Rearrangeable Nonblocking Network Research Articles

Assessment of reliability and signature of Benes network using universal generating function

This paper explores the reliability and signature analysis of the multistage interconnection network, especially in a non-blocking network that can be rearranged. In general structure, blocking is a crucial problem faced by multistage interconnection networks. Hence to discuss this issue, here we have taken a most significant part of rearrangeable non-blocking networks, namely Benes network which is the utmost popular rearrangeable non-blocking multistage interconnection networks. In the current study, we propose to assess the reliability having both ‘independent and identically and non-identically distributed components’ of Benes network in the three contexts, viz. terminal, broadcast and network with the help of universal generating function. With the aid of Owen's method, an efficient algorithm was developed to enumerate the signature and mean time to failure of the Benes network having independent, identically distributed lifetime components.

Nonblocking Multicast Networks for Transporting Stream Media

Leaf-spine architecture has been widely adopted as a scalable multistage network. However, for media transport purposes, nonblocking conditions for any combination of multicasts should be taken into account. In this paper, a new approach for building three-stage Clos networks with nonblocking multicast capability is proposed. First, a wide-sense nonblocking (WSNB) condition and a rearrangeable nonblocking (RNB) condition for nonblocking multicast networks are presented. The proposed conditions focus on the distribution of inputs at the middle stage rather than the distribution at the output stage. Second, the proposed conditions are evaluated by mapping to leaf-spine networks with commodity building block switches. The network size is evaluated by calculating the sum of the required building block switches. In the best case of the evaluation results, up to 50% of the switches can be reduced compared with the best-known WSNB condition, and the proposed WSNB networks show good coverage in relatively small but practical network sizes. The proposed RNB networks always show better results than the known RNB multicast conditions.

Four-Stage Multicast Switching Networks: Nonblocking Conditions and Cost Analysis

In this paper, we consider four-stage multicast switching networks with different types of nonblocking capability. The goal of the paper is multifold. First, we evaluate and summarize various nonblocking conditions of four-stage multicast switching networks in recent work [Y. Yang and J. Wang, “A New Design for Wide-Sense Nonblocking Multicast Switching Networks,” IEEE Trans. Commun., vol. 53, no. 3, pp. 497-504, Mar. 2005, and F. Yan et al., “Nonblocking Four-Stage Multicast Network for Mulicast-Capable Optical Cross Connects,” J. Lightw. Technol., vol. 27, no. 17, pp. 3923-2932, Sep. 2009], and then propose a locally-rearrangeable nonblocking (LRNB) multicast switching network as a trade-off for nonblocking capability and network hardware cost between wide-sense nonblocking (WSNB) networks and rearrangeable nonblocking (RNB) networks. We further derive optimized network parameters and present a comprehensive cost analysis for different types of four-stage nonblocking multicast switching networks. Using the terms defined in F. Yan et al., our results show that for an N × N network, a 4(2m)-stage WSNB network and a 4(2 m)-stage LRNB network have 16.114 N3/2 and 12.669 N3/2 crosspoints, respectively; 4(3 m)-stage WSNB and LRNB networks have the same number of crosspoints, 11.657 N3/2; and 4(2 m)-stage RNB network has 7.447 N3/2 crosspoints.

Fast reconfiguration algorithms for time, space, and wavelength dilated optical Benes networks

Benes networks are rearrangeable nonblocking networks and are among the most efficient switching architectures in terms of the number of switching elements (SEs) used. In optical Benes networks, if two I/O connecting paths with the same (close) wavelength(s) share a common SE, crosstalk occurs. In order to reduce the crosstalk effect, three approaches, time, space and wavelength dilations have been proposed. In this paper, we present polylogarithmic-time reconfiguration algorithms for realizing any (partial) permutation in time, space and wavelength dilated optical Benes networks using a linear number of processors. Our algorithms are based on a logarithmic-time permutation decomposition algorithm and apply graph coloring techniques such as edge coloring, equitable coloring and vertex coloring.

Scalable and Practical Nonblocking Switching Networks

Large-scale strictly nonblocking (SNB) and wide-sense nonblocking (WSNB) networks may be infeasible due to their high cost. In contrast, rearrangeable nonblocking (RNB) networks are more scalable because of their much lower cost. However, RNB networks are not suitable for circuit switching. In this paper, the concept of virtual nonblockingness is introduced. It is shown that a virtual nonblocking (VNB) network functions like an SNB or WSNB network, but it is constructed with the cost of an RNB network. The results indicate that for large-scale circuit switching applications, it is only needed to build VNB networks.

Parallel routing algorithms for nonblocking electronic and photonic switching networks

We study the connection capacity of a class of rearrangeable nonblocking (RNB) and strictly nonblocking (SNB) networks with/without crosstalk-free constraint, model their routing problems as weak or strong edge-colorings of bipartite graphs, and propose efficient routing algorithms for these networks using parallel processing techniques. This class of networks includes networks constructed from banyan networks by horizontal concatenation of extra stages and/or vertical stacking of multiple planes. We present a parallel algorithm that runs in O(lg/sup 2/ N) time for the RNB networks of complexities ranging from O(N lg N) to O(N/sup 1.5/ lg N) crosspoints and parallel algorithms that run in O(min{d* lg N, /spl radic/N}) time for the SNB networks of O(N/sup 1.5/ lg N) crosspoints, using a completely connected multiprocessor system of N processing elements. Our algorithms can be translated into algorithms with an O(lg N lg lg N) slowdown factor for the class of N-processor hypercubic networks, whose structures are no more complex than a single plane in the RNB and SNB networks considered.

Two-bounce optical arbitrary permutation network

The two-bounce free-space arbitrary interconnection architecture is presented. It results from a series of three-dimensional topological transformations to the Benes network, the minimum rearrangeable nonblocking network. Although functionally equivalent to the Benes network, it requires only two stages of global (spanning multiple chips) optical interconnections. The remaining stages of the modified Benes interconnection network are local and are implemented electronically (on individual chips). The two-bounce network is optimal in the sense that it retains the Benes minimum number of electronic switching resources yet also minimizes the number of optical links needed for global interconnection. Despite the use of higher-order k-shuffle (k > 2) global optical interconnects, the number of 2 x 2 switching elements is identical to the two-shuffle Benes network: there is no need for k x k crossbar switches for local interconnection at each stage. An experimental validation of the two-bounce architecture is presented.

Arbitrary Size Benes Networks

The Benes network is a rearrangeable nonblocking network which can realize any arbitrary permutation. Overlall, the r-dimensional Benes network connects 2r inputs to 2r outputs through 2r - 1 levels of 2 × 2 switches. Each level of switches consists of 2r - 1 switches, and hence the size of the network has to be a power of two. In this paper, we extend Benes networks to arbitrary sizes. We also show that the looping routing algorithm used in Benes networks can be slightly modified and applied to arbitrary size Benes networks.

Modified gamma network and its optical implementation

A modified gamma network that is based on the bar-plus-2(i) and modulo-N connection patterns is proposed. The gamma network, one class of important O (N log(2)N) interconnection networks, needs arrays of 1 × 3 or 3 × 3 switches, which makes it difficult to realize in optics. We modify the gamma network to meet the characteristics of optics by employing a bar-plus-2(i) connection pattern and a modulo N output stage. Two-by-two switches and regular interconnections are used in the network, so the network is suitable for optics. The optical implementation of the network with a birefringent crystal and an array of programmable half-wave plates is suggested, and a proof-of-principle experiment is presented. The network is a rearrangeable nonblocking network, and the nonblocking routing algorithm for an N × N network is given; (2 log(2)N - 2) switching stages [with a total of (2 log(2)N + 1/2)N - 4 log(2)N - 1 switches] can permute N input nodes to N output nodes in any order in a one-to-one manner. The network is applicable to packet synchronous optical traffic.

Tradeoff of horizontal decomposition versus vertical stacking in rearrangeable nonblocking networks

A class of rearrangeable nonblocking networks is presented. The proposed networks are fault-tolerant, self-routing, and intended for a very-high-speed environment. Self-routing networks have one major problem when applied to switching: they are blocking networks. To solve this problem, two methods have been used to create self-routing rearrangeable nonblocking networks: horizontal cascading (HC) and vertical stacking (VS). The authors unify the two approaches and propose a novel class of switching networks. The proposed design principle allows the best tradeoffs among design parameters such as fault tolerance, hardware cost, and the frequency of rearrangement activities. A study of the frequency of rearrangement activities is also presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Multi-log/sub 2/N networks and their applications in high-speed electronic and photonic switching systems

A class of switching networks is proposed to remove the time and space bottlenecks of conventional RAM-controlled switching architectures. The advantages of these networks, such as tolerance of faults O(log/sub 2/N) stages between each inlet-outlet pair, self-routing capability, easy path hunt, and easy fault diagnosis, and their implementation are discussed. Graph theory is used to construct strictly nonblocking or rearrangeable nonblocking networks that are based on the new architecture. >

A Simple Control Algorithm for Rearrangeable Switching Networks with Time Division Multiplexed Links

A simple control algorithm is proposed for a three-stage rearrangeable switching network with time division multiplexed links. The nonblocking condition is shown for the rearrangeable network controlled by the proposed algorithm. The rearrangeable nonblocking network controlled by the proposed method is more cost effective in hardware than a strictly nonblocking network for a large number of channels multiplexed on links. The computing complexity of the algorithms is not more than that for controlling the strictly nonblocking network. In the proposed algorithm, only one path must be moved in the rearrangement, thus reducing the difficulty in implementing the rearrangeable network. This algorithm is efficient for broadband switching systems or cross-connect devices where nonblocking switches are needed.