An accurate analytical model of adaptive wormhole routing in k-ary n-cubes interconnection networks

Sarbazi-Azad, Hamid; Ould‐Khaoua, Mohamed; Mackenzie, Lewis

doi:10.1016/s0166-5316(00)00049-3

Cited by 61 publications

(54 citation statements)

References 24 publications

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“…As can be seen in simulation results, contributing the probability P V x, y in calculating the probability of traversing network nodes and channels has definitely increased the precision of the model. In previous studies [9,11,17] the mentioned probabilities are calculated without considering P V x, y .…”

Section: The Analytical Modelmentioning

confidence: 99%

“…In this method, finding possible positions of the message in its j th hop is still a major concern although the problem can be reduced to finding next hops in message traversals. As an example, the analytical models in [11,17] derived complex formulas to find the next hops in message traversals. It is worth noting that these models are derived based on a specific topology where a mathematical relation exists between network nodes and channels.…”

Section: Strong Points Of the Modelmentioning

confidence: 99%

“…However, solving the problem of finding the next hop enables the model to deal with a wide range of deadlock-free routing algorithms. The most restricting and yet most common assumption of all previous analytical models has been the topology of the network which has been considered as a particular topology such as hypercube [14], torus [17], mesh [11], product networks [9], star [6], and k-ary n-cube [2,17]. As stated in the previous section, in these works determining the next channel to be traveled by the S-D message is done by considering the mathematical relationship between network nodes and channels.…”

Section: Strong Points Of the Modelmentioning

confidence: 99%

“…Analytical modeling is perhaps the most cost-effective and versatile approach, which can be used for testing and evaluating system's performance under different working conditions and configurations. So far, many analytical models have been reported in the literature for known regular topologies such as hypercube, torus, mesh, product networks, star, and k-ary n-cube [1,2,6,9,11,14,17]. However, no analytical model has been proposed to evaluate irregular networks (i.e.…”

Section: Introductionmentioning

confidence: 99%

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A general mathematical performance model for wormhole-switched irregular networks

Moraveji¹,

Moinzadeh²,

Sarbazi-Azad

2009

Cluster Comput

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Irregular topologies are desirable network structures for building scalable cluster systems and very recently they have also been employed in SoC (system-on-chip) design. Many analytical models have been proposed in the literature to evaluate the performance of networks with different topologies such as hypercube, torus, mesh, hypermesh, Cartesian product networks, star graph, and k-ary n-cube; however, to the best of our knowledge, no mathematical model has been presented for irregular networks. Therefore, as an effort to fill this gap, this paper presents a comprehensive mathematical model for fully adaptive routing in wormhole-switched irregular networks. Moreover, since our approach holds no assumption for the network topology, the proposed analytical model covers all the aforementioned models (i.e. it covers both regular and irregular topologies). Furthermore, the model makes no preliminary assumption about the deadlock-free routing algorithm applied to the network. Finally, besides the generality of the model regarding the topology and routing algorithm, our analysis shows that the analytical model exhibits high accuracy which enables it to be used for almost all topologies with all traffic loads.

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Section: The Analytical Modelmentioning

confidence: 99%

Section: Strong Points Of the Modelmentioning

confidence: 99%

Section: Strong Points Of the Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A general mathematical performance model for wormhole-switched irregular networks

Moraveji¹,

Moinzadeh²,

Sarbazi-Azad

2009

Cluster Comput

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“…Analytical models of routing algorithms with virtual channels in wormhole-switched networks have been widely reported in the literature [6,11,16,17 and references there in]. A Markov chain proposed by Dally [8] has been used by almost all the models reported in the literature to capture the performance behaviour of virtual channels in the network.…”

Section: Introductionmentioning

confidence: 99%

The Impacts of Timing Constraints on Virtual Channels Multiplexing in Interconnect Networks*

Khonsari

Ould‐Khaoua²,

Nayebi

et al.

2006 IEEE International Performance Computing and Communications Conference

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Towards a more realistic comparative analysis of multicomputer networks

Sarbazi-Azad

Ould‐Khaoua

Mackenzie

2004

Concurrency and Computation

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SUMMARYSeveral studies have examined the relative performance merits of the torus and hypercube taking into account the channel bandwidth constraints imposed by implementation technology. While the torus has been shown to outperform the hypercube under the constant wiring density constraint, the opposite conclusion has been reached when the constant pin-out constraint is considered. However, these studies have assumed a pure uniform traffic pattern and deterministic routing. The 'uniform traffic' assumption is not always justifiable in practice as there are many real-world parallel applications that exhibit nonuniform traffic patterns, which can create unbalanced traffic such as hotspots in the network. This paper re-examines the performance merits of the torus and hypercube in the presence of hotspot traffic. The comparative analysis is based on fully adaptive routing as this has been gaining popularity in recent practical multicomputers. Moreover, it uses a new cost model that takes into account the implementation cost of the network and its routers. The results reveal that for moderate and large system sizes, lower dimensional k-ary n-cubes (e.g. 2D torus) always outperform their higher dimensional counterparts even under the pin-out constraint.

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An accurate analytical model of adaptive wormhole routing in k-ary n-cubes interconnection networks

Cited by 61 publications

References 24 publications

A general mathematical performance model for wormhole-switched irregular networks

A general mathematical performance model for wormhole-switched irregular networks

The Impacts of Timing Constraints on Virtual Channels Multiplexing in Interconnect Networks*

Towards a more realistic comparative analysis of multicomputer networks

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