Fault-tolerant wormhole routing in tori

A fault-tolerant routing algorithm for torus networks that uses only three virtual channels is presented. The proposed algorithm is based on the block fault model, which is suitable for modelling faults at the board level in networks with grid structures. Messages are routed via shortest paths when there are no faults. However, if a message is blocked by a faulty block, the message will use a detour path to route around the faulty block. Previously at least six virtual channels were needed to achieve the same fault-tolerant ability. Simulation results using various workloads and fault patterns are presented.

A balanced ring (b-ring) proposed by Gu et al. [Journal of Systems Architecture, 53, (2007), 902–912.] is more effective than a fault ring (f-ring) in providing fault tolerance for mesh and torus networks. By properly utilizing the b-ring, an efficient fault tolerant routing algorithm can be achieved without using any virtual channel. Traffic congestion can also be significantly reduced. However, the algorithm presented by Gu et al. for the formation of b-ring has the demerits that it involves all the nodes of the network each time a b-ring needs to be formed, and thereby increasing the overhead to the whole system. In this paper, we first present an improved algorithm for the formation of b-ring by considering only the nodes on the fault ring in contrast to all. We next present a distributed algorithm for the same, which is also based on the local knowledge, thereby avoiding overhead and thus, enhancing the overall network performances. We show that our sequential algorithm requires O(|f-ring|) time and the distributed algorithm runs in constant time.

Cluster networks are seen as the future access networks for multimedia streaming, e-commerce, network storage, etc. For these applications, performance and high availability are particularly crucial. Regular topologies are preferred when performance is the primary concern. However, due to spatial constraints or fault-related issues, the network structure may become irregular, which makes more difficult to find deadlock-free minimal paths. Over the recent years, several solutions have been proposed. One of them is the LASH routing, which enables minimal routing by assigning paths to different virtual layers. In this paper, we propose an extension of LASH in order to reduce the number of required virtual layers by allowing transitions between virtual layers. Evaluation results show that the new routing scheme (LASH-TOR) is able to obtain full minimal routing with a reduced number of virtual channels. For torus and mesh networks, with only two virtual channels, LASH throughput is increased by an average factor of improvement of 3.30 for large networks. For regular networks with some unconnected (faulty) links, equal performance improvements are achieved. Even for highly irregular networks of size up to 128 switches the new routing scheme only needs three virtual channels for guaranteeing minimal routing. Besides, LASH-TOR performs well compared to dimension order routing for mesh and torus networks.

This paper presents a deadlock-free fault-tolerant routing algorithm for irregular mesh network-on-chips based on a region-based approach. In this approach, a set of rectangular faulty regions called faulty blocks is formed for faulty nodes and a detour path is defined for each faulty block to indicate how packets must detour thefaulty block. The most recent routing algorithm on this approach is Message-Route (Holsmark and Kumar J Inf Sci Eng 23:1649---1662, 2007) which does not have restrictions on the number of tolerable faulty nodes and its distribution. However, this algorithm has three crucial problems; (1) this algorithm fails to provide complete and deadlock-free routing, (2) many nonfaulty nodes are contained in faulty blocks and thus deactivated, and (3) complex routing functions are not feasible for hardware implementation. In this paper, we give a solution for each of the above three problems. We correct the errors of Message-Route to make it complete and deadlock-free. Then, we propose a deadlock-free fault-tolerant routing algorithm which can work under small-sized faulty blocks with a simple routing control. Experimental results show that the proposed algorithm significantly reduces the size of faulty blocks and improves communication latency for both random and cluster faults. Moreover, an FPGA implementation of the proposed algorithm is also discussed.

In the network of Tori with faults, many fault-tolerant routing schemes have been proposed based on the fault models. Although these schemes enable the packets to bypass the fault regions without causing any deadlock in the network, they have the common shortcoming. Since all blocked packets would be misrouted on the fault ring, the fault ring would undertake heavier traffic load, which makes it be the bottleneck of the network. In this paper, targeting this drawback in the faulty network, we have proposed the concept of outer ring, which is comprised of the nodes neighboring to the fault ring and shares the shape with the fault ring. Through designing a kind of fault-tolerant routing scheme to lessen the traffic load into the fault ring, the bottleneck effect of the fault ring could be alleviated so that the performance of the network could be improved.

Fault tolerance is one of the most important issues for the design of cost-effective and high performance interconnection networks. In this paper, a new fault tolerance routing algorithm for n-dimensional meshes is presented. The presented algorithm is based on a planer fault model which only disables minimum fault-free nodes to form rectangular fault regions. The algorithm uses three virtual channels per physical channel and only employs a very simple deadlock avoidance scheme. In spit the variety fault regions in n-dimensional mesh, the presented algorithm is always connected as long as fault regions do not disconnect the network. The result of simulation shows that the proposed routing algorithm is of feasibility of gracefully degraded operation.

A new performance measure for characterizing fault rings in interconnection networks

We present a new routing policy, called maximum shortest paths (MP) routing policy, within the class of shortest-path routing policies for mesh-connected topologies which include popular 2-D and 3-D meshes, 2-D and 3-D tori, and n-dimensional hypercubes (n-cubes). In this policy, the routing message is always forwarded to a neighbor from which there exists a maximum number of shortest paths to the destination. An optimal routing defined in this paper is the one that maximizes the probability of reaching the destination from a given source without delays at intermediate nodes. We show that the MP routing policy is equivalent to the e-cube routing in n-cubes which is optimal, and it is also equivalent to the Badr and Podar's zig-zag (Z/sup 2/) routing policy in 2-D meshes which is also optimal. We prove that the Z/sup 2/ routing policy is not optimal in any N/spl times/N torus, where N is an even number larger than four. A routing algorithm is proposed to implement the MP routing policy in 2-D tori and if is proved to be at least suboptimal (optimal for some cases). Our approach is the first attempt to address optimal routing in the torus network which is still an open problem.

Multiprocessor is another great technology that helps in advancing human civilization due to high demands for solving complex problems. A multiprocessing system can have a lot of replicated processor-memory pairs (henceforth regard as net) or also called as processing nodes. Each of these nodes is connected to each other through interconnection networks and passes message using a standard message passing mechanism. In this paper, we present a routing algorithm based on enhanced simulated annealing technique to provide the connection between nodes in a semi-diagonal torus (SD-Torus) network. This network is both symmetric and regular; thus, make it very beneficial in the implementation process. The main objective is to maximize the number of established connection between nodes in this SD-Torus network. In order to achieve this objective, each node must be connected in its shortest way as possible. We start our algorithm by designing shortest path algorithm based on Dijkstra’s method. While this algorithm guarantees to find the shortest path for each single net, if it exists, each routed net will form obstacle for later paths. This increases the complexity to route later nets and makes routing longer than optimal, or sometimes impossible to complete. The solution is further refined by re-routing all nets in different orders using simulated annealing method. Through simulation program, our proposed algorithm succeeded in performing complete routing up to 81 nodes with 40 nets in 9×9 SD-Torus network size.

An interconnection network based on a star graph of arbitrary order n, is analysed. Star graphs belong to a family of Cayley graphs, in which vertices correspond to elements of a permutation group, and edges correspond to generators of the group. Generators of the star graph of order n are n-1 transpositions, which may be represented with a star transposition tree. The algebraic properties of these graphs are investigated through analysis of the corresponding transposition tree. The algebraic expression for the shortest path between two nodes is found, and it is shown that every shortest path consists of a number of subpaths, which may be combined in an arbitrary order. From the analysis of shortest paths follows the minimum number of virtual channels, into which every physical channel must be split in order to avoid deadlock. Finally, a routing algorithm is developed which repetitively extracts subpaths, by sorting the source permutation to the destination permutation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

We propose a deterministic fault-tolerant and deadlock-free routing protocol in 2-dimensional (2-D) meshes based on dimension-order routing and the recently proposed odd-even turn model. The proposed protocol, called extended X-Y routing, does not use any virtual channels by prohibiting certain locations of faults and destinations. Faults are contained in a set of disjointed rectangular regions called faulty blocks. The number of faults to be tolerated is unbounded as long as nodes outside faulty blocks are connected in the mesh network. The extended X-Y routing can also be used under a special convex fault region called orthogonal faulty block, which can be derived from a given faulty block by activating some nonfaulty nodes in the block. Extensions to partial adaptive routing, traffic- and adaptivity-balanced using virtual networks, and routing without constraints using virtual channels and virtual networks are also discussed.

Compressionless Routing (GR) is a new 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 potential deadlock situations and recover from them. Fault-tolerant Compressionless Routing (FCR) extends Compressionless Routing to support end-to-end fault-tolerant delivery. Detailed routing algorithms, implementation complexity and performance simulation results for CR and FCR are presented.CR has the following advantages: deadlock-free adaptive routing in torus 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. FCR has the following advantages: tolerates transient faults while maintaining data integrity (nonstop fault-tolerance), tolerates permanent faults, can be applied to a wide variety of network topologies, and eliminates the need for software buffering and retry for reliability. These advantages of CR and FCR not only simplify hardware support for adaptive routing and fault-tolerance, they also can simplify communication software layers.

We develop on-line routing and wavelength assignment (RWA) algorithms for WDM bidirectional ring and torus networks with N nodes. The algorithms dynamically support all k-allowable traffic matrices, where k denotes an arbitrary integer vector [k/sub 1/, k/sub 2/,... k/sub N/], and node i, 1 /spl les/ i /spl les/ N, can transmit at most k/sub i/ wavelengths and receive at most k/sub i/ wavelengths. Both algorithms support the changing traffic in a rearrangeably nonblocking fashion. Our first algorithm, for a bidirectional ring, uses [(/spl Sigma//sub i=1//sup N/ k/sub i/)/3] wavelengths in each fiber and requires at most three lightpath rearrangements per new session request regardless of the number of nodes N and the amount of traffic k. When all the k/sub i/'s are equal to k, the algorithm uses [kN/3] wavelengths, which is known to be the minimum for any off-line rearrangeably nonblocking algorithm. Our second algorithm, for a torus topology, is an extension of a known off-line algorithm for the special case with all the k/sub i/'s equal to k. For an R /spl times/ C torus network with R /spl ges/ C nodes, our on-line algorithm uses [kR/2] wavelengths in each fiber, which is the same as in the off-line algorithm, and is at most two times a lower bound obtained by assuming full wavelength conversion at all nodes. In addition, the on-line algorithm requires at most C - 1 lightpath rearrangements per new session request regardless of the amount of traffic k. Finally, each RWA update requires solving a bipartite matching problem whose time complexity is only O (R), which is much smaller than the time complexity O(kCR/sup 2/) of the bipartite matching problem for an off-line algorithm.

The adaptive routing approach has been expected as a promising way to improve network performance by utilizing available network bandwidth. Previous adaptive routing strategies in wormhole-routed multicomputer networks restrict the routing of messages by the routing algorithm to prevent deadlock. This results in low degree of adaptivity and low utilization of physical or virtual channels. In this paper, we examine the possibility of performing restriction-free adaptive routing in wormhole-routed networks as an approach to further improving the performance of these networks. A new flow control policy, called message cutting-in, is proposed, and two adaptive routing strategies are presented. Freedom of communication deadlock is achieved by the proposed flow control policy. The proposed adaptive routing strategies do not restrict routing and maximally utilize the physical and virtual channels. Simulation results show that the restriction-free adaptive routing approach is promising from the fact that it has the lowest latency and highest throughput depending on the number of virtual channels per physical channel and patterns of message traffic.

In this paper, we would present a fault-tolerant wormhole routing scheme, called two-level-turn-model scheme, in the tori with convex faults. The reason why we choose the convex faults is that the shape of the convex faults is instrumental to design an effective fault-tolerant routing algorithm. Compared with many other solutions, which mainly focus on providing extra virtual channels to tolerate the faults, one of the advantages of our solution is that it is based on the turn model, which itself could tolerate some faults for some messages. At the same time, our solution could work effectively no matter where the fault region locates and no matter whether the fault regions are connected. In our solution, two patterns of the turn model are complementary to tolerate the faults. With a few limits to the shape of the convex faults, at most five virtual channels per physical channel are required to avoid the deadlock.