Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Analytical models for the performance analysis of banyan networks
Analytical models for the performance analysis of banyan networks
An introduction to photonic switching fabrics
An introduction to photonic switching fabrics
Wide-Sense Nonblocking Clos Networks Under Packing Strategy
IEEE Transactions on Computers
The performance of multicast banyan networks
Journal of Parallel and Distributed Computing
Banyan networks for partitioning multiprocessor systems
ISCA '73 Proceedings of the 1st annual symposium on Computer architecture
Wide-sense nonblocking Banyan-type switching systems based on directional couplers
IEEE Journal on Selected Areas in Communications
A comparison study of optical MIN networks with parallel planes
PDCN'06 Proceedings of the 24th IASTED international conference on Parallel and distributed computing and networks
Performance modelling for vertically stacked optical banyan networks with extra stage
International Journal of Computational Science and Engineering
Strictly nonblocking f-cast photonic networks
IEEE/ACM Transactions on Networking (TON)
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
A New Dimension Analysis on Blocking Behavior in Banyan-Based Optical Switching Networks
IEICE - Transactions on Information and Systems
Rearrangeable and nonblocking [w, f] -distributors
IEEE/ACM Transactions on Networking (TON)
On path dependent loss and switch crosstalk reduction in optical networks
Information Sciences: an International Journal
On the routing algorithms for optical multi-log2N networks
NPC'07 Proceedings of the 2007 IFIP international conference on Network and parallel computing
NPC'07 Proceedings of the 2007 IFIP international conference on Network and parallel computing
Journal of Combinatorial Optimization
Towards peta-bit photonic networks
ISPA'05 Proceedings of the Third international conference on Parallel and Distributed Processing and Applications
An upper bound on blocking probability of vertical stacked optical benes networks
ISPA'05 Proceedings of the Third international conference on Parallel and Distributed Processing and Applications
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Banyan networks are attractive for constructing directional coupler (DC)-based optical switching networks for their small depth and self-routing capability. Crosstalk between optical signals passing through the same DC is an intrinsic drawback in DC-based optical networks. Vertical stacking of multiple copies of an optical banyan network is a novel scheme for building nonblocking (crosstalk-free) optical switching networks. The resulting network, namely vertically stacked optical banyan (VSOB) network, preserves all the properties of the banyan network, but increases the hardware cost significantly. Though much work has been done for determining the minimum number of stacked copies (planes) required for a nonblocking VSOB network, little is known on analyzing the blocking probabilities of VSOB networks that do not meet the nonblocking condition (i.e., with fewer stacked copies than required by the nonblocking condition). In this paper, we analyze the blocking probabilities of VSOB networks and develop their upper and lower bounds with respect to the number of planes in the networks. These bounds depict accurately the overall blocking behaviors of VSOB networks and agree with the conditions of strictly nonblocking and rearrangeably nonblocking VSOB networks respectively. Extensive simulation on a network simulator with both random routing and packing strategy has shown that the blocking probabilities of both strategies fall nicely within our bounds, and the blocking probability of packing strategy actually matches the lower bound. The proposed bounds are significant because they reveal the inherent relationships between blocking probability and network hardware cost in terms of the number of planes, and provide network developers a quantitative guidance to trade blocking probability for hardware cost. In particular, our bounds provide network designers an effective tool to estimate the minimum and maximum blocking probabilities of VSOB networks in which different routing strategies may be applied. An interesting conclusion drawn from our work that has practical applications is that the hardware cost of a VSOB network can be reduced dramatically if a predictable and almost negligible nonzero blocking probability is allowed.