Clos, Beneš, and multi-Log2Nnetworks are all multistage networks, where the latter adopts the most generalized topology among the three. For a given network, shell s consists of both the sth and the sth-to-last node stages. The fault tolerance capabilities in each shell, namely, the maximum number of tolerable non-contact faults for realizing any permutation, have been investigated in earlier studies for rearrangeable nonblocking Clos and Beneš networks. However, the fault tolerance capabilities of rearrangeable nonblocking multi-Log2Nnetworks have not been studied yet despite their use in many applications. Due to the complicated topology of such a network, analyzing its fault tolerance capability is a difficult task. In this paper, we propose a novel deterministic method, which is very different from that for analyzing the fault-tolerance of Clos and Beneš networks, to derive the fault tolerance capability in each shell of an RNB multi-Log2Nnetwork. Specifically, the proposed method analyzes the impact of non-contact faults on multi-Log2Nnetworks and enumerates the maximum number of such non-contact faults that can be tolerated while ensuring the availability of a path for each connection, allowing for rearrangements. Our results show that the fault tolerance capability in a single shell of anN×NRNB multi-Log2Nnetwork outperforms that for anN×NRNB Beneš (or Clos) network.

Beneš networks are well-known rearrangeable nonblocking (RNB) multistage networks. The so-called conventional Beneš networks are based on$2\times 2$switches. In this paper, Beneš network is a general term used to refer to an$N\times {N}~n$-nary Beneš network. Such networks, denoted by B($n$,$t)$, where$N = n^{t}$and$t \ge2$, are based on regular$n\times n$switches, and are RNB as well. A Beneš network is constructed recursively from a 3-stage Clos network. For an$N\times N$RNB Clos network C($n$,$m$,$r)$, where$N = nr$and$m \ge n$, the maximum allowable number of non-contact faults in each single shell for realizing any permutation has been investigated in an earlier study, where shell$k$in a network consists of both the$k$th and the$k$th-to-last node stages. That study showed that, for a given integer$N$, an RNB C($n$,$n$,$r)$network with larger$n\times n$switches leads to tolerance of more non-contact faults in shell 1. In this paper, for an$N\times N$B($n$,$t)$network, we study the maximum allowable number, say$f_{k}$, of non-contact faults for any permutation not only in each single shell$k$, but also in all shells simultaneously under the fault condition that at most$f_{k}$non-contact faults are arbitrarily located in the switches in each shell$k$. We call the former the fault tolerance capability in a single shell, and the latter the fault tolerance capability of the network. We show that a larger switch size, i.e.,$n\times n$, in an${N} \times N$B($n$,$t)$network leads to a higher fault tolerance capability of the network and a higher fault tolerance capability in each non-middle shell. An$N\times N$Beneš network B($n$,$t)$considers only the value of$N$which is a power of$n$. To consider a flexible$N$with$N = n^{s}\cdot \textit {q}$, where$s\ge2$,$1 < {q} < n$and${q}\vert n$, which means that$n$is divisible by${q}$, we propose in this paper an$N\times N$RNB Beneš-type network using regular$n\times n$switches, which is called an extended Beneš and denoted by B($n$,$s$,${q})$. Both Beneš and extended Beneš networks are based on regular switches, and they have better scalabilities than a Clos network. We define a network’s fault tolerance rate as the ratio of the fault tolerance capability to the total crosspoints in the network. For given integers$N$and$n$, we derive that the fault tolerance capability and fault tolerance rate of an${N} \times N$Beneš (or extended Beneš) network are higher than or equal to those of an$N\times N$RNB C($n$,$n$,$r)$network, and the former outperforms the latter in most cases.

Abstract All‐optical cross‐connects need to perform switching not only in the space domain, but also in the wavelength domain. Switching in the wavelength domain requires wavelength converters (WCs), and WCs capable of simultaneously performing multiple wavelength conversions have been invented. We can use multiple stages of such WCs to form a wavelength exchange network to allow an even larger number of simultaneous wavelength conversions. However, WCs with a full conversion range are often difficult to implement. In the paper, we develop new techniques and theories that can reduce the conversion range requirement and still maintain the full connectivity of all‐optical space/wavelength switches.

An optical network based on elastic optical switches allows requests using different spectrum widths to improve utilisation efficiency. This study considers one three‐stage WSW (waveband switching‐space switching‐waveband switching), optical node architecture for elastic optical networks. A sufficient condition for a rearrangeable non‐blocking WSW architecture with limited input/output links has been derived in an earlier work. In this study, the author improves the upper bound by adopting a new interstage link partition scheme associated with a tricky routing algorithm. Suppose a WSW architecture has r input/output links each of which has n frequency slot units (FSUs). Compared with earlier results, the results of the proposed scheme show that s − 1 (or 3 s − 4) FSUs per interstage link can be reduced for even (or odd) min{ r , n }, where s = min{⌈ r /2⌉, ⌈ n /2⌉}. The reduction gain is at least 3.5% (or 10%) for even (or odd) min{ r , n } if r = n ≤ 26, even achieving 23.3% for limited odd r = n .

An NoC (network on chip) constructed with silicon photonic microrings can be implemented with CMOS technology and integrated with processor cores on the same die. Each microring in the NoC has two switching states, one consuming significantly less power than the other. Different routing schemes can lead to different numbers of microrings in the high-power consumption state, and result in different power consumptions for the NoC. In an earlier work, a looping-based routing algorithm was proposed which exploits the different power consumption characteristics of the two switching states of a microring so as to minimize the power consumption of a Benes-type NoC; but this algorithm cannot provide an optical solution. In this paper, we will show the necessary and sufficient conditions for finding the optimal solution for a Benes-type NoC. We also present a new routing algorithm. Compared with the algorithm of the previous work, the new algorithm can reduce the number of microrings in the high-power-consumption state by as many as (n - 2) · 2n-2in a 2n× 2nBenes-type NoC for certain interconnection patterns.

Abstract We study necessary and sufficient conditions for multirate, multicast, and wide‐sense nonblocking (WSNB) log 2(N, m, p) networks. We show necessary and sufficient conditions for different values of m. The results allow us to find a speedup requirement in the network for a given traffic load. We also present a sufficient condition for making the network nonblocking when a limit is imposed on the multicast group size. © 2008 Wiley Periodicals, Inc. NETWORKS, 2008

Recently, Tscha and Lee proposed a fixed-size window algorithm for the multicast Log/sub 2/(N,0,p) network and expressed a desire to see its extension to the Log/sub 2/(N,m,p) network. Later, Kabacinski and Danilewicz generalized the fixed-size window to variable size to improve the results. In this paper, we further extend the variable-size results from the Log/sub 2/(N,0,p) network to Log/sub 2/(N,m,p). Note that this extension is difficult since each link in the channel graph of Log/sub 2/(N,0,p) has the same blocking effect, but not so in Log/sub 2/(N,m,p). We also determine the optimal window size and optimal m.