D. Basak and D. K. Panda. Scalable Architectures with k-ary n-cube cluster-c organization. In Proc. of the Symposium of Parallel and Distributed Processing, pages 780--787, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... topological component in our model because they constitute an important family of direct interconnection networks that have been demonstrated to be highly suitable for multicomputer systems and because their structure lends itself to an efficient mapping onto the physical interconnection hierarchy [21]. In clustered k ary n cubes a distinct k i ary n i cube network topology is used to interconnect all the nodes within the i th level of the interconnection hierarchy. Example k ary n cubes include the ring (n = 1) 2D torus (n = 2) and hypercube (k = 2) network topologies [22] While ....

....topologies have been put forth where the interconnection and packaging aspects have been abstracted away in terms of wirability and wire delay associated with generic single level 2D and 3D wire based system implementations. The studies that have focused more on the technological characteristics [21, 26] have also abstracted the physical parameters associated with the wiring resources available for system implementation. The abstractness of these studies make assessing the technology impact on system performance difficult. The interconnection resources present in diffractive, reflective MCM ....

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D. Basak and D. K. Panda, "Scalable architectures with k-ary n-cube cluster-c organization," in 1993 Symposium on Parallel and Distributed Processing, pp. 780--787, 1993.

....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 levels of the ....

D. Basak and D. K. Panda, "Scalable Architectures with k- ary n-cube cluster-c organization", Proceedings 5 th IEEE Symposium on Parallel and Distributed Processing, pages 780-787, 1993.

....application characteristics also lead to an expected minimal demand on performance from the system in terms of sustained average throughput and maximum allowable message latency. Sustaining a desired performance places a demand on the latency throughput characteristics of a system configuration [4, 22]. Thus, an architect should identify such demand on performance and use it as a criterion to select good configurations satisfying the demand. However, the demanded performance is not a fixed parameter. It is a function of processor and interconnection speeds. For example, faster processors can ....

....with k ary n cube cluster c Organization 2.1 k ary n cube cluster c Organization Many current parallel systems like the CRAY T3D [8] Intel Paragon [14] and the Stanford DASH [11] are taking a two level clustering approach. Recently, we have introduced a new k ary n cube cluster c organization [4, 5, 19] to capture this upcoming trend in building scalable parallel systems. In this organization, the lower level consists of k n processor clusters. These clusters are interconnected by a higher level direct k ary n cube network (also referred to as inter cluster network or internet) Each cluster ....

D. Basak and D. K. Panda. Scalable Architectures with k-ary n-cube cluster-c organization. In Proc. of the Symposium of Parallel and Distributed Processing, pages 780--787, 1993.

....the techniques which work for two level hierarchies can be easily extended to design more levels. Examples of previous work in this area include two level systems based on hypercube and other network topologies[5, 15, 18] MINs and n hop networks [18] twolevel systems with k ary n cube topologies[2], and combination of bus and mesh hypercube networks[10] However, most of these analyses either did not consider packaging and interconnecting constraints, or provided guidelines based only on fixed board sizes with fixed pinouts, not considering changes in board sizes and alternate pinout ....

....amongst the good configurations. This is done on the basis of relative performance and cost of these systems. Simulation modeling may be employed to decide among very close candidates. The paper is organized as follows. In section 2 we discuss the two level k ary n cube cluster c architecture [2] used in this paper to illustrate the working of the design framework. In section 3 we discuss the trends in growth of processor board sizes, alternate pinout technologies, channel width technology, and derive the design feasible configurations and their characterestics. Processor speeds, ....

[Article contains additional citation context not shown here]

D. Basak and D. K. Panda. Scalable Architectures with k-ary n-cube cluster-c organization. In Proc. of the Symposium of Parallel and Distributed Processing, 1993.

....techniques which work for two level hierarchies can be easily extended to design more levels. Examples of previous work in this area include two level systems based on hypercube and other network topologies[12, 20, 24] MINs and n hop networks [24] two level systems with k ary n cube topologies[4], and combination of bus and mesh hypercube networks[14] However, most of these analyses did not take into account packaging and interconnecting constraints. Guidelines developed in [14, 24] were based only on fixed board sizes with fixed pinouts, and did not consider changes in board sizes and ....

....changes in board sizes and alternate pinout technologies. The impact of the changes in processor and interconnect technologies in relation to packaging technology was also not studied. Analogously in our analysis we focus on two level clustered architectures based on a k ary n cube cluster c [4, 6] interconnection. These are clustered extensions of the flat k ary n cube systems. Our design model is more comprehensive and flexible in terms of considering packaging and interconnect constraints. Among other things we allow varying board sizes, only reasonable channel widths, and flexible ....

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D. Basak and D. K. Panda. Scalable Architectures with k-ary n-cube cluster-c organization. In Proc. of the Symposium of Parallel and Distributed Processing, pages 780--787, 1993.

....to the set of design feasible configurations and their performance characteristics as what the packaging technology offers, we call this the supply side. On the other hand, to sustain processor performance in terms of throughput places a demand on the size of the required bisection bandwidth [1, 5] of the system. The design feasible configurations which offer performance greater than what is demanded are defined as good configurations. Among the good choices the one which provides desired performance at optimal cost is defined as the best configuration. Our goal is to derive this best ....

....defined as the best configuration. Our goal is to derive this best topology. Simulation modeling is also employed to determine exact performance to decide between very close good candidates. The paper is organized as follows. In Sec. 2 we present the two level k ary n cube cluster c architecture [1] used in later discussion. In Sec. 3 we discuss the trends in growth of processor board sizes, alternate pinout technologies, channel width technology, and derive the design feasible configurations. Processor speeds, communication link speeds and the performance demand are discussed in Sec. 4. In ....

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D. Basak and D. K. Panda. Scalable Architectures with k-ary n-cube cluster-c organization. In Proc. of the SPDP, pp 780--787, 1993.

....clustered organizations, indicate that such organizations have potential to support larger systems in a more cost effective manner, and then discuss some architectural details of such organizations. 3. 1 Clustered Organizations Recently, we have introduced a new k ary n cube cluster c organization [4, 5, 18] to capture the upcoming trend in building scalable parallel systems. In this organization, the lower level consists of k n clusters of processors. These clusters are interconnected by a higher level direct k ary n cube network (also referred to as inter cluster network) Each cluster consists ....

....processor speed etc. Similarly, packaging constraints like maximum board size, pinout limitations, system bisection size put bounds on the maximum channel width (W max ) and maximum cluster size (c max ) 1, 5, 20] Design under such constraints has been analyzed by us in detail and presented in [4, 5]. It was shown that the design process is sensitive to technological and packaging advancements. In this paper without going into such details, we capture similar limitations on design by imposing maximum limits on the inter cluster channel width (W W max ) and the cluster size (c c max ) In ....

D. Basak and D. K. Panda. Scalable Architectures with k-ary n-cube cluster-c organization. In Proc. of the Symposium of Parallel and Distributed Processing, pages 780--787, 1993.

....application characteristics also lead to an expected minimal demand on performance from the system in terms of sustained average throughput and maximum allowable message latency. Sustaining a desired performance places a demand on the latency throughput characteristics of a system configuration [4], 19] Thus, an architect should identify such demand on performance and use it as a criterion to select good configurations satisfying the demand. However, the demanded performance is not a fixed parameter. It is a function of processor and interconnection speeds. For example, faster ....

....WITH k ARY n CUBE CLUSTER c ORGANIZATION A. k ary n cube cluster c Organization Many current parallel systems like the CRAY T3D [7] Intel Paragon [13] and the Stanford DASH [10] are taking a two level clustering approach. Recently, we have introduced a new k ary n cube cluster c organization [4], 5] 16] to capture this upcoming trend in building scalable parallel systems. In this organization, the lower level consists of k n processor clusters. These clusters are interconnected by a higher level direct k ary n cube network (also referred to as inter cluster network or internet) ....

D. Basak and D. K. Panda. Scalable Architectures with k-ary n-cube cluster-c organization. In Proc. of the Symposium of Parallel and Distributed Processing, pages 780--787, 1993.

....cluster. Such clusters can be interconnected together to build large scale systems. This has opened a new vista for building scalable parallel systems using clustered configurations. The potential advantages of clustered organizations have already been demonstrated by us in our earlier work [3] by introducing and analyzing a two level clustered organization called k ary n cube cluster c. The upper level k ary n cube direct network offers scalability while interconnecting k n clusters with c processors in each cluster. The clusters offer cheap building blocks that effectively exploit ....

....a comprehensive design framework, as shown in Fig. 1, to derive optimal design choices with cluster organization. 2 k ary n cube cluster c organization A popular interconnection being used currently to build large scalable systems is the class of k ary n cube cluster c two level systems [3, 4]. Some examples are Intel Paragon, Stanford DASH, and Cray T3D. The lower level consists of k n clusters of processors interconnected by a higher level direct k ary n cube network (also referred to as inter cluster network or internet) Each cluster consists of c processors leading to a total ....

[Article contains additional citation context not shown here]

D. Basak and D. K. Panda. Scalable Architectures with k-ary n-cube cluster-c organization. In Proc. of the Symposium of Parallel and Distributed Processing, pages 780--787, 1993.

....by Dally[2] has demonstrated the attractiveness of k ary n cube topology with wormhole routing switching technique. It has been shown that low dimensional(n) k ary n cube networks have potential to build scalable systems with low average message latency under physical wiring constraint. In[1] we have proposed a general class of k ary n cube cluster c scalable architectures by combining the scalability of k ary n cube wormhole routed networks with the cost effectiveness of processor cluster designs. Each cluster consists of c processors and the possible intra cluster interconnections ....

Basak D. and Panda D.K., "Scalable Architectures with k-ary n-cube cluster-c organization. " Submitted to the Symposium of Parallel and Distributed Processing, 1993.

....intra sat ) c) outgoing bandwidth constraint at CI(m out sat ) and d) incoming bandwidth constraint at CI(m in sat ) These constraints refer to the maximum possible message injection rate(m) by each processor such that the respective channel capacities and bandwidths are not exceeded. In[4], we have derived these constraints leading to the following inequality: m inter sat m out sat ; m in sat m intra sat (1) The constraints m inter sat is most strict and its value is dependent only on the size of the cluster and quite independent of the cluster topology. This fact leads ....

....cluster dimensionality does not affect system throughput but the average message latency increases. This leads to: Observation 2 Keeping the internet topology, internet size, and cluster size fixed, a ring cluster offers the least average latency. The expression m inter sat = 4 CL(1 Gammap) [4] leads us to: Observation 3 The maximum system throughput falls as cluster size and message length grow. From the above observation one would tend to conclude that clustering is not that a good idea. However, all the above analysis is determining saturated throughput under uniform traffic which ....

[Article contains additional citation context not shown here]

D. Basak and D. K. Panda. Scalable Architectures with k-ary n-cube cluster-c organization. TR28-1993, Dept. of Computer and Information Science, The Ohio State University, Aug 1993.

....cost for multicasting can be effectively used to provide fast cache coherency on wormhole networks. Since the BRCP model has potential to implement dense communications faster, it will also be interesting to see how it can help in building scalable wormhole systems with clustered configurations [5]. From the perspectives of distributed memory systems, we are also investigating the impact of the multidestination mechanism to reduce program execution time of programs using multicast communication [29] Acknowledgements: The author would like to thank members of his research group for ....

D. Basak and D. K. Panda. Scalable Architectures with k-ary n-cube cluster-c Organization. In Symposium on Parallel and Distributed Processing, pages 780--787, 1993.

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