Dally, W. J. (1990) Performance analysis of k-ary n-cube interconnection networks. IEEE Trans. Computers, 39, 775-- 785.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....idempotent messaging protocol described in Chapter 5 implemented using both circuit switching and wormhole routing on three different network topologies. The literature contains a myriad of analytical models for dynamic network behaviour. Models have been proposed for specific network topologies ([Dally90], Stamoulis91] Saleh96] Greenberg97] routing algorithms ( Draper94] Sceideler96] Ould98] and traffic patterns [Sarbazi00] While the vast majority of this work has focused on non discarding networks, discarding networks have also been considered ( Parviz79] Rehrmann96] Datta97] ....

William J. Dally, "Performance Analysis of k-ary n-cube Interconnection Networks", IEEE Transactions on Computers, Vol. 39, No. 6, June 1990, pp. 775-785. 147

....on to further investigate the techniques through the SPIDERS project. Section 2. It supports both 2 and 3 dimensional torus (a mesh with wraparound connections) network topologies with up to 256 processing nodes. In addition to the proposed techniques, the simulator features wormhole switching [9] and virtual channel flow control [10] The former pipelines the flit transfer and the latter reduces the packet blocking. It also utilizes fully adaptive deadlock recovery routing scheme proposed in [11] This scheme is believed to be the most efficient routing algorithm to date. Therefore, our ....

William J. Dally, "Performance Analysis of k-ary n- cube Interconnection Networks," in IEEE Transaction on Computers, 775-785 (1990).

....class of networks which is utilized in several multiprocessor systems such as the CRAY T3E or Intel Teraflops. Topologies for this class of networks have channels which span n dimensions and have k nodes connected in each dimension (radix) The network analysis here assumes wormhole switching [7] which pipelines the transfer of flits along the path from source to destination. Once a node receives the header flit of a message (which contains all the relevant routing information) the header flit is routed to an appropriate output channel. If that channel is free, the header is transferred ....

William J. Dally, "Performance Analysis of k-ary n-cube Interconnection Networks," IEEE Transaction on Computers, 775-785(1990).

....the performance of wormhole switching with minimal and fully adaptive routing in a twodimensional torus. Most previous papers presenting analytical models consider either different switching techniques (such as circuit switching [4] and virtualcut through [10] or deterministic routing [1] 3] [5], 6] To the best of our knowledge, an analytical evaluation of wormhole with adaptive routing is done colajanni unimo.it ciciani dis.uniroma1.it quaglia dis.uniroma1.it only in [8] Such analysis differs from our work as it considers Duato s adaptive routing [7] instead of ....

....with a Poisson process with rate 1= bit (bit cycle) This assumption and the symmetry of torus topology guarantee that the network is balanced [9] that is, we can assume that channels are equally likely to be visited independently of the message destination distribution. As in Dally s approach [5], we assume that the network has no virtual channels. We consider the transmission of a message as consisting of two consecutive and separate phases: path hole and data trail. During the path hole phase, the header flit builds the path from the source to the destination. All delays due to channel ....

W.J. Dally, "Performance analysis of k-ary n-cube interconnection networks", IEEE Trans. on Computers, vol. 39, no. 6, June 1990, pp. 775--785.

....the third section presents a topology independent framework for classifying these distributed routing algorithms. This framework defines the space of synchronous distributed routing algorithms, which is then explored for three network topologies: hypercubes, star graphs [3, 4] and torus graphs [5]. A Plethora of Routing Strategies The basis of any routing strategy is an algorithm for finding circuits from a given source node to a given destination node. Ngai and Seitz [6] classify such source to destination routing algorithms as either minimal or non minimal; under a minimal algorithm ....

.... quite accurately, by pc = 1 pb) N [9] Routing on Star Graphs Recently, it has been suggested that for large n , the extreme complexity of the nn switches and the large number of links required by the n cube outweigh the cube s advantages of simplicity and flexibility [3, 4, 5]. Accordingly, Akers and Krishnamurthy [4] introduced the star graph topology as an alternative network structure with lower degree. An n star graph connects N = n vertices, where each vertex is labelled with a permutation on n elements. Two vertices in a star graph are connected if the label of ....

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W. J. Dally, "Performance Analysis of k-ary n-Cube Interconnection Networks," IEEE Transactions on Computers 39(6), (June, 1990), pp. 775--785.

....Moreover, this pipelined message transmission makes latency less sensitive to the distance in the network provided that messages are long enough, facilitating the search for optimal topologies. Several researchers recommended the use of low dimensional direct networks in the k ary n cube class [1, 8]. As a result, the use of bidimensional or threedimensional meshes and tori or limited degree hypercubes is common in multicomputers and DSMs. However, wormhole switching has also some disadvantages. A main one is that messages block in place when the link requested by the header is busy. So, ....

W. J. Dally, "Performance analysis of k-ary n-cube interconnection networks," IEEE Transactions on Computers, vol. C--39, no. 6, pp. 775--785, June 1990.

....of communication intensive tasks, such as random routing, sorting, FFT, and total exchange. When the unit link capacity model is used, the bisection bandwidth of a network is equal to its bisection width; when the unit bisection capacity model is used (similar to the one proposed by Dally in [11], which is a reasonable model for single chip multiprocessors (SCMP) the bisection bandwidths of networks are the same regardless their bisection widths; however, when the unit node capacity model or the unit chip capacity model is used, the bisection bandwidth of a network needs to be computed ....

Dally, W.J. " Performance analysis of k-ary n-cube interconnection networks," IEEE Trans. Comput., Vol. 39, no. 6, Jun. 1990, pp. 775-785.

....remote data. The communication subsystem of these machines is composed of a number of interconnected routers arranged in a specific topology. The performance of these direct interconnection networks is governed by that of the router and the interconnect. With respect to network topology, Dally [11] and Agarwal [1] recommended the use of low degree networks belonging to the class of the k ary n cubes. Rings, meshes, tori and hypercubes are representative networks of this class. Some parallel computer manufacturers followed their advice and machines such as the Cray T3D and Cray T3E use ....

W. J. Dally, "Performance analysis of k-ary n-cube interconnection networks," IEEE Trans. on Computers, vol. C--39, no. 6, pp. 775--785, June 1990.

....communication capacity between any two halves of the network when dealing with random or non local traffic. Other implementation factors such as wiring density and chip pinouts should be also taken into account when searching for an optimal topology. In particular, a milestone performance study [5] showed that lower dimensional networks, such as 2D and 3D tori, outperform higher dimensional ones such as the hypercube under constant wiring density constrains. This work is supported in part by TIC98 1162 C02 01 The Midimew (MInimal DIstance Mesh with Wrap around links) 2] is an optimal ....

W.J. Dally, "Performance Analysis of k-ary n-cube Interconnection Networks", IEEE Trans. On Comp., Vol 39,No. 6 pp. 775-785, June 1990.

....time. The studies differ in the techniques used to quantify these metrics. Crovella and LeBlanc [10] use experimentation, while simulation is used in our approach. III. Related Work There have been a number of studies addressing architectural issues such as network latency and contention [11] [12], 13] 14] and synchronization [15] 16] in isolation. While such issues are extremely important, their performance impact should be put in perspective by considering them in the context of the overall application. Recognizing this importance, the current trend in architectural 4 evaluation ....

....topology. The cube represents a highly scalable network where the bisection bandwidth grows linearly with the number of processors. Even though cubes of 1024 nodes have been built [2] cost and technology factors often play an important role in its physical realization. Agarwal [11] and Dally [12] show that wire delays (due to increased wire lengths associated with planar layouts) of higher dimensional networks make low dimensional networks more viable. The 2 dimensional [50] and 3 dimensional [51] 52] toroids are common topologies used in current day networks, and it would be ....

W. J. Dally, "Performance analysis of k-ary n-cube interconnection networks," IEEE Transactions on Computer Systems, vol. 39, no. 6, pp. 775--785, June 1990.

....is described in Section 4. Simulation results are presented in Section 5, followed by the concluding remarks in Section 6. 2P RELIMINARIES In this section, we define the terminologies associated with the adaptive routing scheme. Some of these definitions are reiterated from previous works [7] [13], 14] for the sake of completeness. DEFINITION 1. A physical interconnection network, PN, is a strongly connected graph, PN(PV, PC) where PV represents the set of processing nodes and PC represents the set of physical channels connecting the nodes. DEFINITION 2. A virtual interconnection ....

W.J. Dally, "Performance Analysis of k-ary n-cube Interconnection Networks," IEEE Trans. Computers, vol. 39, no. 6, pp. 775--785, June 1990.

....increased hardness it is questionable if standard variance estimation techniques can be used. To evaluate the proposed variance estimation method we use the wormhole switched system studied in [2] as an example. Specifically, data from a simulated unbuffered k ary n cube direct network topology [14] is used. This class of networks has k nodes in each of n dimensions giving a total of N = k n nodes. We use unidirectional links and wrap arounds in each dimension to obtain connectivity. The network is simulated under uniform traffic characteristics and the load corresponds to 80 of the ....

....especially susceptible to deadlocks. The example system avoid deadlocks by routing packets deterministicly in order of decreasing channel index [15] Two virtual channels in combination with dimension order routing is used. Systems with similar features have been subject to a number of studies [14, 16 18]. Hence, we consider the example system to be a representative for a class of networks characterized by highly correlated latency recordings. Further details about the simulated system and traffic conditions can be found in [2] Note finally that the plots in figures 3 and 5 are based on data ....

W.J. Dally, "Performance analysis of k-ary-n-cube interconnection networks, " IEEE Transactions on Computers, vol. 39, no. 6, pp. 775--785, 1990.

....is negligible. We argue that more sophisticated variance estimation methods, like spectral based methods, should be considered for wormhole switched networks. Keywords Wormhole switching, performance evaluation, latency, estimation methods, simulation I. INTRODUCTION W ORMHOLE SWITCHING [1 4] is a new packet switching principle which uses almost no buffering at each switching point. By reducing the storage requirements silicon area can rather be used to provide more ports per chip. Simplified buffer handling and tighter integration make switching faster. The primary application of ....

....hypothesis. The paper is closed in section VII with some concluding remarks. 1 e.g. Var [X Y ] Var [X ] Var [Y ] Cov [X, Y ] 2 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS. SUBMITTED APRIL 1998 II. SIMULATED SYSTEM The simulated system is a k ary n cube direct network topology [4]. This class of networks has k nodes in each of n dimensions giving a total of N = k n nodes. In particular we use a 16 ary 2 cube, i.e. a two dimensional mesh with 16 nodes in each direction giving a total of 256 nodes. This is a moderately sized network which is large enough to be of interest ....

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W.J. Dally, "Performance analysis of k-ary-n-cube interconnection networks, " IEEE Transactions on Computers, vol. 39, no. 6, pp. 775--785, 1990.

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Dally, W. J. (1990) Performance analysis of k-ary n-cubes interconnection networks. IEEE Trans. Computers, C39, 775--785.

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Dally, W. J. (1990) Performance analysis of k-ary n-cube interconnection networks. IEEE Trans. Computers, 39, 775-- 785.

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W.J. Dally,"Performance analysis of k-ary n-cube interconnection networks", IEEE Trans. Computers. ,Vol. 39, No. 6, June 1990, 775--785.

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William J. Dally, "Performance analysis of k-ary n-cube interconnection networks," IEEE Transactions on Computers, Vol. C-39, No. 6, pp. 775785, June 1990.

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W. J. Dally, "Performance Analysis of k-ary n-cube Interconnection Networks," IEEE Trans. on Computers, vol. 39, no. 6, pp. 775-785, June 1990.

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William J. Dally, "Performance Analysis of k-ary n-cube Interconnection Networks", IEEE Transactions on Computers, vol. C-39, no. 6, pp. 775-785, June 1990.

No context found.

W. J. Dally, "Performance analysis of k-ary n-cube interconnection networks. " IEEE Trans. Comput., vol. 39, no. 6, June 1990, pp. 775-785.

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Dally, W. J., "Performance analysis of k-ary n-cube interconnection networks," IEEE Trans. on Computers, vol. 39, pp. 775--785, Jun 1990.

No context found.

W. J. Dally, "Performance analysis of k-ary n-cube interconnection networks," IEEE Transactions on Computers, vol. 39, pp. 775--785, June 1990.

No context found.

Dally, W. J. (1990) Performance analysis of k-ary n-cube interconnection networks. IEEE Trans. Comput., 39, 775--785.

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Dally, W.J., "Performance analysis of k-ary n-cube interconnection networks," IEEE Trans. Comput., Vol. 39, no. 6, Jun. 1990, pp. 775-785.

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W.J.Dally, "Performance Analysis of k-ary n-cube Interconnection Networks," IEEE Trans. Comput., Vol.39, pp.775-785, Jun.1990.

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