VLSI Performance Comparison of Banyan and Crossbar Communications Networks

“…With banyan structure only a unique path exists between an input-output pair, in which the network is degraded as a blocking one. As shown in [5] [6], the blocking probability of banyan networks is usually very high. For example, the blocking probability for a 256×256 banyan network can be as high as 0.65 (at full load condition), even without any crosstalk constraint.…”

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confidence: 99%

Pruned optical banyan networks on vertical stacking scheme for faster connection establishment

Khandker¹,

Jiang²,

Fukushi³

et al. 2006

Optics Communications

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In this paper we address the issue of faster connection establishment in a large vertically stacked optical Banyan (VSOB) network. The best known global routing algorithm, which turns an N×N crosstalk-free VSOB network into a rearrangeably nonblocking one, has time complexity O(NlogN). This is quite large compared to O(logN) time complexity of a single plane banyan network, which is a self-routing network with very high blocking probability. For a large size of switching network this O(NlogN) time complexity may result unacceptably long delay. Therefore, an optical network with very low blocking probability and O(logN) time complexity will be useful. Previously proposed Plane Fixed Routing (PFR) algorithm has O(logN) time complexity but results in higher than 2% blocking probability with zero-crosstalk constraint for a network as large as 4096×4096 at full load. In this paper, first we propose the pruning of VSOB networks that reduces the hardware cost by almost 30%. The networks can still use the PFR algorithm and results in the same blocking probability. However, we show that the blocking probability can be reduced dramatically while keeping the optimum time complexity O(logN) by allowing only a small amount of crosstalk. Then, we propose a new kind of switching networks in which extra regular banyan planes have been added with the pruned VBOS (P-VSOB) networks. Necessary routing algorithms, namely, PFR_RS and PFR_LS show that this new switching network can reduce the blocking probability to very low value even with zero-crosstalk constraint while keeping the hardware cost almost the same as for P-VSOB networks. Both these algorithms also have time complexity O(logN).

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“…A related performance measure is the blocking probability of a network over all permutation requests, as defined above. Franklin has presented simulation results for the blocking probability of banyan networks (built with 2 x 2 switches) under the assumption of permutation requests [13].…”

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confidence: 99%

On the Permutation Capability of Multistage Interconnection Networks

Szymański

Hamacher²

1987

IEEE Trans. Comput.

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Abstract-We present analytic models for the blocking probability of both unique path and multiple path multistage interconnection networks under the assumption of either permutation or random memory request patterns. The blocking probability of an interconnection network under the assumption of permutation requests is a quantitative measure of the network's permutation capability. We compare the performance of networks with approximately equivalent hardware complexity. It is shown that variations of banyan networks can be designed with extremely low blocking probabilities under the assumption of permutation requests.

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VLSI Performance Comparison of Banyan and Crossbar Communications Networks

Cited by 62 publications

References 17 publications

A study of the on-chip interconnection network for the IBM Cyclops64 multi-core architecture

A study of the on-chip interconnection network for the IBM Cyclops64 multi-core architecture

Pruned optical banyan networks on vertical stacking scheme for faster connection establishment

On the Permutation Capability of Multistage Interconnection Networks

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