虚网叠加构造自适应路由算法的有效框架

大规模并行处理机系统中路由算法对互联网络通信性能和系统性起着重要作用。     

A Necessary and Sufficient Condition for Deadlock-Free Wormhole Routing

An important open problem in wormhole routing has been to find a necessary and sufficient condition for deadlock-free adaptive routing. Recently, Duato has solved this problem for a restricted class of adaptive routing algorithms. In this paper, a necessary and sufficient condition is proposed that can be used for any adaptive or nonadaptive routing algorithm for wormhole routing, as long as only local information is required for routing. The underlying proof technique introduces a new type of dependency graph, thechannel waiting graph, which omits most channel dependencies that cannot be used to create a deadlock configuration. The necessary and sufficient condition can be applied in a straightforward manner to most routing algorithms. This is illustrated by proving deadlock freedom for a partially adaptive nonminimal mesh routing algorithm that does not require virtual channels and a fully adaptive minimal hypercube routing algorithm with two virtual channels per physical channel. Both routing algorithms are more adaptive than any previously proposed routing algorithm with similar virtual channel requirements.     

LCFAA:一个低代价的完全自适应路由算法

大规模并行处理机系统（ＭＰＰ）中路由算法对互联网络通信性能和系统性能起着重要作用。自适应路由算法具有灵活性好、网络的通道利用率高和网络容错能力强等优点,但其实现难度较大,因而目前仅在少数ＭＰＰ系统中得以实现。文中在ｍｅｓｈ结构上提出了一个低代价无死锁的安全自适应最短虫孔路由算法ＬＣＦＡＡ,该算法所需虚通道数少,具有代价低、自适应性强的特点。文中证明了算法的无死锁、无活锁性和完全自适应性,并模拟验证     

A general theory for deadlock-free adaptive routing using a mixedset of resources

This paper presents a theoretical framework for the design of deadlock-free fully adaptive routing algorithms for a general class of network topologies and switching techniques in a single, unified theory. A general theory is proposed that allows the design of deadlock avoidance-based as well as deadlock recovery-based wormhole and virtual cut-through adaptive routing algorithms that use a homogeneous or a heterogeneous (mixed) set of resources. The theory also allows channel queues to be allocated nonatomically, utilizing resources efficiently. A general methodology for the design of fully adaptive routing algorithms applicable to arbitrary network topologies is also proposed. The proposed theory and methodology allow the design of efficient network routers that require minimal resources for handling infrequent deadlocks     

Routing Function and Deadlock Avoidance in a Star Graph Interconnection Network

In this paper the properties of paths in a star graph are investigated through the analysis of the corresponding star transposition tree. The general algebraic expression for all shortest paths between any two nodes (routing function) is found, and it is shown that every shortest path consists of a number of subpaths which can be combined in an arbitrary order or even mutually nested. Further, due to the known routing function the deadlock problem is solved using the method of virtual channels. A minimal deterministic routing algorithm is developed which recognizes the structure of the path by extracting subpaths and allows optimal adaptive management of virtual channels. Finally, based on the sufficient number of virtual channels, the minimal fully adaptive routing algorithm is suggested which offers an opportunity to reroute the message a number of times, while maintaining the shortest path between two nodes.     

Characterization of deadlocks in k-ary n-cube networks

A spate of deadlock avoidance-based and deadlock recovery-based routing algorithms have been proposed in recent years without full understanding of the likelihood and characteristics of actual deadlocks in interconnection networks. This work models the interrelationships between routing freedom, message blocking, correlated resource dependencies, and deadlock formation. It is empirically shown that increasing routing freedom, as achieved by allowing unrestricted routing over multiple physical and virtual channels, reduces the probability of deadlocks and the likelihood of other types of correlated message blocking that can degrade performance. Moreover, when true fully adaptive routing is used in k-ary n-cube networks with two or more virtual channels (wormhole OF virtual cut-through switched), it is empirically shown that deadlocks are virtually eliminated in networks with n⩾2. These results indicate that deadlocks are very infrequent when the network and routing algorithm inherently provide sufficient routing freedom, thus increasing the viability of deadlock recovery routing strategies     

k元n—立方体网络的死锁特征剖析

研究死锁形成几率随网络参数的变化规律 ,对于选择合适的寻径算法、改良网络设计方案都具有重要意义 .环形等多种网络都是 k元 n-立方体网络系列的拓扑同构体 .因此 ,k元 n-立方体网络死锁特征的研究结果具有一定的普遍适用性 .本文根据刻画死锁特征的死锁循环密度属性划分死锁类型 .利用死锁类型分析寻径适应性、物理通道、虚拟通道、缓冲区大小 ,消息长度以及缓冲区结构等参数对死锁形成几率的影响     

An effective methodology to improve the performance of the up*/down* routing algorithm

Networks of workstations (NOWs) are being considered as a cost-effective alternative to parallel computers. Most NOWs are arranged as a switch-based network and provide mechanisms for discovering the network topology. Hence, they provide support for both regular and irregular topologies, which makes routing and deadlock avoidance quite complicated. Current proposals use the up*/down* routing algorithm to remove cyclic dependencies between channels and avoid deadlock. However, routing is considerably restricted and most messages must follow nonminimal paths, increasing latency and wasting resources. We propose and evaluate a simple and effective methodology to compute up*/down* routing tables. The new methodology is based on computing a depth-first search (DPS) spanning tree on the network graph that decreases the number of routing restrictions with respect to the breadth-first search (BFS) spanning tree used by the traditional methodology. Additionally, we propose different heuristic rules for computing the spanning trees to improve the efficiency of up*/down* routing. Evaluation results for several different topologies show that computing the up*/down* routing tables by using the new methodology increases throughput by a factor of up to 2.48 in large networks with respect to the traditional methodology, and also reduces latency significantly.     

Layered routing in irregular networks

Freedom from deadlock is a key issue in cut-through, wormhole, and store and forward networks, and such freedom is usually obtained through careful design of the routing algorithm. Most existing deadlock-free routing methods for irregular topologies do, however, impose severe limitations on the available routing paths. We present a method called layered routing, which gives rise to a series of routing algorithms, some of which perform considerably better than previous ones. Our method groups virtual channels into network layers and to each layer it assigns a limited set of source/destination address pairs. This separation of traffic yields a significant increase in routing efficiency. We show how the method can be used to improve the performance of irregular networks, both through load balancing and by guaranteeing shortest-path routing. The method is simple to implement, and its application does not require any features in the switches other than the existence of a modest number of virtual channels. The performance of the approach is evaluated through extensive experiments within three classes of technologies. These experiments reveal a need for virtual channels as well as an improvement in throughput for each technology class.     

A Generic Design Methodology for Deadlock-Free Routing in Multicomputer Networks

This paper introduces a generic methodology for defining deadlock-free wormhole routing schemes in any arbitrary network. The basic strategy is to partition a graph into subdigraphs with no cyclic dependencies and selectively assign virtual channels. The usefulness of our scheme is shown for the n-dimensional hypercube, the n-dimensional mesh, and the k-ary n-cube torus by identifying subdigraph characteristics that ensure acyclic routing. Further generalization which allows partial cyclic dependencies without deadlock is achieved by our extended generic methodology. We also illustrate how to identify shortest fixed path and nonminimal adaptive routing schemes using minimum required channels.     

Fault-tolerant routing methodology for hypercube and cube-connected cycles interconnection networks

This paper presents a fault-tolerant routing methodology for both injured hypercube and cube-connected cycles interconnection topologies. The proposed routing methodology efficiently tolerates any pattern of faulty regions with any number of faulty nodes in the network which is based on the best-first search and backtracking strategy. Deadlock freedom of the proposed routing methodology is obtained by only one virtual channel per physical channel. In order to evaluate the proposed routing methodology, a 7-dimensional hypercube network is simulated in various conditions, i.e., different traffic rates, different number of faulty nodes and different message lengths. Simulation results confirm that the proposed routing methodology in comparison with the previous methods provides acceptable performance while it significantly increases the reliability of the network. It also guarantees delivery of messages between any pair of source and destination while the network is connected.     

PDR: A protocol for dynamic network reconfiguration based on deadlock recovery scheme

Dynamic network reconfiguration is described as the process of replacing one routing function with another while the network keeps running. The main challenge is avoiding deadlock anomalies while keeping limitations on packet injection and forwarding minimal. Current approaches which have a high complexity and as a result have a limited practical applicability either require the existence of extra network resources, or they will affect the network performance during the reconfiguration process. In this paper we present a simple, fast and efficient mechanism for dynamic network reconfiguration which is based on regressive deadlock recovery instead of avoiding deadlock. The mechanism which is referred to as PDR guarantees a deadlock-free reconfiguration based on wormhole switching. In PDR, a particular approach is taken to handle both deadlocks and performance degradation. We propose the use of a packet injection restriction mechanism that prevents performance degradation near the saturation by controlling the network traffic. Further, in this approach, to accurately detect deadlocks, the deadlock detection mechanism is implemented and also improved by using only the local information, thereby considerably reducing false deadlock detections. In the rare cases when deadlocks are suspected, we propose a new technique that absorbs the deadlocked packet at the current node instead of dropping deadlocked packets and re-injects it later into the network. The main advantage of this method is its simplicity and also it does not require any additional buffers in intermediate nodes to handle deadlocks. It requires only some buffer space in the local node to temporarily hold the deadlocked packets removed from the network. Evaluating results reveal that the mechanism shows substantial performance improvements over the other methods and it works efficiently in different topologies with various routing algorithms.     

ORA——一种负载平衡的虚通道分配算法

MPP互联网中通常使用虚通病来防止死锁和提高网络吞吐率。但通常的虚通道分配算法会导致通道的负载不平衡,从而降低网络的性能。针对采用虫孔路由技术和维序路由算法下的Torus互联网,提出了ORA虚通道负载平衡分配算法。与Naive分配算法和Scott分配算法的比较表明,ORA能够较好地实现负载平衡,能够较好地提高网络的性能。     

A theory of fault-tolerant routing in wormhole networks

Fault-tolerant systems aim at providing continuous operation in the presence of faults. Multicomputers rely on an interconnection network between processors to support the message-passing mechanism. Therefore, the reliability of the interconnection network is very important for the reliability of the whole system. This paper analyzes the effective redundancy available in a wormhole network by combining connectivity and deadlock freedom. Redundancy is defined at the channel level. We propose a sufficient condition for channel redundancy, also computing the set of redundant channels. The redundancy level of the network is also defined, proposing a theorem that supplies its value. This theory is developed on top of our necessary and sufficient condition for deadlock-free adaptive routing. The new theory also considers the failure of physical channels when virtual channels are used. Finally, we propose a methodology for the design of fault-tolerant routing algorithms, showing its application to n-dimensional meshes     

Compressionless wormhole routing: an analysis for hypercube with virtual channels

Several recent studies have shown that adaptive routing algorithms based on deadlock recovery have superior performance characteristics than those based on deadlock avoidance. Most of these studies, however, have relied on software simulation due to the lack of analytical modelling tools. In an effort towards filling this gap, this paper presents a new analytical model of compressionless routing in wormhole-routed hypercubes. This routing algorithm exploits the tight coupling between wormhole routers for flow control to detect and recover from potential deadlock situations. The advantages of compressionless routing include deadlock-free adaptive routing with no extra virtual channels, simple router design, and order-preserving message transmission. The proposed analytical model computes message latency by determining the message transmission time, blocking delay at each router, multiplexing delay at each network channel, and waiting time in the source before entering the network. The validity of the model is demonstrated by comparing analytical results with those obtained through simulation experiments.     

FRoots: A Fault Tolerant and Topology-Flexible Routing Technique

Existing solutions for fault-tolerant routing in interconnection networks either work for only one given regular topology, or require slow and costly network reconfigurations that do not allow full and continuous network access. In this paper, we present FRroots, a routing method for fault tolerance in topology-flexible network technologies. Our method is based on redundant paths, and can handle single dynamic faults without sending control messages other than those that are needed to inform the source nodes of the failing component. Used in a modus with local rerouting, the source nodes need not be informed and no control messages are necessary for the network to stay connected despite of a single fault. In fault-free networks under nonuniform traffic our routing method performs comparable to, or even better than, topology specific routing algorithms in regular networks like meshes and tori. FRoots does not require any other features in the switches or end nodes than a flexible routing table, and a modest number of virtual channels. For that reason, it can be directly applied to several present day technologies like InfiniBand and Advanced Switching.     

Compressionless routing: a framework for adaptive andfault-tolerant routing

Compressionless routing (CR) is an adaptive routing framework which provides a unified framework for efficient deadlock free adaptive routing and fault tolerance. CR exploits the tight coupling between wormhole routers for flow control to detect and recover from potential deadlock situations. Fault tolerant compressionless routing (FCR) extends CR to support end to end fault tolerant delivery. Detailed routing algorithms, implementation complexity, and performance simulation results for CR and FCR are presented. These results show that the hardware for CR and FCR networks is modest. Further, CR and FCR networks can achieve superior performance to alternatives such as dimension order routing. Compressionless routing has several key advantages: deadlock free adaptive routing in toroidal networks with no virtual channels, simple router designs, order preserving message transmission, applicability to a wide variety of network topologies, and elimination of the need for buffer allocation messages. Fault tolerant compressionless routing has several additional advantages: data integrity in the presence of transient faults (nonstop fault tolerance), permanent fault tolerance, and elimination of the need for software buffering and retry for reliability. The advantages of CR and FCR not only simplify hardware support for adaptive routing and fault tolerance, they also can simplify software communication layers     

FC3D: flow control-based distributed deadlock detection mechanism for true fully adaptive routing in wormhole networks

Two general approaches have been proposed for deadlock handling in wormhole networks. Traditionally, deadlock-avoidance strategies have been used. In this case, either routing is restricted so that there are no cyclic dependencies between channels or cyclic dependencies between channels are allowed provided that there are some escape paths to avoid deadlock. More recently, deadlock recovery strategies have begun to gain acceptance. These strategies allow the use of unrestricted fully adaptive routing, usually outperforming deadlock avoidance techniques. However, they require a deadlock detection mechanism and a deadlock recovery mechanism that is able to recover from deadlocks faster than they occur. In particular, progressive deadlock recovery techniques are very attractive because they allocate a few dedicated resources to quickly deliver deadlocked messages, instead of killing them. Unfortunately, distributed deadlock detection is usually based on crude time-outs, which detect many false deadlocks. As a consequence, messages detected as deadlocked may saturate the bandwidth offered by recovery resources, thus degrading performance. Additionally, the threshold required by the detection mechanism (the time-out) strongly depends on network load, which is not known in advance at the design stage. This limits the applicability of deadlock recovery on actual networks. We propose a novel distributed deadlock detection mechanism that uses only local information, detects all the deadlocks, considerably reduces the probability of false deadlock detection over previously proposed techniques, and is not significantly affected by variations in message length and/or message destination distribution.     

Mesh网中高效无死锁自适应路由算法

提出了一种新的应用于三维Mesh网中的无死锁路由算法.在当今的商用多计算机系统中,二维和三维的Mesh网是多处理器网络最为常用的拓扑结构之一.在应用于Mesh网的平面自适应路由(Planar Adaptive Routing)算法中,每条物理通道只需三条虚拟通道就可以有效地在三维以及更高维的Mesh网中避免死锁的产生.然而,采用该算法,网络拓扑一维和三维分别有两条和一条虚拟通道始终处于空闲状态.该文所提出的算法针对三维Mesh网,每条物理通道只需两条虚拟通道就可以有效地避免死锁.文中通过充分的模拟数据验证了此算法的有效性.     

Origin-based fault-tolerant routing in the mesh

The ability to tolerate faults is critical in multicomputer employing large numbers of processors. This paper describes a class of fault-tolerant routing algorithms for n-dimensional meshes that can tolerate large numbers of faults without using virtual channels. We show that these routing algorithms prevent livelock and deadlock while remaining highly adaptive.