Optical Banyan Networks Research Articles

Blocking performance of extended pruned vertically stacked optical banyan structure under different link failure conditions

The blocking performance of extended pruned vertically stacked optical banyan (VSOB) networks under different link failure conditions has been analyzed in this paper. We applied plane fixed routing with linear search and plane fixed routing with random search algorithms to route the optical data through the network in our simulation. Our simulation results show that adding one or two extra planes to the pruned VSOB network reduces the blocking probability significantly. Beyond two extra planes, the decrease of blocking probability is not so significant. A close approximation of the minimum number of planes required to make the extended pruned vertically stacked optical banyan networks nonblocking has been presented.

Performance Analysis of $f$ -Cast Crosstalk-Free Optical Banyan Networks

Banyan networks serve as a class of important switching network architecture, whose multicast capability is critical for future high-performance switches to support multicast-intensive applications. The available literature indicates that, in order to construct optical multicast banyan networks based on the directional coupler (DC) technology, a high-hardware cost is usually involved to ensure the nonblocking property. In this paper, we conduct blocking probability analysis for such networks to explore the inherent tradeoff between blocking probability and hardware cost. In particular, we focus on a class of DC-based optical networks built on the replicated banyan network (RBN) architecture, and develop a theoretical upper bound on blocking probability for such networks under the general $f$ -cast traffic, which covers the unicast and multicast as special cases. This bound captures the overall blocking behavior of $f$ -cast optical RBN networks and agrees with the conditions of strictly nonblocking $f$ -cast optical RBN networks. The proposed bound is significant because it provides a fundamental guideline to achieve the desirable tradeoff between blocking probability and hardware cost. This paper shows that the hardware cost of an $f$ -cast optical RBN network can be dramatically reduced if a small blocking probability is allowed.

Distributed Control Routing Algorithms for Rearrangeably Nonblocking Optical Banyan Networks

Optical banyan networks can be made rearrangeably nonblocking using its multiple copies in unison. Such rearrangeably nonblocking networks are known as vertically stacked optical banyan (VSOB) networks. Centralized control routing algorithm for this rearrangeably nonblocking optical banyan networks has time complexity O ( N log2 N ). A distributed control routing algorithm with time complexity O (log2 N ) has been proposed recently in which authors have considered N completely connected processors to take routing decision which practically would be very difficult to implement for large N . In this paper we propose two distributed control routing algorithms where processors are loosely connected. In the first algorithm ) ( N O processors work in pipelined fashion, and take the routing decision in linear time. In the second algorithm N inputs synchronously hunt for a free route among ) ( N O copies of a banyan network using a look up table. This algorithm has time complexity ) ( N O . Also the processors do not need to be completely connected, which makes it more practical for implementation.

Upper Bound on Blocking Probability for Vertically Stacked Optical Banyan Networks with Link Failures and Given Crosstalk Constraint

Vertical stacking of multiple copies of an optical banyan network is a novel scheme for building nonblocking 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 under first order crosstalk-free constraint. However, stringent crosstalk constraint may not always be necessary. Considering the fact that some designer may want to compromise the blocking probability and crosstalk constraint to a certain degree with the hardware cost, blocking behaviour of such VSOB networks have been analyzed to studying network performance and finding a graceful compromise between hardware costs and blocking probability under or without crosstalk constraint. In this paper, we present the simulation results for upper bound on blocking probability of VSOB networks with link failures and given degree of crosstalk constraint. We show how crosstalk adds a new dimension to the performance analysis on a VSOB networks. The simulation results presented in this paper can guide network designer in finding the trade-off among the blocking probability, the degree of crosstalk and the hardware cost in terms of vertical copies of banyan network in the presence of link failures.Keywords: Banyan networks; Blocking probability; Vertical stacking; Link-failures; Crosstalk.© 2009 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.DOI: 10.3329/jsr.v1i3.1191 J. Sci. Res. 1 (3), 484-494 (2009)

Blocking probability analysis of pruned optical banyan networks on vertical stacking scheme with extra banyan planes

Vertically stacked pruned optical banyan networks with extra planes (in short, EP-VSOB networks) have lower switch count and optimal time complexity (O(log2N)) for routing N input requests. However, blocking probability is relatively higher than that of a VSOB networks using regular banyan planes. In the EP-VSOB architecture, the number of pruned planes has always been considered as N, and a few extra planes (regular banyan) have been added with these pruned planes. In this paper we present the results of blocking analysis of a more generalized architecture in which the number of pruned planes can be 2x, where x⩾0 in addition to the variable extra planes. This generalization helps us make a compromise between different constraints and performance metrics. Our simulation results show that for some given performance requirements (e.g. cost, speed or blocking probability) we can choose a network that has lower switch count compared to N-plane pruned crosstalk-free optical banyan networks. For example, to ensure blocking probability <0.02, previously we would chose a pruned network of 32 pruned planes and 1 extra planes (a regular banyan); however, our simulations results show that a network of 16 pruned planes and 2 extra planes is enough to ensure the same performance. It is notable that, the hardware cost decreases by 28.65% in this new combination of pruned and extra planes. We believe our results will provide more flexibility in choosing a particular EP-VSOB network satisfying given requirements.

On Number of Planes of Rearrangeably Nonblocking Optical Banyan Networks with Link Failures

Vertically stacked optical banyan (VSOB) networks are attractive for serving as optical switching systems due to the desirable properties (such as the small depth and self-routing capability) of banyan network structures. Although banyan-type networks result in severe blocking and crosstalk, both these problems can be minimized by using sufficient number of banyan planes in the VSOB network structure. The number of banyan planes is minimum for rearrangeably nonblocking and maximum for strictly nonblocking structure. Both results are available for VSOB networks when there exist no internal link-failures. Since the issue of link-failure is unavoidable, we intend to find the minimum number of planes required to make a VSOB network nonblocking when some links are broken or failed in the structure. This paper presents the approximate number of planes required to make a VSOB networks rearrangeably nonblocking allowing link-failures. We also show an interesting behavior of the blocking probability of a faulty VSOB networks that the blocking probability may not always increase monotonously with the increase of link-failures; blocking probability decreases for certain range of link-failures, and then increases again. We believe that such fluctuating behavior of blocking probability with the increase of link failure probability deserves special attention in switch design.  Keywords: Banyan networks; Blocking probability; Switching networks; Vertical stacking; Link-failures. © 2009 JSR Publications. ISSN: 2070-0237(Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v1i1.1070

Overall Blocking Behavior Analysis of General Banyan-Based Optical Switching Networks

Banyan networks are attractive for serving as the optical switch architectures due to their nice properties of small depth and absolutely signal loss uniformity. Combining the horizontal expansion and vertical stacking of optical banyan networks is a general scheme for constructing banyan-based optical switching networks. The resulting horizontally expanded and vertically stacked optical banyan (HVOB) networks usually take either a high hardware cost or a large network depth to guarantee the nonblocking property. Blocking behavior analysis is an effective approach to studying network performance and finding a graceful compromise among hardware cost, network depth, and blocking probability; however, little has been done to analyze the blocking behavior of general HVOB networks. In this paper, we study the overall blocking behavior of general HVOB networks, where an upper bound on the blocking probability of a HVOB network is developed with respect to the number of planes (stacked copies) and the number of stages. The upper bound accurately depicts the overall blocking behavior of a HVOB network as verified by an extensive simulation study, and it agrees with the strictly nonblocking condition of the network. The derived upper bound is significant because it reveals the inherent relationship among blocking probability, network depth, and network hardware cost, so that a desirable tradeoff can be made among them. In particular, our bound gives network developers an effective tool to estimate the maximum blocking probability of a HVOB network, in which different routing strategies can be applied with a guaranteed performance in terms of blocking probability, hardware cost and network depth. Our upper bound model predicts some unobvious qualitative behaviors of HVOB networks, and it draws an important conclusion that a very low blocking probability (e.g., less than 0.001 percent) can be achieved in a HVOB network without introducing either a significantly high hardware cost or a large network depth.

Performance modelling for vertically stacked optical banyan networks with extra stage

A combination of horizontal expansion and vertical stacking of optical banyan (HVOB) is the general scheme for building banyan-based optical switching networks. The HVOB networks usually require either higher hardware cost or larger depth to guarantee the nonblocking property. In this paper, we analyse the blocking probabilities of HVOB networks with one extra stage and develop their upper bound. The bound depicts accurately the overall blocking behaviours of HVOB networks and reveals the inherent relationships among blocking probability, network depth and network hardware cost and enables a desirable tradeoff to be made among them.

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

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 non-blocking one, has time complexity O(NlogN). This is quite large compared to O(NlogN) 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(NlogN) 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 3almost the same as for P-VSOB networks. Both these algorithms also have time complexity O(NlogN).

Design of Optical Rearrangeable Nonblocking MINs Under Various Crosstalk Constraints

Optical interconnection networks suffer from the intrinsic crosstalk problem that should be overcome to make them work properly. Vertical stacking of optical banyan networks is a novel scheme for constructing nonblocking optical multistage interconnection networks (MINs). Rearrangeable nonblocking optical MINs are feasible since they have lower complexity than their strictly nonblocking counterparts. In this paper, we determine the sufficient condition for these MINs to be rearrangeable nonblocking under various crosstalk constraints. We show how the crosstalk constraint affects the design of rearrangeable nonblocking MINs and demonstrate that these networks can tolerate a stricter crosstalk constraint without increasing their hardware complexity significantly. The results in the paper will be useful in designing optical MINs with reasonable hardware cost and crosstalk level.

Performance of Fast Routing Algorithms in Large Optical Switches Built on the Vertical Stacking of Banyan Structures

Vertical stacking of multiple optical banyan networks is a novel scheme for building banyan-based nonblocking optical switches. The resulting network, namely vertically stacked optical banyan (VSOB) network, preserves the properties of small depth and absolutely loss uniformity but loses the nice self-routing capability of banyan networks. To guarantee a high switching speed, routing in VSOB network needs special attentions so that paths can be established as fast as possible. The best known global routing algorithm for an N × N nonblocking VSOB network has the time complexity of O(Nlog N), which will introduce an unacceptable long delay in path establishment for a large size optical switch. In this paper, we propose two fast routing algorithms for the VSOB network based on the idea of inputs grouping. The two algorithms, namely plane fixed routing (PFR) algorithm and partially random routing (PRR) algorithm, have the time complexities of O(log N) and O$(\sqrt{N})$ respectively, and FR algorithm can actually turn a VSOB network into a self-routing one. Extensive simulation based on a network simulator indicates that for large VSOB networks our new algorithms can achieve a reasonably low blocking probability while guarantee a very high switching speed.

Blocking behaviors of crosstalk-free optical banyan networks on vertical stacking

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.

Design of Two-Dimensional Optimized Banyan Networks

A smart two-dimensional optical Banyan network is proposed. Polarization switching logic of light is applied for the design of this network. The main element for the connections of the network is an optical crossbar switch that is composed of a half-wave plate, a programmable polarization switch, and a couple of birefringent plates. By the proposed optical crossbar switches, all permutations of the link patterns required in the network are generated due to the optimized design of the switching logic. As a result, complicated routing control of ordinary Banyan networks is much reduced and a simple two-dimensional optical Banyan network with straight interconnections between successive stages of the networks can be realized.