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 Routing Algorithm in Meshes with Solid Faults

A fault-tolerant routing method that can tolerate solid faults using only two virtual channels is presented. The proposed routing algorithm, called FT-Ecube, not only uses a fewer number of virtual channels but also tolerates f-chains in the meshes. Furthermore, the proposed scheme misroutes messages both clockwise and counter clockwise directions to reduce channel contention on f-rings. It is shown that the proposed algorithm is deadlock-free and livelock-free in meshes when it has nonoverlapping multiple f-regions. Further, we conducted flit-level simulations to evaluate the performance of the proposed routing algorithm. As our simulation results show, FT-Ecube tolerates multiple faulty blocks using only two virtual channels per physical channel, and has good performance in terms of average latency. This work is supported by the NSF grant MIP-9705738     

A theory of deadlock-free adaptive multicast routing in wormholenetworks

A theory for the design of deadlock-free adaptive routing algorithms for wormhole networks, proposed by the author (1991, 1993), supplies sufficient conditions for an adaptive routing algorithm to be deadlock-free, even when there are cyclic dependencies between channels. Also, two design methodologies were proposed. Multicast communication refers to the delivery of the same message from one source node to an arbitrary number of destination nodes. A tree-like routing scheme is not suitable for hardware-supported multicast in wormhole networks because it produces many headers for each message, drastically increasing the probability of a message being blocked. A path-based multicast routing model was proposed by Lin and Ni (1991) for multicomputers with 2D-mesh and hypercube topologies. In this model, messages are not replicated at intermediate nodes. This paper develops the theoretical background for the design of deadlock-free adaptive multicast routing algorithms. This theory is valid for wormhole networks using the path-based routing model. It is also valid when messages with a single destination and multiple destinations are mixed together. The new channel dependencies produced by messages with several destinations are studied. Also, two theorems are proposed, developing conditions to verify that an adaptive multicast routing algorithm is deadlock-free, even when there are cyclic dependencies between channels. As an example, the multicast routing algorithms of Lin and Ni are extended, so that they can take advantage of the alternative paths offered by the network     

Near-optimal message routing and broadcasting in faulty hypercubes

A distributed routing algorithm for faulty hypercubes is described. This algorithm uses a directed depth-first approach to find a path between the sender and receiver of a message whenever at least one non-faulty path exists. We show that, when an arbitrary number of elements of the hypercube can be faulty, the algorithm always routes messages using fewer than 2N hops, whereN is the number of nodes in the hypercube. This performance is shown to be within a factor of two of the optimal worst-case routing efficiency. Through foult simulations, we show that, even when up to half of the elements in the cube are faulty, complete the analysis, we prove that our algorithm is deadlock-free. Finally, we present two extensions of the algorithm. The first uses local storage to reduce the overhead of the algorithm while the second allows reliable broadcasting in the presence of an arbitrary number of faults.Supported in part by the National Science Foundation under Grant CCR-9010547.Supported in part by the National Science Foundation Instrumentation Grant CDA-8820627.     

Pseudo-cycle-based multicast routing in wormhole-routed networks

This paper addresses the problem of fault-tolerant multicast routing in wormholerouted multicomputers.A new pseudo-cycle-based routing method is presented for constructing deadlock-free multicast routing algorithms.With at most two virtual channels this technique can be applied to any connected networks with arbitrary topologies.Simulation results show that this technique results in negligible performance degradation even in the presence of a large number of faulty nodes.     

Routing in wormhole-switched clustered networks with applicationsto fault tolerance

This paper presents a novel technique for routing in wormhole-switched multiprocessor interconnection networks with clustered configuration. The network model used here consists of a set of clusters interfaced through a common central network. We assume that the central network and the clusters use independent algorithms to route messages between their internal nodes. A technique for deriving a global routing algorithm based on the local algorithms is presented, which allows the transfer of messages between any pair of nodes in the network. This proposed method is shown to be deadlock-free with two virtual channels. The clustered network model and the proposed routing technique can be used to enhance the fault tolerance capability of existing routing algorithms. In particular, we describe fault-tolerant routing methods for meshes, which can tolerate any arbitrary fault distribution without disabling connected healthy nodes     

2D Mesh片上网络分区容错路由算法

为了减小路由表的规模且避免使用较多虚通道(VC),从而降低硬件资源用量,针对虫孔交换的2D Mesh片上网络提出了一种分区容错路由(RFTR)算法。该算法根据故障节点和链路的位置将2D Mesh网络划分为若干个相连的矩形区域,数据包在矩形区域内可使用确定性或自适应路由算法进行路由,而在区域间则按照up^*/down^*算法确定路由路径。此外,利用通道依赖图(CDG)模型,证明了该算法仅需两个虚通道就能避免死锁。在6×6 Mesh网络中,RFTR算法能减少25%的路由表资源用量。仿真结果表明,在队列缓存资源相同的情况下,RFTR算法能实现与up^*/down^*算法和segment算法相当甚至更优的性能。     

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.     

TTPM – An efficient deadlock-free algorithm for multicast communication in 2D torus networks

A torus network has become increasingly important to multicomputer design because of its many features including scalability, low bandwidth and fixed degree of nodes. A multicast communication is a significant operation in multicomputer systems and can be used to support several other collective communication operations. This paper presents an efficient algorithm, TTPM, to find a deadlock-free multicast wormhole routing in two-dimensional torus parallel machines. The introduced algorithm is designed such that messages can be sent to any number of destinations within two start-up communication phases; hence the name Torus Two Phase Multicast (TTPM) algorithm. An efficient routing function is developed and used as a basis for the introduced algorithm. Also, TTPM allows some intermediate nodes that are not in the destination set to perform multicast functions. This feature allows flexibility in multicast path selection and therefore improves the performance. Performance results of a simulation study on torus networks are discussed to compare TTPM algorithm with a previous algorithm.     

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.     

A general methodology for direction-based irregular routing algorithms

This paper presents a general methodology for generating deadlock-free routing algorithms for irregular networks. Constructing a spanning tree on the given network, assigning directions to the network channels, creating deadlock-free zones, and specifying a logical sequence of the produced deadlock-free zones are the four fundamental steps that the proposed methodology takes to generate deadlock-free and connected routing algorithms. By applying the proposed methodology with two known labeling methods we have generated six irregular routing algorithms: three of them are novel routing algorithms and three of them (the Up/Down, Left/Right, and L-turn routing algorithms) have already been proposed in the literature. Extensive simulation experiments have been performed considering various network topologies, different network sizes (considering different network nodes and network channels), various message lengths, a variety of spanning tree roots, and a wide range of message (traffic) generation rates. Simulation results show that the six routing algorithms can be divided into three pairs. Routing members of each pair show similar behavior in terms of message latencies and saturation generation rates. However, it is worth noting that for a given topology the performance of the six routing algorithms may be totally different and it mainly depends on the network topology.     

Adaptive-trail routing and performance evaluation in irregularnetworks using cut-through switches

Cut-through switching promises low latency delivery and has been used in new generation switches, especially in high speed networks demanding low communication latency. The interconnection of cut-through switches provides an excellent network platform for high speed local area networks (LANs). For cost and performance reasons. Irregular topologies should be supported in such a switch-based network. Switched irregular networks are truly incrementally scalable and have potential to be reconfigured to adapt to the dynamics of network traffic conditions. Due to the arbitrary topologies of networks, it is critical to develop an efficient deadlock-free routing algorithm. A novel deadlock-free adaptive routing algorithm called adaptive-trail routing is proposed to allow irregular interconnection of cut-through switches. The adaptive routing algorithm is based on two unidirectional adaptive trails constructed from two opposite unidirectional Eulerian trails. Some heuristics are suggested in terms of the selection of Eulerian trails, the avoidance of long routing paths, and the degree of adaptivity. Extensive simulation experiments are conducted to evaluate the performance of the proposed and two other routing algorithms under different topologies and traffic workloads     

A learning automata-based fault-tolerant routing algorithm for mobile ad hoc networks

Reliable routing of packets in a Mobile Ad Hoc Network (MANET) has always been a major concern. The open medium and the susceptibility of the nodes of being fault-prone make the design of protocols for these networks a challenging task. The faults in these networks, which occur either due to the failure of nodes or due to reorganization, can eventuate to packet loss. Such losses degrade the performance of the routing protocols running on them. In this paper, we propose a routing algorithm, named as learning automata based fault-tolerant routing algorithm (LAFTRA), which is capable of routing in the presence of faulty nodes in MANETs using multipath routing. We have used the theory of Learning Automata (LA) for optimizing the selection of paths, reducing the overhead in the network, and for learning about the faulty nodes present in the network. The proposed algorithm can be juxtaposed to any existing routing protocol in a MANET. The results of simulation of our protocol using network simulator 2 (ns-2) shows the increase in packet delivery ratio and decrease in overhead compared to the existing protocols. The proposed protocol gains an edge over FTAR, E2FT by nearly 2% and by more than 10% when compared with AODV in terms of packet delivery ratio with nearly 30% faulty nodes in the network. The overhead generated by our protocol is lesser by 1% as compared to FTAR and by nearly 17% as compared to E2FT when there are nearly 30% faulty nodes.     

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.     

基于局部故障块三维mesh/torus网的容错路由

当系统包含很少的故障点时．mesh/torus网整个系统就有可能是不可靠的．该文采用扩展的局部可靠性信息来指导三维mesh／torus网的容错路由．扩展的局部可靠性信息在每个平面内部对无故障节点分类，所以系统中的故障块也是在不同的平面上构成的，而不是基于整个系统．很多基于整个系统不可靠的节点在二维的平面中都会变成可靠的节点．不管是在可靠的系统内，甚或不可靠的系统内，扩展的局部可靠性信息都能有效地指导容错路由．不同于以往的方法，作者的方法不会将任何无故障节点设置为无效节点．所有的故障块都是在平面内构成的，而不是基于整个系统；在一个平面内．任何包含在故障块里的无故障节点仍然可作为出发点或者目标点，这样将大大提高系统的计算能力和性能．模拟结果表明该文方法大大优于已有的方法．     

An Adaptive Routing Algorithm for WK-Recursive Topologies

This paper presents an easy and straightforward routing algorithm for WK-recursive topologies. The algorithm, based on adaptive routing, takes advantage of the geometric properties of such topologies. Once a source node S and destination node D have been determined for a message communication, they characterize, at some level l, two virtual nodes and that respectively contain S but not D and D but not S. Such virtual nodes characterize other (where is the node degree for a fixed topology) virtual nodes of the same level that contain neither S nor D. Consequently, it is possible to locate triangles whose vertices are these virtual nodes with property to share the same path, called the self-routing path, directly connecting to . When the self-routing path is unavailable to transmit a message from S to D because of deadlock, fault, and congestion conditions, the routing strategy can follow what we call the triangle rule to deliver it. The proposed communication scheme has the advantage that 1) it is the same for all three conditions; 2) each node of a WK-recursive network, to transmit messages, does not require any information about their presence or location. Furthermore, this routing algorithm is able to tolerate up to faulty links. Received: July 19, 1998; revised May 17, 1999     

Deadlock-free multicast wormhole routing in 2-D mesh multicomputers

Multicast communication services, in which the same message is delivered from a source node to an arbitrary number of destination nodes, are being provided in new-generation multicomputers. Broadcast is a special case of multicast in which a message is delivered to all nodes in the network. The nCUBE-2, a wormhole-routed hypercube multicomputer, provides hardware support for broadcast and a restricted form of multicast in which the destinations form a subcube. However, the broadcast routing algorithm adopted in the nCUBE-2 is not deadlock-free. In this paper, four multicast wormhole routing strategies for 2-D mesh multicomputers are proposed and studied. All of the algorithms are shown to be deadlock-free. These are the first deadlock-free multicast wormhole routing algorithms ever proposed. A simulation study has been conducted that compares the performance of these multicast algorithms under dynamic network traffic conditions in a 2-D mesh. The results indicate that a dual-path routing algorithm offers performance advantages over tree-based, multipath, and fixed-path algorithms     

Embedding and reconfiguration of spanning trees in faultyhypercubes

The problem of tolerating faulty nodes in hypercubes has been studied by many researchers either by using spares or by reconfiguration. Algorithms for tolerating faulty nodes and links in hypercubes are presented. The algorithms are based on using general spanning trees (GST), complete unbalanced spanning trees (CUST), and balanced spanning trees (BST) for reconfiguring the hypercube to avoid faulty nodes and links. The algorithms contain two phases: the first phase involves the construction of the spanning tree and the second one is for reconfiguring the hypercube should a faulty node be detected. The reconfiguration process consists of two basic steps. First, the faulty node is disconnected from the spanning tree. Then, a new spanning tree is constructed by reconnecting the children of the faulty node to the spanning tree. One hundred percent single fault correction (avoidance) and almost 100 percent fault correction (avoidance) of double and triple faults are achieved by the proposed algorithms for hypercubes having a dimension of n⩾6. Simulation results for the algorithm under more than three faults also are presented. For any k faulty nodes (1⩽k⩽2ⁿ-1), the reconfiguration algorithm may be applied k times to avoid these k faulty nodes as long as no combination of any two of the faults results in a blocking situation. The proposed reconfiguration algorithms tolerate all possible single-link faults. The reconfiguration algorithms are extended to tolerate (k⩽n-1) multiple faults, causing blocking situation, with a backtracking     

An Effective Design of Deadlock-Free Routing Algorithms Based on 2D Turn Model for Irregular Networks

System area networks (SANs), which usually accept arbitrary topologies, have been used to connect hosts in PC clusters. Although deadlock-free routing is often employed for low-latency communications using wormhole or virtual cut-through switching, the interconnection adaptivity introduces difficulties in establishing deadlock-free paths. An up*/down* routing algorithm, which has been widely used to avoid deadlocks in irregular networks, tends to make unbalanced paths as it employs a one-dimensional directed graph. The current study introduces a two-dimensional directed graph on which adaptive routings called left-up first turn (L-turn) routings and right-down last turn (R-turn) routings are proposed to make the paths as uniformly distributed as possible. This scheme guarantees deadlock-freedom because it uses the turn model approach, and the extra degree of freedom in the two-dimensional graph helps to ensure that the prohibited turns are well-distributed. Simulation results show that better throughput and latency results from uniformly distributing the prohibited turns by which the traffic would be more distributed toward the leaf nodes. The L-turn routings, which meet this condition, improve throughput by up to 100 percent compared with two up*/down*-based routings, and also reduce latency     

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