Scott, S. L. and Goodman, J. R. (1994) The impact of pipelined channel on k-ary n-cube networks. IEEE Trans. Parallel Distributed. Syst., 5, 2--16.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Reference [4] combines a wire bisection limit with a pin limit and concludes that a slightly higher dimensionality is optimal. Reference [8] adds express channels to cube to balance wire and router delay and shows how channel bandwidth can be matched to the packaging technology. In [19] the impact of pipelining the channels in ary cube is studied. SOENets are tree like networks. Many variations on hierarchical, tree topologies have been proposed over the years. Clos networks [6] and Benes networks [5] are nonblocking hierarchical networks. An X tree [11] is a tree ....

S. Scott and J. Goodman. Impact of pipelined channels on k-ary n-cube networks, 1994.

....the amount of information in a message that a router can process each cycle. Such flits are in turn composed of phits, which are the transmission unit on the physical links connecting the routers. Each router chip is furnished with a number of bidirectional, clock decoupled, wave pipelined ports [15], operating at four times the frequency of the chip and able to accept a new phit every clock cycle independently of the wire length. Each phit is 16 bit wide and each router flit is composed of four phits, thus matching link and router bandwidth while keeping the number of pins per port ....

....simulated are hypercubes built out of 7 port routers. We examine the following configurations: 4 way 8 node, 2 way 16 node, and 1 way 32node hypercubes. We have assumed that all topologies are implemented in three physical dimensions. We derived wire lengths and delays using the formulas in [15]. However, for the system sizes that we are analysing, the experimental values are not much different from what we obtained using a uniform single unit link delay. Therefore, we are presenting results under the latter assumption. An invalidation based cache coherence protocol similar to the one in ....

S. L. Scott. "The Impact of Pipelined Channels on k-ary n-cube Networks". IEEE Trans. on Parallel and Distributed Systems, Vol. 5, No. 1, January 1994.

....longer than others. The delay of links with medium length wires [54] can be estimated by the model in T m link = 9:64 0:6 log V ns: 6. 4) It is worth noting that using an aggressive tecnique known as wave pipelining it is possible to propagate several phits at the same time on a physical link [140], thus avoiding the limit of longer links. We didn t use this tecnique in our studies. In our experiments we will consider three variants of the adaptive algorithm, with one, two and four virtual channels. As in the cubes, the input and output buffers can CHAPTER 6. BASIC NETWORK PERFORMANCE 81 V ....

....becomes increasingly limited by the wire delay, we expect that low dimensional cubes will eventually outperform the fat trees, because they can be easily mapped on the thre dimensional space. On the other hand the fat trees can benefit from the pipelining of more phits on a single physical link [140], an aggressive optimization that we did not use in our studies, and this leaves the door opened for further improvements. Chapter 7 Collective Communication Patterns Communication between nodes in a parallel machine can generally be described as x to y communication where x and y can be ....

Steven L. Scott and James R. Goodman. The Impact of Pipelined Channels on k-ary n-cube Networks. IEEE Transactions on Parallel and Distributed Systems, 5(1):2--16, January 1994.

....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 is to use ....

S. L. Scott and J. R. Goodman, "Impact of pipelined channels on k-ary n-cube networks," IEEE Transactions on Parallel and Distributed Systems, vol. 5, no. 1, pp. 2--16, January 1994.

....Analytical work has its origin at the beginning of the century for telephone traffic [112] Significant contributions were made in the mid sixties by [10, 91] Today [92, 93] serve as classical sources for the computer communication community. Some modern references to analytical modeling are [18, 72, 139,140]. A common characteristic for analytical methods is that various stochastic independence assumptions are imposed. In fact, this seems to pervade the entire field. The reason is simply that models become intractable otherwise. As an example, the renowned Independence Assumption [91] for arriving ....

....section 2.4 consider the throughput of wormhole switched k ary n cube networks. Throughput and latency are the most important performance measures. Finally, section 2.5 addresses routing which is a critical design factor for wormhole switched networks. 2. 1 Topology A k ary n cube network [23,31,32,104,139,143]has k nodes in each of n dimensions, giving a total of N = k n nodes. Figure 2.1 illustrates a 3 ary 3 cube with a total of 27 nodes. The topology is direct and regular [44, 162] and the number k is called the radix. As suggested by the expanded view each node has both a computing unit and a ....

SCOTT, S., AND GOODMAN, J. The impact of pipelined channels on k-ary n-cube networks. IEEE Transactions on Parallel and Distributed Systems 5, 1 (1994), 2--16.

.... : 35 11 Conclusions and Future Work 35 3 1 Introduction Rapid developments in the field of processor, interconnect, and, packaging technologies make the task of efficient design of large multiprocessor systems a difficult one [7, 10, 12, 15, 25]. Design guidelines need to take into account technological changes to yield system configurations delivering best performance. Several previous studies have considered packaging constraints [3] while selecting the best system configuration. These studies include Dally s [9] analysis of k ary ....

....of packaging have significant impact on the length of connecting wires in the system. The length of wires to connect channels depends on the distance between the connecting boards. Longer wires have higher capacitance [2] leading to elongation of the channel cycle time. However, it has been shown [25] that this problem can be alleviated by applying pipelining techniques over long wires. Such techniques are being commonly employed in recently developed systems like the Intel Paragon [14] In this study we assume such pipelining techniques being used to limit the channel cycle time in the ....

S. L. Scott and J. R. Goodman. The impact of pipelined channels on k-ary n-cube networks. IEEE Trans. on Parallel and Distributed Systems, pages 2--16, Jan 1994.

....the amount of information in a message that a router can process each cycle. Such its are in turn composed of phits, which are the transmission unit on the physical links connecting the routers. Each router chip is furnished with a number of bidirectional, clock decoupled, wave pipelined ports [15], operating at four times the frequency of the chip and able to accept a new phit every clock cycle independently of the wire length. Each phit is 16 bit wide and each router it is composed of four phits, thus matching link and router bandwidth while keeping the number of pins per port relatively ....

....Network 12 20 per Hop Hypercube Table 2: Basic system characteristics used in the experiments. Delays are expressed in processor cycles. Cache and memory delays correspond to a round trip access from the processor. physical dimensions. We derived wire lengths and delays using the formulas in [15]. However, for the system sizes that we are analysing, the experimental values are not much different from what we obtained using a uniform single unit link delay. Therefore, we are presenting results under the latter assumption. An invalidation based cache coherence protocol similar to the one in ....

S. L. Scott. \The Impact of Pipelined Channels on k-ary n-cube Networks". IEEE Trans. on Parallel and Distributed Systems, Vol. 5, No. 1, January 1994.

....others, so the number of ports per node grows as the log of the network size. Also, the complexity of physically realizing an n dimensional structure in three dimensions creates the need for long wires 2 , which may either increase the network cycle time [22] or result in multi cycle wire delays [85, 89]. Low dimensional networks offer a fixed number of ports per node, and the interconnection wires are shorter because of the more limited locality of connections. This disadvantage is that diameter increases as the n th root of the number of nodes. In many research and commercial systems, ....

S. L. Scott and J. R. Goodman. The impact of pipelined channels on k-ary n-cube networks. IEEE Transactions on Parallel and Distributed Systems, 5(1):2--16, January 1994.

....conclusions are based on non contention models. This is inappropriate since these networks behave very differently as the offered traffic load changes, and non contention models may favor networks with superior light load performance but inferior traffic handling capability. Scott and Goodman [22] consider the effects of pipelining the messages on unidirectional communication links. This technique reduces the effects of long wire delays and decouples throughput and latency issues. They also examine the time required for switching a message compared to the time required to transmit the ....

....low dimensional networks would be favored due to the smaller switch size. Wire delay is proportional to the wire length, which is dependent on the layout and configuration of the network. As network dimensionality increases, the length of the longest wire in the network also increases. As in [22], we assume that the network is implemented in three physical dimensions. Define scaling factor, wf, as the factor by which the clock cycle time grows as the longest wire (or maximum wire delay) grows with increased network dimensionality. Also, let S be the ratio of switch delay to wire delay in ....

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S. L. Scott and J. R. Goodman, "The impact of pipelined channels on k-ary n-cube networks," IEEE Trans. Parallel and Distributed Systems, vol. 5, no. 1, pp. 2-16, Jan. 1994.

....1 x log p) If x 0.5, then the overall isoefficiency is determined by communication overheads, and is exponential. If x # 0.5, then the overall isoefficiency is determined by concurrency. Thus, the best isoefficiency function of #(p 1.5 log p) can be obtained at x = 5. Many researchers [33, 124, 2, 1] prefer to compare architectures while keeping the number of communication ports per processor (as opposed to bisection width) the same across the architectures. Dutt and Trinh [33] show that for FFT like computations, hypercubes are more cost effective even with this cost criterion. 3.1.7 ....

S. L. Scott and J. R. Goodman. The impact of pipelined channels on k-ary n-cube networks. IEEE Transactions on Parallel and Distributed Systems, pages 2--16, January 1994.

....interconnection hierarchy. Example k ary n cubes include the ring (n = 1) 2D torus (n = 2) and hypercube (k = 2) network topologies [22] While previous k ary n cube network studies have identified which topology performs best for a particular type of traffic pattern and technological constraint [22 25], they have focused primarily on the topological component with the packaging and interconnection technology component held constant. For example, multiple studies regarding the relative merits of k ary n cube topologies have been put forth where the interconnection and packaging aspects have ....

S. L. Scott and J. R. Goodman, "The impact of pipelined channels on k-ary n-cube networks," IEEE Trans. Parallel Distributed Syst., vol. 5, pp. 2--16, Jan. 1994.

....n cube Interconnection, Packaging Constraints, Parallel Architectures, Interconnection Networks. I. INTRODUCTION R APID developments in the field of processor, interconnect, and, packaging technologies make the task of efficient design of large multiprocessor systems a difficult one [9] 11] [22]. Design guidelines need to take into account technological changes to yield system configurations delivering best performance. Several previous studies have considered packaging constraints [3] while selecting the best system configuration. These studies include Dally s [8] analysis of k ary ....

....wires in the system. The length of wires to connect channels depends on the distance between the connecting boards. Longer wires can lead to longer propagation delays and hence longer channel cycle times. However, this problem is alleviated by applying pipelining techniques over long wires [22]. In this study we assume such techniques being used to limit channel cycle time. V. PARAMETERIZING PACKAGING TECHNOLOGIES The characteristics and limitations of each level of packaging has an extreme impact on the set of achievable or feasible configurations and their cost and performance. In ....

S. L. Scott and J. R. Goodman. The impact of pipelined channels on k-ary n-cube networks. IEEE Trans. on Parallel and Distributed Systems, pages 2--16, Jan 1994.

....Though it is natural to think of a transmission line as a device for pipelining bits, it is only more conservative to think of pipelining packets and to continue measuring delay in terms of packet steps. Use of transmission lines is occurring in real parallel machines, e.g. see the references in [22]. Theorem 4 Using transmission lines, a fat pyramid F of area Theta(A) can simulate any network of area A with O(log A) overhead. Proof. To apply the packet routing results of Leighton, Maggs, and Rao [15, 16] we can imagine additional switches on each wire of the fat pyramid in number equal ....

S. L. Scott and J. R. Goodman. The impact of pipelined channels on k-ary n-cube networks. IEEE Trans. Parallel and Distributed Systems, 5(1):2--16, Jan. 1994.

....has more dimensions than the number of physical dimensions used to implement it, some channels require long wires. In this case, channel delay has a major impact on clock frequency. Some researchers have proposed the use of pipelined channels to reduce the impact of wire length on clock frequency [19]. Pipelined channels use wave pipelining. New data are injected into a channel before previously injected data reached the other end of the channel. Propagation speed is only limited by wire capacitance. At a given time, several data are propagating along a channel. As wires have some capacitance, ....

S.L. Scott and J.R. Goodman, "The impact of pipelined channels on k-ary n-cube networks," IEEE Trans. Parallel and Distributed Systems, vol. 5, no. 1, pp. 2--16, January 1994.

....and directions for future work. 3 NEW ROUTER ARCHITECTURE When the network topology has more dimensions than the number of physical dimensions used to implement it, some channels require long wires. Pipelined channels reduce the impact of wire length on clock frequency by using wave pipelining [21]. New data are injected into a channel before previously injected data reached the other end of the channel. Propagation speed is only limited by wire capacitance. At a given time, several data are propagating along a channel. The use of pipelined channels allows the designer to compute clock ....

S.L. Scott and J.R. Goodman, "The impact of pipelined channels on k-ary n-cube networks," IEEE Transactions on Parallel and Distributed Systems, vol. 5, no. 1, pp. 2--16, January 1994.

....of equal size offset cube and bidrectional 3D mesh networks. We choose the mesh as a standard for comparison because its performance advantages under bisection bandwidth and pinout constraints over other direct topologies (such as binary hypercubes) have been demonstrated in numerous studies [1, 2, 12, 32]. Furthermore, the 3D mesh can be efficiently implemented using the stacked MCM technique depicted in Figure 1. Flit level network simulations assuming constant pin out show that the latency throughput characteristics of the offset cube are generally comparable to those of an equal size ....

.... and packaging aspects have been abstracted away in terms of the wireability (e.g. constant bisection bandwidth or constant node size) and wire delay (e.g. constant, linear, or logarithmic with nonpipelined or pipelined channels) associated to generic 2D and 3D wire based system implementations [1, 2, 5, 12, 32]. While these studies have identified which interconnection topology per 6 forms best given a particular set of algorithmic (traffic patterns) and technological constraints, the assumption of an electrical interconnect technology model limits the insight that can be garnered with respect to ....

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S. L. Scott and J. R. Goodman, "The impact of pipelined channels on k-ary n-cube networks, " IEEE Trans. Parallel Distributed Syst., vol. 5, pp. 2-16, Jan. 1994.

....(which typically requires trace based simulation) it does provide insights on the impact chip size partitioning, interconnect driver techniques, VLSI feature sizes, and message lengths have on average message latency. The work presented in this paper builds upon previous work in single level [5] [8] and two level [9] k ary n cube implementations in that it (1) includes physical parameters, characterizing each level by its particular wirability and delay characteristics; 2) allows technological advances to be explicitly included; and (3) considers the interaction of design choices at both ....

....parameters; and (3) message lengths. In order to calculate the allowable channel widths for level 0 and level 1 networks, a general expression for the average interconnection length of a k ary n cube network (with folded wrap around links) is obtained in a manner analogous to that employed in [8], where the length was determined for a k ary n cube network embedded across a three dimensional volume. The average interconnection length for an n dimensional network embedded across a two dimensional plane is incorporated in our model. This computed wiring length requirement is compared against ....

S. L. Scott and J. R. Goodman, "The Impact of Pipelined Channels on k-ary n-cube networks", IEEE Transactions on Parallel and Distributed Systems, 5:(1), pages 2-16, January 1994.

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Scott, S. L. and Goodman, J. R. (1994) The impact of pipelined channel on k-ary n-cube networks. IEEE Trans. Parallel Distributed. Syst., 5, 2--16.

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S.L. Scott, J.R. Goodman, The impact of pipelined channels on k-ary n-cube networks, IEEE Trans. Parallel and Distributed Sys. 5 (1) (1994) 216.

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