Tolerating multiple faults in multistage interconnection networks with minimal extra stages

Adams and Siegel (1982) proposed an extra stage cube interconnection network that tolerates one switch failure with one extra stage. We extend their results and discover a class of extra stage interconnection networks that tolerate multiple switch failures with a minimal number of extra stages. Adopting the same fault model as Adams and Siegel, the faulty switches can be bypassed by a pair of demultiplexer/multiplexer combinations. It is easy to show that, to maintain point to point and broadcast connectivities, there must be at least S extra stages to tolerate I switch failures. We present the first known construction of an extra stage interconnection network that meets this lower-bound. This 12-dimensional multistage interconnection network has n+f stages and tolerates I switch failures. An n-bit label called mask is used for each stage that indicates the bit differences between the two inputs coming into a common switch. We designed the fault-tolerant construction such that it repeatedly uses the singleton basis of the n-dimensional vector space as the stage mask vectors. This construction is further generalized and we prove that an n-dimensional multistage interconnection network is optimally fault-tolerant if and only if the mask vectors of every n consecutive stages span the n-dimensional vector space

Zero Algorithms for Avoiding Crosstalk in Optical Multistage Interconnection Network

Multistage Interconnection Networks (MINs) are popular in switching and communication applications. It had been used in telecommunication and parallel computing systems for many years. The broadband switching networks are built from 2 x 2 electro-optical switches such as Lithium Niobate switches. Each switch has two active inputs and outputs. Optical signals, carried on either inputs are coupled to either outputs by applying an appropriate voltage to the switch. One of the problems associated with these electro-optical switches is the crosstalk problem, which is caused by undesired coupling between signals carried in two waveguides. This thesis propose an efficient solution to avoid crosstalk, which is routing of traffic through an N x N optical network to avoid coupling two signals within each switching element. Under the constraint of avoiding crosstalk, the research interest is to realize a permutation that will use the minimum number of passes (to route the input request to output without crosstalk). This routing problem is an NP-hard problem. Many heuristic algorithms have been proposed and designed to perform the routing such as the sequential algorithm, the sequential down algorithm, the degree-ascending algorithm, the degree-descending algorithm, the Simulated Annealing algorithm and the Ant Colony algorithm. The Zero algorithms are the new algorithms that have been proposed in this thesis. In Zero algorithms, there are three types of algorithms namely; The Zero X, Zero Y and zeroXY algorithms. The experiments conducted have proven that the proposed algorithms are effective and efficient. They are based on routing algorithms to minimize the number of passes to route all the inputs to outputs without crosstalk. In addition, these algorithms when implemented with partial ZeroX and ZeroY algorithms would yield the same results as the other heuristic algorithms, but over performing them when the execution time is considered. Zero algorithms have been tested with many cases and the results are compared to the results of the other established algorithms. The performance analysis showed the advantages of the Zero algorithms over the other algorithms in terms of average number of passes and execution time

Removal of Cross Talk in Omega Switch Network by Using Improve Windowing Technique

An optical computer network is a network that relies primarily on the computing power and bandwidth of the participants in the network rather than concentrating it in a relatively low number of servers. Such networks are useful for many purposes. Sharing content files (see file sharing) containing audio, video, data or anything in digital format is very common, and real time data, such as telephony traffic, is also passed using Optical technology. The proposed work is about to handle the network fault in case of cross talk in a switched network. In this work we are presenting the complete work with Omega Network. The work includes the analysis of existing methodologies to detect the confliction in cross talk. As the confliction is detected the next work is perform the talk with a smaller delay such that it will avoid the cross talk over the networ

Reduce the Cross Talk in Omega Network by Using Windowing Techniques

When we work on a distributed network with n number of systems attached with m number of resources. In such case there are number of approaches to connect the system and the resources. One of such approach is Multistage networks. Where some middle level interface systems or the switches are attached between the systems and the resources. But such kind of networks having the problem of confliction when more than one transmission is taken place at one time. In such case there is the possibility that any one line can share more than one transmissions. As the conflictions occur there are much chances of data loss over the network. We are providing the solution for the above defined problem in case of Omega Networks. In this paper we proposed solution the system will first detect the confliction using windowing method. Once the confliction detected the next step is to vary the time of transmission between these two transmissions. As the communication is performed at different time lines it will resolve the problem of confliction in omega networks

Crosstalk-Free Scheduling Algorithms for Routing in Optical Multistage Interconnection Networks

Multistage Interconnection Networks (MINs) have been used in telecommunication networks for many years. Significant advancement in the optical technology have drawn the idea of optical implementation of MINs as an important optical switching topology to meet the ever increasing demands of high performance computing communication applications for high channel bandwidth and low communication latency. However, dealing with electro-optic switches instead of electronic switches held its own challenges introduced by optics itself. Limited by the properties of optical signals, optical MINs (OMINs) introduce optical crosstalk, as a result of coupling two signals within each switching element. Therefore, it is not possible to route more than one message simultaneously, without optical crosstalk, over a switching element in an OMIN. Reducing the effect of optical crosstalk has been a challenging issue considering trade-offs between performance and hardware and software complexity. To solve optical crosstalk, many scheduling algorithms have been proposed for routing in OMIN based on a solution called the time domain approach, which divides the N optical inputs into several groups such that crosstalk-free connections can be established. It is the objective of the research presented in this thesis to propose a solution that can further optimize and improve the performance of message scheduling for routing in the optical Omega network. Based on Zero algorithms, a Modified Zero algorithm is developed to achieve a crosstalk-free version of the algorithm. Then, the Fast Zero (FastZ) algorithm is proposed, which uses a new concept called the symmetric Conflict Matrix (sCM) as a pre-scheduling technique. Extended from the FastZ algorithms, another three new algorithms called the FastRLP, BRLP and FastBRLP algorithms are developed to achieve different performance goals. Lastly, a comparison is made through simulation between all algorithms developed in this research with previous Zero-based algorithms as well as traditional Heuristic algorithms since equal routing results can be obtained between all algorithms. Through simulation technique, all three FastZ, BRLP and FastBRLP algorithms have shown the best results when the average execution time is considered. The FastRLP and FastBRLP algorithms on the other hand have shown the best results when the average number of passes is considered. It is proven in this thesis that the new approach has by far achieved the best performance among all the algorithms being tested in this researc

Evaluation of Two Terminal Reliability of Fault-tolerant Multistage Interconnection Networks

This paper iOntroduces a new method based on multi-decomposition for predicting the two terminal reliability of fault-tolerant multistage interconnection networks. The method is well supported by an efficient algorithm which runs polynomially. The method is well illustrated by taking a network consists of eight nodes and twelve links as an example. The proposed method is found to be simple, general and efficient and thus is as such applicable to all types of fault-tolerant multistage interconnection networks. The results show this method provides a greater accurate probability when applied on fault-tolerant multistage interconnection networks. Reliability of two important MINs are evaluated by using the proposed method