Hierarchical Torus Network Research Articles

Reconfiguration and Yield of a Hierarchical Torus Network

This paper presents the reconfiguration and yield of a new interconnection network, Hierarchical Torus Network (HTN). An HTN is a 2D-torus network of multiple basic modules, in which the basic modules are 3D-torus networks that are hierarchically interconnected for higher level networks. The static network performance and dynamic communication performance under dimension-order routing of the HTN have already been studied and network performances are good. However, the fault tolerance performance of the HTN has not yet been evaluated. The goal of this paper is to derive a theoretical estimate of system yield for the HTN as a function of defect density with a reconfiguration approach by hardware redundancy. Yield is the probability of obtaining a fault-free network. Despite the dramatic improvement in fault tolerance in recent years, it is still necessary to provide redundancy and fault circumvention to achieve efficient system yield for large multicomputer systems. Thus, we provide redundant hardware to reconfigure the faulty nodes, switches, and links to healthy nodes, switches, and links. The results indicate that with a 25% redundancy the yield of the HTN is satisfactory. We also discuss the 3D-WSI implementation issue and show that HTN permits efficient VLSI/ULSI/WSI realization due to the fewer numbers of vertical links between the silicon wafers. The longest wire has a length of 4.5 cm, which represents 4.20 times improvement over the planar implementation.

Dynamic Communication Performance Enhancement in Hierarchical Torus Network by Selection Algorithm

A Hierarchical Torus Network (HTN) is a 2D-torus network of multiple basic modules, in which the basic modules are 3D-torus networks that are hierarchically interconnected for higher-level networks. The static network performance of the HTN and its dynamic communication performance using the deterministic, dimension-order routing algorithm have already been evaluated and shown to be superior to the performance of other conventional and hierarchical interconnection networks. However, the assessment of the dynamic communication performance improvement of HTN by the efficient use of both the physical link and virtual channels has not yet been evaluated. This paper addresses three adaptive routing algorithms -- link-selection, channel-selection, and a combination of link-selection and channel-selection -- for the efficient use of physical links and virtual channels of an HTN to enhance dynamic communication performance. It also proves that the proposed adaptive routing algorithms are deadlock-free with 3 virtual channels. The dynamic communication performances of an HTN is evaluated by using dimension-order routing and proposed adaptive routing algorithms under various traffic patterns. It is found that the dynamic communication performance of an HTN using these adaptive routing algorithms are better than when the dimension-order routing is used, in terms of network throughput.

High Performance Hierarchical Torus Network Under Adverse Traffic Patterns

A Hierarchical Torus Network (HTN) is a 2D-torus network of multiple basic modules, in which the basic modules are 3D-torus networks that are hierarchically interconnected for higher level networks. The dynamic communication performance of the HTN using the dimension-order routing under common traffic patterns have been evaluated, and have been shown to be good. However, dynamic communication performance of HTN under adverse traffic patterns has not been evaluated yet. In this paper, we evaluate the dynamic communication performance of HTN using a deadlock-free dimension order routing with 3 virtual channels under adverse traffic patterns, and compare it with H3D-mesh, mesh, and torus networks. It is shown that even under adverse traffic patterns, the HTN yields high throughput and low average transfer time, which provide better dynamic communication performance than H3D-mesh, mesh, and torus networks.

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A deadlock-free routing algorithm using minimum number of virtual channels and application mappings for Hierarchical Torus Network

A Hierarchical Torus Network (HTN) is a 2D-torus network of multiple Basic Modules (BM), in which the BM are 3D-torus networks that are hierarchically interconnected for higher level networks. In this paper, we present a deadlock-free dimension-order routing using minimum number of Virtual Channels and evaluate the network's dynamic communication performance under the uniform traffic pattern by computer simulation and compare it with other contemporary conventional and hierarchical networks. We find that the dynamic communication performance of the HTN is better than that of the H3D-mesh, TESH, mesh, and torus networks. We also present the mapping of some primitive applications on the HTN. It is shown that the number of communication steps for various advanced applications mapping on the HTN is lower than that of those networks.

Routing performance enhancement in hierarchical torus network by link-selection algorithm

A hierarchical torus network (HTN) is a 2D-torus network of multiple basic modules, in which the basic modules are 3D-torus networks that are hierarchically interconnected for higher-level networks. The static network performance of the HTN and its dynamic communication performance using the popular dimension-order routing algorithm have already been evaluated and shown to be superior to the performance of other conventional and hierarchical interconnection networks. In this paper, we propose a link-selection algorithm for efficient use of physical links of the HTN, while keeping the link-selection algorithm as simple as the dimension-order routing algorithm. We also prove that the proposed algorithm for the HTN is deadlock-free using three virtual channels. We evaluate the dynamic communication performance of an HTN using dimension-order routing and link-selection algorithms under various traffic patterns. We find that the dynamic communication performance of an HTN using the link-selection algorithm is better than when the dimension-order routing algorithm is used.