Mesh网络容错广播路由算法的概率分析

One-to-all or broadcast communication is one of the most important communication patterns and occurs in many important applications in parallel computing. This paper proposes a fault tolerant, local-irdormation-based, and distributed broadcast routing algorithm based on the concept of k-submesh-cormectivity in all-port mesh networks.The paper analyzes the fault tolerance of the algorithm in terms of node failure probability. Suppose that every nodehas independent failure probability, and deduce the success probability of the broadcast routing, which successfully routes a message from a source node to all non-faulty nodes in the networks. The paper strictly proves that the broadcast routing algorithm with the success probability of 99％ to route among all non-faulty nodes on mesh networks with forty thousand nodes, in case that the node failure probability is controlled within 0.12％ Simulation results show that the algorithm is practically efficient and effective, and the time steps of the algorithm are very closeto the optimum.     

Enhanced fault tolerant routing algorithms using a concept of “balanced ring”

Fault rings can be used to guide messages bypass faulty nodes/links in a fault tolerant interconnection network. However, nodes on the fault ring become hot spots, thus causing uneven distribution of the traffic loads. To avoid such traffic congestion, a concept of the balanced ring is proposed in this paper. The proposed balanced ring, defined as concentric rings of a given fault ring, can be applied to the fault tolerant routing algorithms for mesh and torus topologies. By properly guiding messages to route on the balanced ring and the fault ring, more balanced link utilization and greatly reduced traffic congestion can be achieved on a fault tolerant network. Methods of applying the balanced ring concept to some published fault tolerant routing algorithms are discussed. Proof of deadlock and livelock freedom is also presented. The use of balanced ring does not need to add new virtual channels. The performance of two routing algorithms with and without the balanced ring is simulated and evaluated. The results indicate that routing algorithms with the balanced rings constantly yield larger throughput and smaller latency than those without.     

网络容错路由算法概率分析的一种新的方法

该文提出了一种新的概率分析方法来研究在给定结点错误概率的情况下超立方体网络强容错路由算法的容错性的概率。针对文中提出的基于新的局部连通性网络容错模型的高效的强容错路由算法犤1犦,该文首次严格证明了一个具有1024个结点的10维超立方体网络能够容许多达4.7%的错误结点而具有99%的概率确保找到正确结点组成的路径,而如果结点的错误概率不超过0.1%,则所有实际规模的超立方体网络能够具有99.9%的概率确保找到正确结点组成的路径。该算法的时间性能是最优的,且该算法构造的路径的长度不超过源结点和目的结点之间海明距离的两倍加上一个很小的常数。     

Fuzzy rule-based faulty node classification and management scheme for large scale wireless sensor networks

In a wireless sensor network (WSNs), probability of node failure rises with increase in number of sensor nodes within the network. The, quality of service (QoS) of WSNs is highly affected by the faulty sensor nodes. If faulty sensor nodes can be detected and reused for network operation, QoS of WSNs can be improved and will be sustainable throughout the monitoring period. The faulty nodes in the deployed WSN are crucial to detect due to its improvisational nature and invisibility of internal running status. Furthermore, most of the traditional fault detection methods in WSNs do not consider the uncertainties that are inherited in the WSN environment during the fault diagnosis period. Resulting traditional fault detection methods suffer from low detection accuracy and poor performance. To address these issues, we propose a fuzzy rule-based faulty node classification and management scheme for WSNs that can detect and reuse faulty sensor nodes according to their fault status. In order to overcome uncertainties that are inherited in the WSN environment, a fuzzy logic based method is utilized. Fuzzy interface engine categorizes different nodes according to the chosen membership function and the defuzzifier generates a non-fuzzy control to retrieve the various types of nodes. In addition, we employed a routing scheme that reuses the retrieved faulty nodes during the data routing process. We performed extensive experiments on the proposed scheme using various network scenarios. The experimental results are compared with the existing algorithms to demonstrate the effectiveness of the proposed algorithm in terms of various important performance metrics.     

点对点并行路由算法及容错性概率分析

用概率性分析方法,研究了在结点错误概率性分布的情形下,超立方体网络的点对点并行路由算法,并对算法的容错性概率、路径长度、算法复杂性进行了严格的推导。提出的算法是基于任意给定两个正确结点可以找出n条不相交的路径。分析了算法保证一条或多条路径同时联通的概率达到99.99%时结点的错误概率上界,同时考虑了两点间的海明距离变化,得出了较好的理论结论与计算结果。方法为研究超立方体网络容错性与并行路由算法提供了一种新的途径与新的考虑角度,具有更一般与更接近实际的意义。     

基于NPV广义超立方体最佳容错路由算法

在网络可靠性研究中,设计较好的容错路由策略、尽可能多地记录系统中最优通路信息,一直是一项重要的研究工作.超立方体系统的容错路由算法分为可回溯算法和无回溯算法.一般说来,可回溯算法的优点是容错能力强:只要消息的源节点和目的节点有通路,该算法就能够找到把消息传递到目的地的路径;其缺点是在很多情况下传递路径不能按实际存在的最短路径传递.其代表是深度优先搜索(DFS)算法.无回溯算法是近几年人们比较关注的算法.该算法通过记录各邻接节点的故障信息,给路由算法以启发信息,使消息尽可能按实际存在的最短路径传递.这些算法的共同缺点是只能计算出Hamming距离不超过n的路由.在n维超立方体系统连通图中,如果系统存在大量的故障,不少节点对之间的最短路径大于n,因此,这些算法的容错能力差.提出了一个实例说明采用上述算法将遗失60%的路由信息.另外,由于超立方体的结构严格,实际中的真正超立方体系统不多.事实上,不少的网络系统可转换为具有大量错误节点和错误边的超立方体系统.因此,研究能适应具有大量错误节点和错误边的超立方体系统的容错路由算法是一个很有实际价值的工作.研究探讨了:(1) 定义广义超立方体系统;(2) 在超立方体系统中提出了节点通路向量(NPV)概念及其计算规则;(3) 提出了中转点技术,使得求NPV的计算复杂度降低到O(n);(4) 提出了基于NPV的广义超立方体系统最佳容错路由算法(OFTRS),该算法是一种分布式的和基于相邻节点信息的算法.由于NPV记录了超立方体系统全部最优通路和次最优通路的信息,在具有大量故障的情况下,它不会遗漏任何一条最优通路和次最优通路信息,从而实现了高效的容错路由.在这一点上,它优于其他算法.     

无向双环网络的容错路由研究

在节点出现故障的情况下,如何保证网络节点之间的路由是一个重要的问题。将无向双环网络的节点按照最短路径访问方式映射到直角坐标系形成最优路由构图[CG(N;±r,±s)];基于该构图根据源节点和目的节点是否位于坐标轴上以及它们周围的故障节点数,提出故障节点封闭区和逃逸区的概念;存在故障逃逸区的情况下,源、目的节点之间仍然可以进行最优路由,针对出现故障节点封闭区而无法进行最优路由的情况下,增加等价节点形成扩展路由构图[ECG(N;±r,±s)],从而寻找容错路由;给出最优路由构图、扩展路由构图和容错路由的算法,并编程仿真了这些算法。     

Fault-Tolerant Wormhole Routing with 2 Virtual Channels in Meshes

In wormhole meshes, a reliable routing is supposed to be deadlock-free and fault-tolerant. Many routing algorithms are able to tolerate a large number of faults enclosed by rectangular blocks or special convex, none of them, however, is capable of handling two convex fault regions with distance two by using only two virtual networks. In this paper, a fault-tolerant wormhole routing algorithm is presented to tolerate the disjointed convex faulty regions with distance two or no less, which do not contain any nonfaulty nodes and do not prohibit any routing as long as nodes outside faulty regions are connected in the mesh network. The processors＇ overlapping along the boundaries of different fault regions is allowed. The proposed algorithm, which routes the messages by X-Y routing algorithm in fault-free region, can tolerate convex fault-connected regions with only two virtual channels per physical channel, and is deadlock- and livelock-free. The proposed algorithm can be easily extended to adaptive routing.     

Fault-tolerant wormhole routing for hypercube networks

We present an adaptive fault-tolerant wormhole routing algorithm for hypercubes by using 3 virtual networks. The routing algorithm can tolerate at least n−1 faulty nodes and can route a message via a path of length no more than the shortest path plus four. Previous algorithms which achieve the same fault tolerant ability need 5 virtual networks. Simulation results are also given in this paper.     

Characterization of spatial fault patterns in interconnection networks

Parallel computers, such as multiprocessors system-on-chip (Mp-SoCs), multicomputers and cluster computers, are consisting of hundreds or thousands multiple processing units and components (such as routers, channels and connectors) connected via some interconnection network that collectively may undergo high failure rates. Therefore, these systems are required to be equipped with fault-tolerant mechanisms to ensure that the system will keep running in a degraded mode. Normally, the faulty components are coalesced into fault regions, which are classified into two major categories: convex and concave regions. In this paper, we propose the first solution to calculate the probability of occurrences of common fault patterns in torus and mesh interconnection networks which includes both convex (-shaped, □-shaped) and concave (L-shaped, T-shaped, +-shaped, H-shaped) regions. These results play a key role when studying, particularly, the performance analysis of routing algorithms proposed for interconnection networks under faulty conditions.     

A heuristic fault-tolerant routing algorithm in mesh using rectilinear-monotone polygonal fault blocks

A new, rectilinear-monotone polygonally shaped fault block model, called Minimal-Connected-Component (MCC), was proposed in [D. Wang, A rectilinear-monotone polygonal fault block model for fault-tolerant minimal routing in mesh, IEEE Trans. Comput. 52 (3) (2003) 310–320] for minimal adaptive routing in mesh-connected multiprocessor systems. This model refines the widely used rectangular model by including fewer non-faulty nodes in fault blocks. The positions of source/destination nodes relative to faulty nodes are taken into consideration when constructing fault blocks. Adaptive routing algorithm was given in Wang (2003), that constructs a minimal “Manhattan” route avoiding all fault blocks, should such routes exist. However, if there are no minimal routes, we still need to find a route, preferably as short as possible. In this paper, we propose a heuristic algorithm that takes a greedy approach, and can compute a nearly shortest route without much overhead. The significance of this algorithm lies in the fact that routing is a frequently performed task, and messages need to get to their destinations as soon as possible. Therefore one would prefer to have a fast answer about which route to take (and then take it), rather than spend too much time working out an absolutely shortest route.     

Mesh网络路由算法容错性的概率分析

该文基于k-Mesh子网的概念提出了两个简单的基于局部信息和分布式的Mesh网络容错路由算法，并对其容错性进行概率分析；在每个结点具有独立的出错概率的假设条件下，推导出路由算法成功返回由正确结点组成的路径的概率．该文运用严格的数学推理，证明了Mesh网络结点出错概率只要控制在1．87％以内，则对于多达几十万个结点的Mesh网络，提出的路由算法具有99％的概率确保找到正确结点组成的路径．路由算法的时间复杂性是线性的．模拟结果表明路由算法所构造的路由路径长度非常接近于两结点之间的最优路径长度．     

Fault-tolerant adaptive and minimal routing in mesh-connectedmulticomputers using extended safety levels

The minimal routing problem in mesh-connected multicomputers with faulty blocks is studied. Two-dimensional meshes are used to illustrate the approach. A sufficient condition for minimal routing in 2D meshes with faulty blocks is proposed. Unlike many traditional models that assume all the nodes know global fault distribution, our approach is based on the concept of an extended safety level, which is a special form of limited fault information. The extended safety level information is captured by a vector associated with each node. When the safety level of a node reaches a certain level (or meets certain conditions), a minimal path exists from this node to any nonfaulty nodes in 2D meshes. Specifically, we study the existence of minimal paths at a given source node, limited distribution of fault information, and minimal routing itself. We propose three fault-tolerant minimal routing algorithms which are adaptive to allow all messages to use any minimal path. We also provide some general ideas to extend our approaches to other low-dimensional mesh-connected multicomputers such as 2D tori and 3D meshes. Our approach is the first attempt to address adaptive and minimal routing in 2D meshes with faulty blocks using limited fault information     

Periodically regular chordal rings

Chordal rings have been proposed in the past as networks that combine the simple routing framework of rings with the lower diameter, wider bisection, and higher resilience of other architectures. Virtually all proposed chordal ring networks are node-symmetric, i.e., all nodes have the same in/out degree and interconnection pattern. Unfortunately, such regular chordal rings are not scalable. In this paper, periodically regular chordal (PRC) ring networks are proposed as a compromise for combining low node degree with small diameter. By varying the PRC ring parameters, one can obtain architectures with significantly different characteristics (e.g., from linear to logarithmic diameter), while maintaining an elegant framework for computation and communication. In particular, a very simple and efficient routing algorithm works for the entire spectrum of PRC rings thus obtained. This flexibility has important implications for key system attributes such as architectural satiability, software portability, and fault tolerance. Our discussion is centered on unidirectional PRC rings with in/out-degree of 2. We explore the basic structure, topological properties, optimization of parameters, VLSI layout, and scalability of such networks, develop packet and wormhole routing algorithms for them, and briefly compare them to competing fixed-degree architectures such as symmetric chordal rings, meshes, tori, and cube-connected cycles     

A high performance optimal dynamic routing algorithm with unicast multichannel QoS guarantee in communication systems

Dynamic routing protocols play an important role in today??s networks. In communication networks, in a current data transmission session, failing nodes and links is a destructor event which loses packets immediately and it can also waste network resources and services seriously. Sometimes failing nodes can disconnect data transmission and, therefore, lost packets must be retransmitted by new session. In this situation, the routing algorithm must discard failed nodes and must repair paths of session by rerouting them. In this case, static routing algorithms and some existing dynamic routing algorithms cannot manage faulty paths fairly and network efficiency is seriously declined. The capability to compensate for topology changes is the most important advantage dynamic routing offers over static routing. An efficient dynamic routing algorithm tries to reroute and change faulty paths without disconnecting sessions and keeps packet transmission in a desirable rate. It is important to tell that a dynamic routing algorithm should provide multi essential parameters, such as acceptable delay, jitter, bandwidth, multichannel paths, virtual channel connections, label switching technology, optimal resource allocation, optimal efficiency in the case of multimedia, and real time applications. This paper proposes a new dynamic framework which transforms static routing algorithms to dynamic routing algorithms. Using the new dynamic framework, this paper constructs an Optimal Dynamic Unicast Multichannel QoS Routing (ODUMR) algorithm based on the Constrained Based Routing (CBR) and Label Switching Technology which is called as ODUMR Algorithm. The performance of ODUMR is analyzed by network simulator tools such as OpNet, MATLAB, and WinQSB. ODUMR produces results better than the existing static and dynamic routing algorithms in terms of necessary parameters.     

A simple fault-tolerant adaptive and minimal routing approach in 3-D meshes

In this paper we propose a sufficient codition for minimal routing in 3-dimensional (3-D) meshes with faulty nodes,It is based on an early work of the author on minial routing in 2-dimensional(2-D) meshes,Unlike many traditional models that assume all the nodes know global fault distribution or just adjacent fault information,our approach is based on the concept of limited global fault information,First,we propose a fault model called faulty cube in which all faulty nodes in the system are contained in a set of faulty cubes.Fault information is then distributed to limited number of nodes while it is still sufficeint to support minimal routing.The limited fault information collcted at each node is represented by a vector caaled extended safety level.The extended safety level associated with a node can be used to determine the existence of a minimal path from this node to a given destination .Specifically,we study the existence of minimal paths at a given source node,limited distribution of fault information,minimal routing,and deadlock-free and livelock-free routing.our results show that any minimal routing that is partially adaptive can be applied in our model as long as the dstination node meets a certain conditon.We also propose a dynamic planar-adaptive routing scheme that offers better fault tolerance and adaptivity than the planar-adaptive routing scheme in 3-D meshes.Our approach is the first attempt to address adaptive and minimal routing is 3-D meshes with faulty nodes using limited fault information.     

On fault tolerance of 3-dimensional mesh networks

In this paper, the concept of k-submesh and k-submesh connectivity fault tolerance model is proposed. And the fault tolerance of 3-D mesh networks is studied under a more realistic model in which each network node has an independent failure probability. It is first observed that if the node failure probability is fixed, then the connectivity probability of 3-D mesh networks can be arbitrarily small when the network size is sufficiently large. Thus, it is practically important for multicomputer system manufacturer to determine the upper bound for node failure probability when the probability of network connectivity and the network size are given. A novel technique is developed to formally derive lower bounds on the connectivity probability for 3-D mesh networks. The study shows that 3-D mesh networks of practical size can tolerate a large number of faulty nodes thus are reliable enough for multicomputer systems. A number of advantages of 3-D mesh networks over other popular network topologies are given.     

Adaptive and deadlock-free routing for irregular faulty patterns inmesh multicomputer

Message routing achieves the internode communication in parallel computers. A reliable routing is supposed to be deadlock-free and fault-tolerant. While many routing algorithms are able to tolerate a large number of faults enclosed by rectangular faulty blocks, there is no existing algorithm that is capable of handling irregular faulty patterns for wormhole networks. In this paper, a two-staged adaptive and deadlock-free routing algorithm called “Routing for Irregular Faulty Patterns” (RIFP) is proposed. It can tolerate irregular faulty patterns by transmitting messages from sources or to destinations within faulty blocks via multiple “intermediate nodes.” A method employed by RIFP is first introduced to generate intermediate nodes using the local failure information. By its aid, two communicating nodes can always exchange their data or intermediate results if there is at least one path between them. RIFP needs two virtual channels per physical link in meshes     

A new look at fault-tolerant network routing

We model a communication network as a graph in which a processor is a node and a communication link is an edge. A routing for such a network is a fixed path, or route, between each pair of nodes. Given a network with a predefined routing, we study the effects of faulty components on the routing. Of particular interest is the number of routes along which a message must travel between any two non-faulty nodes. This problem is analyzed for specific families of graphs and for classes of routings. We also give some bounds for general versions of the problem. Finally, we conclude with one of the most important contributions of this paper, a list of interesting and apparently difficult open problems.     

自适应路由算法优于确定性路由算法

在研究并行计算机系统的容错时。自适应路由算法是一个极为重要的研究课题．它是在网络结点出错时，算法通过可选择的路径进行路由．在每个结点具有独立的出错概率的模型下，研究Mesh网络上自适应路由算法和确定性路算法的性能．本文提出的技术使得我们能严格地推导出路由算法的成功的概率，从而能分析和比较算法的性能．研究结果表明自适应路由算法具有明显的优势：一方面确定性路算法需要全局错误信息而变得高效性，另一方面自适应路由算法对于结点出错和网络规模具有更好的健壮性而具有更高的成功概率．