A general analytical model of adaptive wormhole routing in k-ary n-cubes

Several analytical models of fully adaptive routing have recently been proposed for k-ary n-cubes and hypercube networks under the uniform traffic pattern. Although,hypercube is a special case of k-ary n-cubes topology, the modeling approach for hypercube is more accurate than karyn-cubes due to its simpler structure. This paper proposes a general analytical model to predict message latency in wormhole-routed k-ary n-cubes with fully adaptive routing that uses a similar modeling approach to hypercube. The analysis focuses Duato's fully adaptive routing algorithm [12], which is widely accepted as the most general algorithm for achieving adaptivity in wormhole-routed networks while allowing for an efficient router implementation. The proposed model is general enough that it can be used for hypercube and other fully adaptive routing algorithms

New Fault Tolerant Multicast Routing Techniques to Enhance Distributed-Memory Systems Performance

Distributed-memory systems are a key to achieve high performance computing and the most favorable architectures used in advanced research problems. Mesh connected multicomputer are one of the most popular architectures that have been implemented in many distributed-memory systems. These systems must support communication operations efficiently to achieve good performance. The wormhole switching technique has been widely used in design of distributed-memory systems in which the packet is divided into small flits. Also, the multicast communication has been widely used in distributed-memory systems which is one source node sends the same message to several destination nodes. Fault tolerance refers to the ability of the system to operate correctly in the presence of faults. Development of fault tolerant multicast routing algorithms in 2D mesh networks is an important issue. This dissertation presents, new fault tolerant multicast routing algorithms for distributed-memory systems performance using wormhole routed 2D mesh. These algorithms are described for fault tolerant routing in 2D mesh networks, but it can also be extended to other topologies. These algorithms are a combination of a unicast-based multicast algorithm and tree-based multicast algorithms. These algorithms works effectively for the most commonly encountered faults in mesh networks, f-rings, f-chains and concave fault regions. It is shown that the proposed routing algorithms are effective even in the presence of a large number of fault regions and large size of fault region. These algorithms are proved to be deadlock-free. Also, the problem of fault regions overlap is solved. Four essential performance metrics in mesh networks will be considered and calculated; also these algorithms are a limited-global-information-based multicasting which is a compromise of local-information-based approach and global-information-based approach. Data mining is used to validate the results and to enlarge the sample. The proposed new multicast routing techniques are used to enhance the performance of distributed-memory systems. Simulation results are presented to demonstrate the efficiency of the proposed algorithms

Performance modeling of fault-tolerant circuit-switched communication networks

Circuit switching (CS) has been suggested as an efficient switching method for supporting simultaneous communications (such as data, voice, and images) across parallel systems due to its ability to preserve both communication performance and fault-tolerant demands in such systems. In this paper we present an efficient scheme to capture the mean message latency in 2D torus with CS in the presence of faulty components. We have also conducted extensive simulation experiments, the results of which are used to validate the analytical mode

New fault-tolerant routing algorithms for k-ary n-cube networks

The interconnection network is one of the most crucial components in a multicomputer as it greatly influences the overall system performance. Networks belonging to the family of k-ary n-cubes (e.g., tori and hypercubes) have been widely adopted in practical machines due to their desirable properties, including a low diameter, symmetry, regularity, and ability to exploit communication locality found in many real-world parallel applications. A routing algorithm specifies how a message selects a path to cross from source to destination, and has great impact on network performance. Routing in fault-free networks has been extensively studied in the past. As the network size scales up the probability of processor and link failure also increases. It is therefore essential to design fault-tolerant routing algorithms that allow messages to reach their destinations even in the presence of faulty components (links and nodes). Although many fault-tolerant routing algorithms have been proposed for common multicomputer networks, e.g. hypercubes and meshes, little research has been devoted to developing fault-tolerant routing for well-known versions of k-ary n-cubes, such as 2 and 3- dimensional tori. Previous work on fault-tolerant routing has focused on designing algorithms with strict conditions imposed on the number of faulty components (nodes and links) or their locations in the network. Most existing fault-tolerant routing algorithms have assumed that a node knows either only the status of its neighbours (such a model is called local-information-based) or the status of all nodes (global-information-based). The main challenge is to devise a simple and efficient way of representing limited global fault information that allows optimal or near-optimal fault-tolerant routing. This thesis proposes two new limited-global-information-based fault-tolerant routing algorithms for k-ary n-cubes, namely the unsafety vectors and probability vectors algorithms. While the first algorithm uses a deterministic approach, which has been widely employed by other existing algorithms, the second algorithm is the first that uses probability-based fault- tolerant routing. These two algorithms have two important advantages over those already existing in the relevant literature. Both algorithms ensure fault-tolerance under relaxed assumptions, regarding the number of faulty components and their locations in the network. Furthermore, the new algorithms are more general in that they can easily be adapted to different topologies, including those that belong to the family of k-ary n-cubes (e.g. tori and hypercubes) and those that do not (e.g., generalised hypercubes and meshes). Since very little work has considered fault-tolerant routing in k-ary n-cubes, this study compares the relative performance merits of the two proposed algorithms, the unsafety and probability vectors, on these networks. The results reveal that for practical number of faulty nodes, both algorithms achieve good performance levels. However, the probability vectors algorithm has the advantage of being simpler to implement. Since previous research has focused mostly on the hypercube, this study adapts the new algorithms to the hypercube in order to conduct a comparative study against the recently proposed safety vectors algorithm. Results from extensive simulation experiments demonstrate that our algorithms exhibit superior performance in terms of reachability (chances of a message reaching its destination), deviation from optimality (average difference between minimum distance and actual routing distance), and looping (chances of a message continuously looping in the network without reaching destination) to the safety vectors

Tree-Based Multicasting in Wormhole-Routed Irregular Topologies

A deadlock-free tree-based multicast routing algorithm is presented for all direct networks, regardless of interconnection topology. The algorithm delivers a message to any number of destinations using only a single startup phase. In contrast to existing tree-based schemes, this algorithm applies to all interconnection topologies, requires only fixed-sized input buffers that are independent of maximum message length, and uses a single asynchronous flit replication mechanism. The theoretical basis of the technique used here is sufficiently general to develop other tree-based multicasting algorithms for regular and irregular topologies. Simulation results demonstrate that this tree-based algorithm provides a very promising means of achieving very low latency multicast

Performance analysis of wormhole routing in multicomputer interconnection networks

Perhaps the most critical component in determining the ultimate performance potential of a multicomputer is its interconnection network, the hardware fabric supporting communication among individual processors. The message latency and throughput of such a network are affected by many factors of which topology, switching method, routing algorithm and traffic load are the most significant. In this context, the present study focuses on a performance analysis of k-ary n-cube networks employing wormhole switching, virtual channels and adaptive routing, a scenario of especial interest to current research. This project aims to build upon earlier work in two main ways: constructing new analytical models for k-ary n-cubes, and comparing the performance merits of cubes of different dimensionality. To this end, some important topological properties of k-ary n-cubes are explored initially; in particular, expressions are derived to calculate the number of nodes at/within a given distance from a chosen centre. These results are important in their own right but their primary significance here is to assist in the construction of new and more realistic analytical models of wormhole-routed k-ary n-cubes. An accurate analytical model for wormhole-routed k-ary n-cubes with adaptive routing and uniform traffic is then developed, incorporating the use of virtual channels and the effect of locality in the traffic pattern. New models are constructed for wormhole k-ary n-cubes, with the ability to simulate behaviour under adaptive routing and non-uniform communication workloads, such as hotspot traffic, matrix-transpose and digit-reversal permutation patterns. The models are equally applicable to unidirectional and bidirectional k-ary n-cubes and are significantly more realistic than any in use up to now. With this level of accuracy, the effect of each important network parameter on the overall network performance can be investigated in a more comprehensive manner than before. Finally, k-ary n-cubes of different dimensionality are compared using the new models. The comparison takes account of various traffic patterns and implementation costs, using both pin-out and bisection bandwidth as metrics. Networks with both normal and pipelined channels are considered. While previous similar studies have only taken account of network channel costs, our model incorporates router costs as well thus generating more realistic results. In fact the results of this work differ markedly from those yielded by earlier studies which assumed deterministic routing and uniform traffic, illustrating the importance of using accurate models to conduct such analyses