A fault-tolerant rearrangeable permutation network
ABSTRACT As optical communication becomes a promising networking choice, the well-known Clos network has regained much attention recently from optical switch designers/manufacturers and cluster computing community. There has been much work on the Clos network in the literature due to its uses as optical crossconnects (OXCs) in optical networks and high-speed interconnects in parallel/distributed computing systems. However, little attention has been paid to its fault tolerance capability, an indispensable requirement for any practical high-performance networks. We analyze the fault tolerance capability of the three-stage rearrangeable Clos network. We first establish a fault model on losing-contact faults in the switches of the network. Then, under this model, we analyze the fault tolerance capability of the Clos network when multiple such faults present in switches in the input stage, middle stage, and/or output stage of the network. Our results show that the rearrangeable condition on the number of middle stage switches for a fault-free rearrangeable Clos network still holds in the presence of a substantial amount of faults, while a more expensive crossbar network cannot tolerate any single such fault. In particular, we obtain that, for an N×N Clos network C(m,n,r), where N = nr and m≥n, it can tolerate any m - 1 losing-contact faults arbitrarily located in input/output stage switches, or any m - n losing-contact faults arbitrarily located in middle stage switches, when realizing any permutations. We also demonstrate that, for a given permutation, the network usually can tolerate much more such faults. We then present a necessary and sufficient condition on the losing-contact faults a Clos network can tolerate for any given permutation. We also develop an efficient fault-tolerant routing algorithm for a rearrangeable Clos network based on these results.
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ABSTRACT: In this paper, we analyze ways of realizing permutations in a class of 2log<sub>2</sub>N- or (2log<sub>2</sub>N-1)-stage rearrangeable networks. The analysis is based on the newly developed inside-out routing algorithm and we derive the upper and lower bounds on the number of possible realizations of a permutation. It is shown that the algorithm can provide us with comparable degrees of freedom in realizing a given permutation as the well-known looping algorithm, while it can be more generally applied to a class of 2log<sub>2</sub>N- or (2log<sub>2 </sub>N-1)-stage rearrangeable networks. In finding a set of complete assignments for the center-stage cycles, alternate realizations of a permutation can be obtained by changing the initial position, changing the assigning direction, or even interchanging the first-level decompositions of the permutation. We also show that these numerable alternate realizations can be utilized to make the networks tolerate some sets of faults, i.e., control faults of SEs including stuck-at-straight and stuck-at-cross. Various cases of single control faults at the center stages and other stages are examined through examples. These new approaches originate from routing outward from center stages to outer stages; therefore, the center stages and two half networks may be treated separatelyIEEE Transactions on Parallel and Distributed Systems 10/1999; · 1.80 Impact Factor
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ABSTRACT: The well-known Clos network has been extensively used for telephone switching, multiprocessor interconnection and data communications. Much work has been done to develop analytical models for understanding the routing blocking probability of the Clos network. However, none of the analytical models for estimating the blocking probability of this type of network have taken into account the very real possibility of the interstage links in the network failing. In this paper, we consider the routing between arbitrary network inputs and outputs in the Clos network in the presence of interstage link faults. In particular, we present an analytical model for the routing blocking probability of the Clos network which incorporates the probability of interstage link failure to allow for a more realistic and useful determination of the approximation of blocking probability. We also conduct extensive simulations to validate the model. Our analytical and simulation results demonstrate that for a relatively small interstage link failure probability, the blocking behavior of the Clos network is similar to that of a fault-free network, and indicate that the Clos network has a good fault-tolerant capability. The new integrated analytical model can guide network designers in the determination of the effects of network failure on the overall connecting capability of the network and allows for the examination of the relationship between network utilization and network failureIEEE Transactions on Parallel and Distributed Systems 11/1999; · 1.80 Impact Factor
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ABSTRACT: With ever increasing demands on bandwidth from emerging bandwidth-intensive applications, such as video conferencing, E-commerce, and video-on-demand services, there has been an acute need for very high bandwidth transport network facilities. Optical networks are a promising candidate for this type of applications. At the same time, many bandwidth-intensive applications require multicast services for efficiency purposes. Multicast has been extensively studied in the parallel processing and electronic networking community and has started to receive attention in the optical network community recently. In particular, as WDM (wavelength division multiplexing) networks emerge, supporting WDM multicast becomes increasingly attractive. In this paper, we consider efficient designs of multicast-capable WDM switching networks, which are significantly different and, hence, require nontrivial extensions from their electronic counterparts. We first discuss various multicast models in WDM networks and analyze the nonblocking multicast capacity and network cost under these models. We then propose two methods to construct nonblocking multistage WDM networks to reduce the network costIEEE Transactions on Parallel and Distributed Systems 01/2001; · 1.80 Impact Factor