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

A survey of routing techniques in store-and-forward and wormhole interconnects.

This paper presents an overview of algorithms for directing messages through networks of varying topology. These are commonly referred to as routing algorithms in the literature that is presented. In addition to providing background on networking terminology and router basics, the paper explains the issues of deadlock and livelock as they apply to routing. After this, there is a discussion of routing algorithms for both store-and-forward and wormhole-switched networks. The paper covers both algorithms that do and do not adapt to conditions in the network. Techniques targeting structured as well as irregular topologies are discussed. Following this, strategies for routing in the presence of faulty nodes and links in the network are described

A fault-tolerant routing strategy for k-ary n-direct s-indirect topologies based on intermediate nodes

[EN] Exascale computing systems are being built with thousands of nodes. The high number of components of these systems significantly increases the probability of failure. A key component for them is the interconnection network. If failures occur in the interconnection network, they may isolate a large fraction of the machine. For this reason, an efficient fault-tolerant mechanism is needed to keep the system interconnected, even in the presence of faults. A recently proposed topology for these large systems is the hybrid k-ary n-direct s-indirect family that provides optimal performance and connectivity at a reduced hardware cost. This paper presents a fault-tolerant routing methodology for the k-ary n-direct s-indirect topology that degrades performance gracefully in presence of faults and tolerates a large number of faults without disabling any healthy computing node. In order to tolerate network failures, the methodology uses a simple mechanism. For any source-destination pair, if necessary, packets are forwarded to the destination node through a set of intermediate nodes (without being ejected from the network) with the aim of circumventing faults. The evaluation results shows that the proposed methodology tolerates a large number of faults. For instance, it is able to tolerate more than 99.5% of fault combinations when there are 10 faults in a 3-D network with 1000 nodes using only 1 intermediate node and more than 99.98% if 2 intermediate nodes are used. Furthermore, the methodology offers a gracious performance degradation. As an example, performance degrades only by 1% for a 2-D network with 1024 nodes and 1% faulty links.This work was supported by the Spanish Ministerio de Economía y Competitividad (MINECO), by FEDER funds under Grant TIN2015-66972-C5-1-R, by Programa de Ayudas de Investigación y Desarrollo (PAID) from Universitat Politècnica de alència and by the financial support of the FP7 HiPEAC Network of Excellence under grant agreement 287759Peñaranda Cebrián, R.; Gómez Requena, ME.; López Rodríguez, PJ.; Gran, EG.; Skeie, T. (2017). A fault-tolerant routing strategy for k-ary n-direct s-indirect topologies based on intermediate nodes. Concurrency and Computation Practice and Experience. 29(13):1-11. https://doi.org/10.1002/cpe.4065S111291

A Dag Based Wormhole Routing Strategy

The wormhole routing (WR) technique is replacing the hitherto popular storeand- forward routing in message passing multicomputers. This is because the latter has speed and node size constraints. The wormhole routing is, on the other hand, susceptible to deadlock. A few WR schemes suggested recently in the literature, concentrate on avoiding deadlock. This thesis presents a Directed Acyclic Graph (DAG) based WR technique. At low traffic levels the proposed method follows a minimal path. But the routing is adaptive at higher traffic levels. We prove that the algorithm is deadlock-free. This method is compared for its performance with a deterministic algorithm which is a de facto standard. We also compare its implementation costs with other adaptive routing algorithms and the relative merits and demerits are highlighted in the text

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

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

High-Speed Message Routing Mechanisms for Massively Parallel Computers

現在超並列処理システム(MPP)は、伝統的なベクトルプロセッサやSIMDマシンの 牙城であった多くの分野に進出している。これらのシステムは、入手が容易な高性能 CPUの急激な進歩をうまく利用し、これらを数百～数千個接続して均質なマルチプ ロセッサのシステムとして構成したものである。しかし、これらのシステムの性能は、 現実の問題を解くときは必ずしも良くなく、常に公称の最高性能にははるかに及ばな いのが現状である。これらのシステムではプロセッサ間の通信はすべて相互結合網に よって行われるので、実現可能な最高性能を決める決定的な要素は相互結合網と、そ れに使われる通信機構である。 本論文ではMPPの相互結合網に使われる、効率的な通信機構を実現する2つの方法 を提案する。第1は「特急ルータ」の提案であり、これを相互結合網に用いた場合の 適合性を検註する。特急ルータは多重の単方向レジスタ挿入パスを利用して、時間 空間混合分割型ネットワークを実現するためのものである。異なる基数や次元数につ いて、特急ルータのスイッチ回路とバッファ回路の性能を予測するための正確なモデ ルを開発した。この結果、特急ルータは効率的な通信を行うためのすべての条件を満 足していることが確かめられた。さらに重要な点は、特急ルータはネットワークに故 障のある場合や、通信が錯綜する場合にも、低遅延時間、高スループットを損なわな い経路制御が行えることである。シミュレーションによって評価した特急ルータのの 性能は、これまでに発表された固定経路選択方式のルータより優れており、また他の 適応経路制御方式のルータに比べても、同程度あるいはそれを越えていることが確か められた。 第2は経路長制限方式のマルチキャスト通信の提案である。マルチキャスト通信は 多くの並列処理問題において速度向上に寄与する通信方式である。そこでワームホー ル通信方式において問題となるマルチキャスト通信におけるデッドロックの問題につ いて研究した。そしてこの問題を解決する方法として経路長制限方式のマルチキャス ト通信を提案し、この方式による通信性能をシミュレーションによって評価し、ユニ キャスト方式やマルチパス方式によるマルチキャスト通信の性能と比較した。その結 果、提案する経路長制限方式のマルチキャスト通信は、パリヤ同期のためのクラスタ へのマルチキャスト通信や、最近傍ノードへのマルチキャストや全ノードへの放送の 場合に、特に優れた解決法となることを明らかにした

Self-stabilizing wormhole routing in hypercubes

Wormhole routing is an efficient technique used to communicate message packets between processors when they are not completely connected. To the best of our knowledge, this is the first attempt at designing a self-stabilizing wormhole routing algorithm for hypercubes. Our first algorithm handles all types of faults except for node/link failures. This algorithm achieves optimality in terms of routing path length by following only the preferred dimensions. In an n-dimensional hypercube, those dimensions in which source and destination address bits differ are called preferred dimensions. Our second algorithm handles topological changes. We propose an efficient scheme of rerouting flits in case of node/link failures. Similar to the first algorithm, this algorithm also tries to follow preferred dimensions if they are nonfaulty at the time of transmitting the flits. However, due to topological faults it is necessary to take non-preferred dimensions resulting in suboptimality of path selection. Formal proof of correctness for both solutions is given. (Abstract shortened by UMI.)

On the relation between network throughput and delay curves

The theoretical background of network throughput and delay has been widely used in the previous studies to efficiently study the behaviour of different interconnection networks. In this paper, we derive a new relationship between the network throughput and delay curves. Specifically, we prove that this relation on the average delay and throughput in x-Folded TM topology by considering the tangent line of each curve. Based on the achievements, we introduce the reflection relation between these two performance metrics, while considering the gradient of the metric curves. Moreover, we show the superiority of x-Folded TM topology, previously introduced with same authors, is obvious with this relation in interconnection networks. Consequently, the obtained results have been verified with simulation results to signify how to relate the performance metrics for various topologies in interconnection networks