topological properties unchanged during network expansion has become a challenging issue. In this paper, we propose an expandable and cost-effective DCN, namely HHCube, which is based on the half hypercube structure. Further, we analyze some characteristics of HHCube, including connectivity, diameter, and bisection bandwidth of the HHCube. We also design an efficient algorithm to find the shortest path between any two distinct nodes and present a fault-tolerant routing scheme to obtain a fault-tolerant path between any two distinct fault-free nodes in HHCube. Meanwhile, we present two local diagnosis algorithms to determine the status of nodes in HHCube under the PMC model and MM* model, respectively. Our results demonstrate that despite the presence of up to 25% faulty nodes in HHCube, both algorithms achieve a correct diagnosis rate exceeding 90%. Finally, we compare HHCube with state-of-the-art DCNs including Fat-Tree, DCell, BCube, Ficonn, and HSDC, and the experimental results indicate that the HHCube is an excellent candidate for constructing expandable and cost-effective DCNs.

Intermittent Fault Diagnosis Of Product Network Based On PMC Model

Abstract Fault diagnosis of processors plays a critical role in assessing the reliability of multiprocessor systems. The interconnection network’s diagnosability is an important metric for measuring its self-diagnostic capability which has been extensively studied in many novel mutiprocessor systems. Permanent fault diagnosability for many mutiprocessor systems has been determined; however intermittent fault diagnosability is hard to obtain due to its crypticity. In this paper, we focus on the problem pertaining to the diagnosability in the intermittent fault situation. First, by learning the characteristics of intermittent fault diagnosis in PMC model, we propose some theorems and lemmas for intermittent fault diagnosability. Secondly, we give the range of intermittent fault diagnosability of product network. Lastly, by adopting the theorems, we propose an Auto-IFD algorithm to find the intermittent faults of the hypercube network and conduct experiments to verify the theorems.

Extra connectivity of networks modeled by the strong product graphs

Given a non-negative integer g, the g-extraconnectivity in a connected graph G is defined as the minimum number of vertices that, when removed, results in G becoming disconnected and each remaining component containing more than g vertices. As an extension of the connectivity, the g-extraconnectivity provides a better measurement for the fault tolerance of an interconnection network. The strong product G1⊠G2 of graphs G1 and G2 is the graph with vertex set V(G1)×V(G2), where two distinct vertices (a1,b1) and (a2,b2) are adjacent if and only if a1=a2 and b1b2∈E(G2), or b1=b2 and a1a2∈E(G1), or a1a2∈E(G1) and b1b2∈E(G2). In this paper, we focus on networks modeled by the strongproductG1⊠G2. We determine the g(≤3)-extraconnectivity of G1⊠G2, where G1 and G2 are regular and maximally connected graphs with girth at least g+4. Additionally, we give the g(≤3)-extra conditional diagnosability of G1⊠G2 under PMC model.

Non-inclusive g-good-neighbour diagnosability of hypercubes

To better measure the fault tolerance and reliability of a network, Yuan et al. introduced the non-inclusive g-good-neighbour diagnosability of a network. The g-good-neighbour faulty set is a special faulty set, which satisfies that every fault-free vertex has at least g fault-free neighbours. The non-inclusive g-good-neighbour diagnosability requires every pair of g-good-neighbour faulty sets is non-inclusive, denoted as t Ng ( G ) . In this paper, we study the non-inclusive g-good-neighbour diagnosability of hypercubes and obtain t Ng ( Q n ) = ( n − 1 − g ) 2 g + 1 + 2 g − 1 for g ∈ { 1 , 2 } under the PMC model, t N 1 ( Q n ) = 3 n − 5 , t N 2 ( Q n ) = 8 n − 21 under the MM* model.

Fault-tolerant Hamiltonian cycle strategy for fast node fault diagnosis based on PMC in data center networks.

System-level fault diagnosis model, namely, the PMC model, detects fault nodes only through the mutual testing of nodes in the system without physical equipment. In order to achieve server nodes fault diagnosis in large-scale data center networks (DCNs), the traditional algorithm based on the PMC model cannot meet the characteristics of high diagnosability, high accuracy and high efficiency due to its inability to ensure that the test nodes are fault-free. This paper first proposed a fault-tolerant Hamiltonian cycle fault diagnosis (FHFD) algorithm, which tests nodes in the order of the Hamiltonian cycle to ensure that the test nodes are faultless. In order to improve testing efficiency, a hierarchical diagnosis mechanism was further proposed, which recursively divides high scale structures into a large number of low scale structures based on the recursive structure characteristics of DCNs. Additionally, we proved that $ 2(n-2){n^{k-1}} $ and $ (n-2){t_{n, k}}/{t_{n, 1}} $ faulty nodes could be detected for $ BCub{e_{n, k}} $ and $ DCel{l_{n, k}} $ within a limited time for the proposed diagnosis strategy. Simulation experiments have also shown that our proposed strategy has improved the diagnosability and test efficiency dramatically.

The intermittent diagnosability for two families of interconnection networks under the PMC model and MM* model

The intermittent diagnosability for two families of interconnection networks under the PMC model and MM* model

Relating g-good-neighbor connectivity and g-good-neighbor diagnosability of strong digraph network

In 2020, Lin and Zhang proposed the concept of g-good-neighbor (respectively, g-good-in-neighbor, g-good-out-neighbor) connectivity of digraphs and their respective diagnosability under PMC model. In this paper, we establish some relationships between connectivity, diagnosability, g-good-neighbor connectivity and g-good-neighbor (respectively, g-good-in-neighbor, g-good-out-neighbor) diagnosability of strong digraph networks. As an application, we use these relationships to obtain g-good-out-neighbor and 1-good-neighbor (respectively, 1-good-in-neighbor) diagnosability of some well-known strong digraph networks.

Reliability evaluation for a class of recursive match networks

Due to system failures in endlessly, efforts are always strived to improve the reliability of the system. As a fundamental problem in large-scale parallel and distributed systems, connectivity and diagnosability, especially g-extra connectivity and g-extra conditional diagnosability, have been widely followed. This work proposes a new class of recursive networks including the BCube—conditional recursive match networks (CRMNs). To explore the reliability of CRMNs, we get the g-extra connectivity and g-extra conditional diagnosability of CRMNs under the PMC model and the MM* model for 0≤g≤3 and g=2m+1−1(m≥0). And these results can not only be applied to the BCube, but also be used to directly obtain the corresponding g-extra connectivity and g-extra conditional diagnosability of some other networks except the BCube. In addition, we put forward the conjectures as regards the g-extra connectivity and g-extra conditional diagnosability of CRMNs with g>0.

Structural diagnosability of hypercubes under the PMC and MM* models

The fault diagnosability has played an important role in the reliability of the interconnection network. In a network, the states of any two adjacent vertices can usually affect each other, and the neighbor of a faulty vertex is more likely to become faulty. These motivate our study of fault diagnosability from the perspective of some structures instead of basing on individual faulty vertices. Therefore, we introduce a novel measure of diagnosability, called structural diagnosability. Given a specific structure H, the H-structure diagnosability of a network G, denoted by ts(G;H), is the maximum number of pairwise disjoint subnetworks H1,H2,…,Hm in G, such that, for i=1,2,…,m, Hi is isomorphic to H and when all vertices in Hi are faulty, these vertices can be diagnosed correctly. In this paper, we will establish ts(Qn;H) for the n-dimensional hypercube Qn under the PMC model and MM* model, respectively, where H∈{K1,1,K1,2,K1,3,C4}.

Non-Inclusive Diagnosability of Alternating Group Graphs

The diagnosability is very important in multiple-processor systems. Ding et al. proposed the non-inclusive diagnosability of systems in 2020. Compared to previous diagnosability, non-inclusive diagnosability requires all faulty sets to be non-inclusive. In this paper, we show the non-inclusive diagnosability of alternating group graphs under the PMC model and the MM* model for [Formula: see text].

Reliability evaluation of half hypercube networks

With the increase of the number of processors in the interconnection network, the failure of processors is inevitable. When the processor fails, the information passing through the failed processor will be unreliable, which may cause fatal consequences. Therefore, the research on the reliability of interconnection networks is an important topic, and the reliability of networks can be characterized by connectivity and diagnosability. In this paper, we first establish that the h-extra connectivity of the n-dimensional half hypercube network HHn is κh(HHn)=−12h2+(⌈n/2⌉−12)h+⌈n/2⌉+1 for n≥7 and 0≤h≤⌈n/2⌉−4, and then determine that the h-extra diagnosability of the HHn under the PMC model (n≥7 and 0≤h≤⌈n/2⌉−4) and the MM* model (n≥7 and 0≤h≤⌈n/2⌉4−1) is th(HHn)=−12h2+(⌈n/2⌉+12)h+⌈n/2⌉+1. Finally, we obtain that HHn is [−12k2+(⌈n/2⌉−12)k+⌈n/2⌉+1]/k-diagnosable under the PMC model.

WACCM6 Projections of Polar Mesospheric Cloud Abundance Over the 21st Century

AbstractPolar mesospheric clouds (PMC), or noctilucent clouds, can be observed over high latitudes with the naked eye from the ground or from space near the summer solstice. PMC are considered a direct and sensitive indicator of climate change and have been reported to appear more frequently in recent decades. How PMC will change in the future under the influence of natural variability and anthropogenic forcing is uncertain. In this study, we utilize model output from the Whole Atmosphere Community Climate Model under several shared socioeconomic pathway (SSP) scenarios and input the water vapor, temperature, and pressure information into a 0‐d PMC model to project the trend and variation of PMC over the 21st century, and their relationship to future changes of temperature, water vapor, and the solar cycle. The 0‐d model calculations indicate that PMC ice water content (IWC) will increase and PMC will extend to lower latitudes under high SSP scenarios. Under these scenarios, more mesospheric water vapor leads to an increased IWC of PMC over the polar region, and colder mesopause temperature leads to more PMC over the mid‐latitudes. There is a significant anti‐correlation between the solar cycle and PMC IWC over the 21st century, but the anti‐correlation is not always significant on the decadal scale. Finally, methane oxidation in the stratosphere and water vapor entering from the troposphere are both responsible for future changes in mesospheric water vapor and thus PMC.

Reliability evaluation of complete graph-based recursive networks

With the development of cloud computing and high-performance computing technologies, the scales of data center networks and interconnection networks become more and more large. As a result, the reliability evaluation of the two kinds of networks is very important. And most scholars study the reliability of specific networks. In this paper, we put forward a kind of complete graph-based recursive networks (short as CGRNs) which includes data center networks—DCell and generalized DCell, as well as the interconnection network dragonfly, etc. Then we further investigate the reliability of such networks—the connectivity, the diagnosability under the pessimistic diagnosis strategy based on the PMC model, g-restrict connectivity, and the g-good-neighbor conditional diagnosabilities under the PMC model and the MM⁎ model. As applications, previous results of DCell networks can be directly obtained and new results on the connectivity, diagnosability under the pessimistic strategy diagnosis based on the PMC model, g-restrict connectivity, and the g-good-neighbor conditional diagnosabilities under the PMC model and the MM⁎ model of networks (such as generalized DCell networks and dragonfly networks), are derived. Even these reliability results can be obtained for some other networks different from DCell networks, generalized DCell networks, and dragonfly networks. In addition, it can be seen that the diagnosability under the pessimistic diagnosis strategy based on the PMC model, the g-restrict connectivity, and the g-good-neighbor conditional diagnosabilities under the PMC model and the MM⁎ model of Gr are about 2 times of its diagnosability, g+1 times of its connectivity, and g+1 times of its diagnosability, respectively.

The Diagnosability of the Generalized Cartesian Product of Networks

Motivated by two typical ways to construct multiprocessor systems, matching composition networks and cycle composition networks, we generalize the definition of the Cartesian product of networks and consider the classical diagnosability of the generalized Cartesian product of networks (GCPNs). In this paper, we determine the accurate value of the classical diagnosability of the generalized Cartesian product of networks (GCPNs) under the PMC model and the MM* model.

An empirical study on the formation mechanism of trust between the owner and the PMC contractor under the PMC model

In implementing the PMC model, trusting relationships between owners and PMC contractors is the key to resolving the dilemmas caused by institutional constraints and conventional thinking, such as frequent organizational conflicts, low management efficiency, and higher transaction costs. This study utilized PMC projects in Guangxi, Jiangsu, Zhejiang, Tibet, and Guizhou as analysis samples and employed semi-structured field interviews to investigate the antecedents of trust between owners and PMC contractors. In addition, questionnaires were used to quantify the mechanism of trust formation between the two parties and the influence of trust on project performance. The findings indicated that the managerial competence and reputation of the PMC contractor, the adequacy of the owner's authorization, and the effectiveness of the owner's supervisory measures were the key drivers of calculative trust. The adequacy of the owner's authorization, the effectiveness of the owner's supervisory measures, and social similarity play the greatest roles in influencing relational trust. Calculative and relational trust significantly impact project performance, with relational trust having a slightly more substantial impact. This study can serve as a resource for enhancing the performance of PMC projects and achieving PMC project success.

The g-Good-Neighbor Conditional Diagnosabilities of Hypermesh Optical Interconnection Networks Under the PMC and Comparison Models

Processor fault diagnosis is intended to identify faulty processors of a multicomputer system, guaranteeing its high reliability and availability. The [Formula: see text]-good-neighbor conditional diagnosability is a novel fault diagnosis method for various networks. Under the PMC model and comparison model, the [Formula: see text]-good-neighbor conditional diagnosabilities of hypermesh optical interconnection networks are determined, respectively. Directly applying the results, the [Formula: see text]-good-neighbor conditional diagnosabilities of hypercubes are derived under the PMC and comparison models.

Fault tolerability analysis of folded crossed cubes based on g-component and g-good neighbor fault pattern

As data center networks and network-on-chip are developing rapidly, many graph invariants have been proposed to measure the reliability and fault tolerance of the network so that the multiprocessor systems can be ensured to operate efficiently and smoothly. The g-component connectivity of a graph G, denoted by cκg(G), is the minimum size of vertex cut such that G has at least g components. The g-good neighbor connectivity of a graph G, represented by κg(G), is the minimum size of vertex cut such that each vertex has at least g fault-free neighbors. Motivated by the conditional connectivities above, the g-component diagnosability (ctg(G)) and g-good neighbor diagnosability (tg(G)) of graph G have been suggested to evaluate the fault diagnostic capability of multiprocessor systems successively. In this paper, we determine the (g+1)-component connectivity of folded crossed cubes FCQn, i.e., cκg+1(FCQn)=ng−g22+g2+1 for 1≤g≤⌊n2⌋, and (g+1)-component diagnosability of FCQn under the PMC model and MM⁎ model, i.e., ctg+1(FCQn)=ng+n−g22−g2+1. Moreover, we establish the g-good neighbor connectivity of FCQn, i.e., κg(FCQn)=(n+1−g)2g for 0≤g≤n−5, and g-good neighbor diagnosability of FCQn under the PMC model and MM⁎ model, i.e., tg(FCQn)=(n+2−g)2g−1.