Abraham, S. and K. Padmanabhan, "Performance of the direct binary n-cube network for multiprocessors, IEEE Trans. Computers, vol. 38, no. 7, Jul. 1989, pp. 1000-1011.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....section at different times. In our simulation, the mutual exclusion 636 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 8, NO. 6, JUNE 1997 requests of processors are characterized by a normal distribution 1 with mean value m and standard deviation s , as used in other studies [7], 8] For a small s under the normal distribution, all involved processors in the system generate mutual exclusion requests in a short period of time, likely to render the memory module containing the lock a hot spot. The request patterns generated by processors are affected by several factors, ....

S. Abraham and K. Padmanabhan, "Performance of the Direct Binary n-Cube Network for Multiprocessors," IEEE Trans. Computers, vol. 38, no. 7, pp. 1,000-1,011, July 1989.

....hot spot traffic pattern . Because the processors in a MIMD system are independent, they send their hot messages at different times. One way to model such hot message generation is a normal distribution of hot message generation over time with a mean and a standard deviation s as proposed in [1]. It is assumed that each hot message has a fixed length of FH flits (FH FU) Furthermore, it is assumed that while the hot spot access is in progress, the processors perform a fast context switch and continue to work on a different program in the meantime. Thus, each processor generates ....

....a different program in the meantime. Thus, each processor generates uniform traffic with load l before and after it emits a hot message. This kind of hot spot scenario was chosen as one type of a worst case dynamic traffic pattern in multistage interconnection networks by many researchers (e.g. [1, 9, 14]) The saturation tree that builds up under hot spot traffic to memory 0 is depicted in Figure 1 by bold lines. In many applications, a priori knowledge about occurrences of unsymmetrical data traffics is available, so that each processor of a parallel computer can distinguish different message ....

S. Abraham and K. Padmanabhan, "Performance of the direct binary n-cube network for multiprocessors," IEEE Transactions on Computers, Vol. C-38, No. 7, July 1989, pp. 1000-1011.

....bandwidth degradation due to hot spots is actually higher in crossbars than in multistage networks. Studies of other direct networks have also shown degradation in performance similar to that in multistage networks. In simulations on a binary n cube network done by Abraham and Padmanabhan [2], in a 1024 node system with hot spots, buffer sizes of less than five always resulted in a deadlock at 100 percent offered load when using dimension order routing. Even with deadlock free LR routing, there is a disastrous performance degradation when a hot spot occurs. Buffer sizes of 10 were ....

Seth Abraham and Krishnan Padmanabhan. Performance of the direct binary n-cube network for multiprocessors. IEEE Transactions on Computers, 38(7):1000--1011, 1989.

....hot spot accesses, this causes temporary overload of the network. Because the processors in a MIMD system are independent, they send their hot messages at different times. One way to model such hot message generation is a normal distribution with a mean and a standard deviation s as proposed in [12]. It is assumed that each hot message has a fixed length of FH flits. Furthermore, it is assumed that while the hot spot access is in progress, the processors perform a fast context switch (e.g. as in the HEP supercomputer [2] and continue to work on a different program in the meantime. To model ....

.... Also, in typical synchronization scenarios, the actual synchronization messages are shorter than the average uniform messages (FH FU) This kind of hotspot scenario was chosen as one type of a worst case dynamic traffic pattern in multistage interconnection networks by many researchers (e.g. [7, 12]) The saturation tree that builds up under hot spot traffic to memory 0 is depicted in Figure 1 by bold lines. In many applications, a priori knowledge about occurrences of unsymmetrical data traffic is available, so that each processor of a parallel computer can distinguish different message ....

S. Abraham and K. Padmanabhan, "Performance of the direct binary n-cube network for multiprocessors," IEEE Transactions on Computers, Vol. C-38, No. 7, July 1989, pp. 1000-1011.

....has been theoretically analyzed in [17] Approximate models aim at giving intuitive support for simulation results. Abraham and Padmanabhan s interesting analysis for the buffered and unbuffered binary hypercube is based on the approximation that each packet moves independently of other packets [1]. This model was later modified to consider locality of references [16] Stability conditions and approximate delay models, when packaging several processors at each hypercube node, have also been investigated [4] Finally, dynamic hot potato routing has good empirical performance on the ....

S. Abraham and K. Padmanabhan, Performance of the direct binary n-cube network for multiprocessors, IEEE Trans. Comp. 38 (1989) 1000--1011.

.... to the hot spot destination are delayed substantially [3, 5] A variety of mechanisms such as synchronization, Gaussian Elimination algorithms, cache coherence protocols, and the access of a single shared variable by multiple processors can cause hot spot traffic patterns in multiprocessor systems [3, 5, 6]. The negative influence of those hot spots on the overall network traffic has to be alleviated to obtain high performance in multiprocessor systems. Several concepts to alleviate saturation tree effects on network performance in direct and indirect networks have been proposed. These concepts can ....

....resides in, which results in a temporary hotspot traffic pattern. Because the processors in a MIMD system are independent, they send their hot messages at different times. One way to model such hot message generation is a normal distribution with a mean and a standard deviation s as proposed in [6]. It is assumed that each hot message has a fixed length of FH flits (with FH FU for typical synchronization scenarios) Furthermore, it is assumed that while the hot spot access is in progress, the processors perform a fast context switch (e.g. as in the HEP supercomputer [2] and continue to ....

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S. Abraham and K. Padmanabhan, "Performance of the direct binary n-cube network for multiprocessors," IEEE Trans. on Comp., Vol. C-38, No. 7, July 1989, pp. 1000-1011.

....analysis. Instead, we will analyze networks under the following constraints: ffl Constant channel widths ffl Constant bisection width ffl Constant node size We develop a model for buffered low dimensional direct networks that yields a simple closed form expression for network contention. See [1] for a model of binary n cube networks for unit packet sizes. The model is thoroughly validated through measurements taken from a simulator. Although the assumptions made by the model are tailored to networks with high radices, in practice we have found that the model is accurate for low radix ....

....in the same dimension with a high probability. Similarly, a packet at an entering channel in a switch will tend to change dimensions with a low probability; the lower the dimension of an outgoing channel, the lower the probability a message from a given high dimension will switch to that channel [7, 1]. We assume the routing probability of an incoming packet at a channel in a given dimension is non negligible only for the continuing channel in that dimension, and for the channel corresponding to one lower dimension. We will also assume that incoming packets from the processing node are steered ....

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Seth Abraham and Krishnan Padmanabhan. Performance of the Direct Binary n-Cube Network for Multiprocessors. IEEE Transactions on Computers, 38(7):1000--1011, July 1989.

....any p 1 [296] Approximate models for dynamic routing aim at giving intuitive support for simulation results. Abraham and Padmanabhan s analysis for the buffered unbuffered binary hypercube is based on the approximately correct assumption that each packet moves independently of other packets [1]. This model was later modified to consider locality of references [282] Stability conditions and approximate delay models, when packaging several processors at each hypercube node, have also been investigated [46] Dynamic routing on the hypercube outperforms the star graph and alternating group ....

Abraham, S., and Padmanabhan, K. Performance of the direct binary n-cube network for multiprocessors. IEEE Trans. Comput. 38 (7), 1989, pp. 1000--1011.

....the message transfer size in the network. Larger messages are divided into such smaller messages packets before being transferred over the network. For example, on the Cray T3D and IBM SP2 such transfer size on the network is approximately 64 and 256 bytes [12, 21] respectively. Earlier research[1, 37] has demonstrated that providing a small amount of memory, corresponding to a few message packet buffers, is sufficient to approximate infinite buffering performance. In the eventuality that all message packet buffers are full, further consumption is stalled and incoming messages forced to block ....

S. Abraham and K. Padmanabhan. Performance of the Direct Binary n-cube Network for Multiprocessors. IEEE Transactions on Computers, pages 1000--1011, July 1989.

....scheme provides substantial improvements in the throughput capacity and in the delays associated with hot spot messages. Further research The focus of hot spot contention studies has been on shared memory systems that use a multistage interconnection network. Except for a few of studies [Abra89,Dand92,Dand91], hot spot contention has not received as much attention in distributed memory multicomputer systems. Since 19 several large parallel systems (e.g. 9000 node Pentium Pro based Teraflop system) from Intel and nCUBE are based on the distributed memory architecture, it is important to study the ....

S. Abraham and K. Padmanabhan, "Performance of the Direct Binary n-Cube Network for Multiprocessors," IEEE Trans. Computers, Vol. C-38, No. 7, July 1989, pp. 1000-1011.

....dimension. Routing strategy does not affect latency when there is no network contention. Neither does it affect maximum network capacity. However, at low to medium traffic, hypercubes and meshes that 14 use LR routing have lower queueing delays than the same systems that use random routing [AbPa89]. We assume random routing in the clustered systems for convenience of analysis, but LR routing in flat systems. Hence, our performance numbers for clustered systems are conservative estimates. We expect network operation to be in regions of moderate channel utilization ( 80 ) where the message ....

S. Abraham and K. Padmanabhan, "Performance of the Direct Binary n-Cube Network for Multiprocessors," IEEE Transactions on Computers, Vol. 38, No. 7, July 1989.

....case of uniform memory reference pattern has been reported in [2, 3] Favorite memory case has been analyzed in [4] However, the assumption of uniform memory reference pattern in a multiprocessor system is not realistic. Different non uniform traffic patterns have been reported in the literature [5, 6, 7, 8]. Hot spot traffic is a particular type of non uniform traffic which arises due to the use of synchronization primitives and shared variables in a shared memory system. The effect of hot spots have been found to degrade the performance of multiprocessor systems using crossbar [9] multiple bus ....

S.Abraham and K. Padmanabhan, "Performance of direct binary n-cube network for multiprocessors, " IEEE Transactions on Computers, vol. 38, no. 7, pp. 1000--1011, July 1989.

....at a fixed rate, assigning to each packet an independently chosen random destination. All packets must then be routed in parallel to their final destinations [17] Good approximations to empirical data have been obtained for dynamic routing on the binary hypercube, using shortest path routing [1]. In this paper, we propose a new model for multicast communication. The term multicast refers to the transmission of data from one source to a set of destinations [5] Both unicast, which involves a single destination node, and broadcast, in which the data is sent to all nodes in the network, are ....

S. Abraham and K. Padmanabhan. Performance of the direct binary n-cube network for multiprocessors. IEEE Trans. Comp., 38(7):1000--1011, July 1989.

....of large diameter and long packets [4] 5] Continuous unicast routing has been used as a reasonable traffic model for communication switches and networks. Good approximations to empirical data have been obtained for continuous routing on the binary hypercube network, using shortest path routing [1]. We propose a variation of continuous routing incorporating multicasts. In continuous multicasting, packet arrival requests are issued at switch input ports with a constant rate p; 0 p 1. Generated packets are assigned to m; 1 m n independently chosen random output ports, where m is the ....

S. Abraham and K. Padmanabhan. "Performance of the direct binary n-cube network for multiprocessors", IEEE Transactions on Computers, Vol. 38 (7), 1989, 1000--1011.

....an in depth study of various aspects of network design and its trade offs, not only in terms of performance but also of cost. However, very few comprehensive and detailed studies address both the performance and cost of a network for a given system. Moreover, most network performance studies [14, 15, 16, 17, 18] are based on open loop systems [19] in which feedback effects [20] are completely ignored. As pointed out in [20, 21] feedback effects play an important role in determining achievable network performance. We need to evaluate and compare interconnection networks in terms of performance and cost, ....

S. Abraham and K. Padmanabhan, "Performance of the direct binary n-cube network for multiprocessor," IEEE Transactions on Computers, vol. 38, pp. 1000--1011, July 1989.

....types or the infinite priority scheme which is inherent in a timestamping system of this type. The third approach is probabilistic mean value analysis. This type of analysis has been applied with success to banyan networks and their equivalents [Jen83] YLL90] KiL90] and to direct binary n cubes [AbP89]. In [Jen83] Jenq presents an analytical model for the performance of Banyan (Omega) networks composed of 2 input, 2 output switching elements in a synchronous, single buffered, packet switching system. This model forms the basis for later work by Yoon et al. YLL90] which extends the model ....

....systems in normal operation, where a random distribution of requests is assumed, and in cases of hot spots [Pfi85] situations in which more requests are targeted for certain outputs. The studies discussed so far have considered only indirect and mostly equidistant network configurations. [AbP89] and [Abr90] take up the analytical study of the performance of directly connected architectures related to the hypercube. Abraham provides mathematical models and discusses performance characteristics of direct binary d cube networks. The results of these analyses compare favorably to those for ....

S. Abraham and K. Padmanabhan, Performance of the Direct Binary n-Cube Network for Multiprocessors, IEEE Trans. on Computers 38,7 (July 1989), 10001011.

....to as a mesh with wrap around or 2D torus. In the figure the mesh has no wrap arounds to keep it simple. In this report we will always use meshes with wrap arounds. In the spanning bus mesh (Fig. 1.3d. the PEs in the rows and columns are connected to each other with busses. Finally, the hypercube [1] (Fig. 1.3c. consist of a d dimensional cube with PEs at it s corners. 1.2 Related Work The interconnection networks discussed in the previous section belong to the oldest ones. Since their invention many researchers have studied ways to generalize them. Almost all resulting generalizations ....

....assumed a uniform reference pattern. In such a model each memory module is referenced with the same probability [23] Later models captured the effects of hot spots and favorite memory modules. Hot spots arise when all processors reference the same memory module more than other memory modules [1] (e.g. all processors reference memory module 0 more than the other memory modules) In the favorite memory module reference pattern each processor has a memory module it references more than other memory modules [5] e.g. processor X references memory module X more than other memory modules) ....

[Article contains additional citation context not shown here]

S. Abraham and K. Padmanabhan, "Performance of the direct binary n-cube network for multiprocessors," IEEE Transactions on Computers, vol. 38, July 1989, pp. 1000--1011.

....network. of random order. This occurs because, under dimension ordered routing, a packet entering a node in one direction generally exits the node traveling in the same direction. This, in turn, reduces the likelihood that packets from different incoming links contend for the same output port [39, 40]. As a result, dimension ordered routing has a higher cut through probability and lower average latency, although the analytical model predicts that the dimension ordered and random selection functions should have the same performance. As shown in Figure 8, the benefit of dimension order routing ....

S. Abraham and K. Padmanabhan, "Performance of the direct binary n-cube network for multiprocessors, " IEEE Transactions on Computers, vol. 38, pp. 1000--1011, July 1987.

....developed. Such a model would be useful for performance evaluation of existing schemes as well as for indicating where extra resources could be added to improve performance. Many papers have presented models for performance evaluation of multicomputer and or multiprocessor interconnection networks [1, 2, 5, 8, 9, 13, 14, 15]. Following their analysis of virtual cut through [13] Kermani and Kleinrock used a tandem queue model that incorporated the effect of channel reservation in order to analyze circuit switching [14] Another circuit switching model was proposed in [5] where the importance of contention rather ....

S. Abraham and K. Padmanabhan. Performance of the direct binary n-cube network for multiprocessors. IEEE Transactions on Computers, 38:1000--11, July 1989.

....routing distance [16] While these static measures are helpful in comparing networks, they fall short of a stochastic performance evaluation and do not closely characterize relative implementation costs. The first in depth direct network stochastic performance study considers only the hypercube [17], comparing its performance to indirect (multistage) networks. Dally was the first to quantify the implementation costs of different multidimensional networks and compare their performance under a constant cost constraint [18] He observed that a 2 dimensional mesh is significantly easier to build ....

....to approximate infinity [25] Also, we assume the output queues can accept messages from multiple input links during a single cycle. In addition, a multiple accepting PE scheme is assumed, in which multiple messages (up to the number of input links) may be accepted by the PE in a single cycle [17]. The average waiting time, w, of a message packet in an output queue can be found from the expectation, E[A] and variance, V[A] of the arrival process A. As shown in [24] w V A E A E A = 2 1 1 2 . 2.1) In the following sections, we will derive E[A] and V[A] using the ....

S. Abraham and K. Padmanabhan, "Performance of the direct binary n-cube network for multiprocessors," IEEE Trans. Comput., vol. 38, no. 7, pp. 10001011, July 1989.

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Abraham, S. and K. Padmanabhan, "Performance of the direct binary n-cube network for multiprocessors, IEEE Trans. Computers, vol. 38, no. 7, Jul. 1989, pp. 1000-1011.

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