Wide-sense Nonblocking Research Articles

Rearrangeability and repackability of a multicast wavelength-space-wavelength elastic optical network

Elastic optical networks (EONs) have been introduced to meet the demands of the rapidly growing Internet. These networks can efficiently keep up with the emerging bandwidth-hungry and highly dynamic services, and can support multicast services using techniques like the path, tree or subtree methods. A multicast wavelength-space-wavelength (M-WSW) network is a switching node architecture for EONs, which adopts the subtree method to support multicast connections. An M-WSW network consists of three node stages in which wavelength, space and wavelength switches are used, respectively. A nonblocking M-WSW network guarantees that any connection between a free input and a free output can always be realized, and studying the nonblockingness of a network has attracted much attention from researchers. Sufficient conditions, in terms of the number of middle space switches, for an M-WSW network to be strict-sense nonblocking (SNB) or wide-sense nonblocking (WSNB) were examined in an earlier study. It is known that SNB networks usually incur a higher hardware cost, for instance, the number of middle space switches, compared to WSNB, rearrangeably nonblocking (RNB), or repackably nonblocking (RPNB) networks. This paper studies the rearrangeability and repackability of M-WSW networks, and derives the sufficient and necessary conditions for an M-WSW network to be RNB (or RPNB). The results show that the derived sufficient conditions for being RNB (or RPNB) require significantly fewer middle switches for SNB and WSNB networks, and the RPNB results require fewer middle switches than those for RNB in most cases.

Wide-Sense Nonblocking Converting-Converting Networks with Multirate Connections.

In this paper, we consider a two-stage converting-converting (CC) switching network. This structure can be used, for instance, in switches of elastic optical networks (EONs) or in time-division switches. We propose a new routing algorithm based on fixed slot assignment in interstage links. This algorithm, called Fixed Input–interstage Slot Assignment (FISA), reduces the switching network complexity compared to the rearrangeable (RNB) switching networks of the same structure. We derive the wide-sense nonblocking (WNB) conditions for the switching network controlled by this algorithm. The obtained WNB conditions are the same as those of the RNB, but the switching network does not need troublesome and time-consuming rearrangements. When implementing the proposed switching network structure, we can also reduce the number of tunable full-range spectrum converters and replace part of them with fixed spectrum converters, or even use space switches in the first stage. This is especially important when this architecture is applied in EONs.

Wide-Sense Nonblocking Multicast in WDM Optical Linear Array and Ring Networks with 3-Length Extension Under Longest Link First Routing

The modern scientific growths in optical networks based on wavelength division multiplexing (WDM) are more attractive to satisfy the high bandwidth requirements of the modern internet infrastructure. Moreover, they potential to satisfy the future bandwidth requirements.WDM optical networks act as the backbone for telecommunication and high-performance communication networks. Multicast communication is the simultaneous transmission of data from one source node to many destination nodes available in the network over wavelength division multiplexing. It is extensively deployed in high performance computing and communication networks. In this article, a linear array and ring networks are extended by directly linking all nodes which are separated by two intermediate nodes with additional fibers which is referred as linear array and ring network with 3-length extension. The wavelength allotment methods are proposed to realize one-to-many communication over wavelength division multiplexing optical linear array and ring with 2-length extension under longest link first routing and the minimum wavelength number needed is determined. The minimum wavelength number needed to support for the extended linear array is reduced approximately by 20% when compared with that of a linear array network and for the extended unidirectional ring is reduced approximately by 25% when compared with that of a unidirectional ring network. And also, for the extended bidirectional ring the minimum wavelength number is reduced approximately by 33% when compared with that of bidirectional ring network.

Wide-Sense Nonblocking Multicast in WDM Optical Linear Array and Ring Networks with 2-Length Extension under Index Based Routing

Multicast communication is the concurrent transmission of data from one source node to many destination. It is widely deployed in high performance computing and communication networks.In this paper, a linear array and ring networks are extended by directly linking all nodes which are separated by one intermediate node with additional fibers which is referred as linear array and ring network with 2-length extension and wide sense nonblocking multicast is studied. The wavelength allotment methods are proposed to realize one-to-many communication over wavelength division multiplexing optical linear array and ring with 2-length extension under index-based routing and the minimum wavelength number needed is determined. The minimum wavelength number needed to support for the extended linear array and ring topologies is reduced approximately by half when compared with that of a linear array network and ring network.

Nonblocking conditions for a multicast WSW architecture based on subtree scheme for elastic optical networks

Elastic optical networks (EONs) are a promising solution for future high-speed optical communication, and multicasting in EONs can efficiently support many emerging services. Different schemes, such as path, tree and subtree schemes, serve multicast services. In this paper, we consider a three-stage wavelength-space-wavelength (WSW) node architecture, which adopts wavelength switches in the first and last stages and space switches in the middle stage, and uses the path scheme to accommodate multicast requests, as proposed in an earlier work for elastic optical networks. We also enhance the WSW architecture to serve multicast requests in a more spectrum-efficient way, namely, using the subtree scheme, by making each switch support multicast capacity, and we term the resulting architecture M-WSW. To the best of our knowledge, this is the first study of the WSW architecture using the subtree scheme to support multicast capacity. We prove the sufficient and necessary conditions, in terms of the number of middle switches, of the M-WSW architecture for being strictly nonblocking (SNB) and wide-sense nonblocking (WSNB) under the two routing algorithms proposed in this paper. Our results show that the number of middle switches required for the architecture to be WSNB under each of the two proposed routing algorithms is much less than the number of middle switches required for SNB, especially when the SNB results meet the boundary condition.

Wide-sense nonblocking multicast in WRMD WDM optical linear array and ring

Multicast communication is the simultaneous transmission of information from a single source to various destinations. It occurs extensively in telecommunication and advanced computing systems including enterprises operating datacenters. WDM optical networks act as the backbone for telecommunication and high performance networks. Wavelengths are scarce resources in WDM optical networks. Wavelengths usage in a network must be limited to decrease its cost and complexity. Optical linear array and ring networks find widespread application in interconnection networks including LAN and WAN. In this paper, wide-sense nonblocking multicast communication is analyzed in wavelength reusable multi-carrier distributed (WRMD) wavelength division multiplexing (WDM) linear array, unidirectional ring and bidirectional ring networks. The sufficient and necessary condition on the minimum wavelength number required for the network to be wide-sense nonblocking is derived for each of the above network topologies in the presence of a single multi-carrier light source (MCLS). An explicit wavelength allotment technique is also proposed for the above network topologies.

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.

Wide-Sense Nonblocking W-S-W Node Architectures for Elastic Optical Networks

Wide-Sense Nonblocking W-S-W Node Architectures for Elastic Optical Networks

Wide-sense nonblocking multicast in optical WDM networks

Multicast communication is the concurrent transmission of data from one source node to many destination nodes. It is widely deployed in high performance computing and communication networks. In this article, wide-sense nonblocking multicast communication is studied in wavelength division multiplexing networks namely modified linear array, unidirectional and bidirectional modified ring networks. The sufficient and necessary condition on the minimum wavelength number required for the network to be wide-sense nonblocking is derived for each of the above network topologies under longest link first routing technique which employs approximately half the number of hops when compared with networks without modification. An explicit wavelength allotment technique for multicast assignment is also given for each of the above network topologies.

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.

Nonblocking multirate log 2 (N ,m ,p ) switching networks with multicast connections

Wide-sense nonblocking (WSNB) multiplane banyan-type multirate switching networks with multicast connections are considered in this article. It is shown that the known results constitute in many cases only lower bounds for WSNB operation under the blocking window algorithm. New necessary and sufficient conditions are derived and proved. The obtained results can also be extended to networks with a limit imposed on the multicast group size. © 2010 Wiley Periodicals, Inc. NETWORKS, Vol. 57(4), 333-343 2011 © 2011 Wiley Periodicals, Inc.

Nonblocking Four-Stage Multicast Network for Multicast-Capable Optical Cross Connects

In this paper, we investigate the four-stage multicast network with only two multicast stages (the second and output stages) being multicast-capable, which is called 4(2 m)-stage multicast network. We first derive the sufficient wide-sense nonblocking (WSNB) and rearrangeable nonblocking (RNB) conditions for the 4(2 m)-stage multicast network. The WSNB and RNB conditions are also presented for multicast request with limited multicast degree. The 4(2 m)-stage multicast network needs at least O(N 3 / 2) crosspoints to be WSNB and RNB, which is a lower bound than the three-stage Clos network with two multicast stages and the same bound with the four-stage network with three multicast stages. Then we design full and partial multicast-capable optical cross connects (MC-OXCs) applying the 4(2 m)-stage multicast network. The proposed WSNB full MC-OXC with two multicast stages is power efficient in reducing splitting loss and has lower multicast cost, compared with the one having three multicast stages. Partial MC-OXC with only one multicast stage is proposed to further reduce the multicast cost and splitting loss. The RNB MC-OXCs with one or two multicast stages provide better performance at the respects of crosspoints, multicast cost, and splitting loss than their WSNB counterparts.

Multirate nonblocking multicast Log2(N, m, p) networks

AbstractWe 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

A New Control Algorithm for Wide-Sense Nonblocking Multiplane Photonic Banyan-Type Switching Fabrics with Zero Crosstalk

A new control algorithm for log2(N, 0, p) switching networks composed of 2 x 2 switching elements has been proposed recently. Under this algorithm, log2(N,0,p) switching networks with even number of stages are wide-sense nonblocking (WSNB) if p is the same as for the rearrangeable nonblocking (RNB) one. The considerred algorithm and WSNB conditions did not take into account crosstalk constraint, which is an important factor in photonic switching. This paper enhanced this algorithm to the case when crosstalk in the switching fabric is not allowed. WSNB conditions for this enhanced algorithm are also derived. It is shown, that the number of planes required is less than those derived earlier in other papers for WSNB multiplane banyan- type switching fabrics under crosstalk constraint. Under this algorithm, log2( N,0,p) switching networks with odd number of stages and with zero crosstalk are WSNB if p is the same as for RNB one.

Wide-Sense Nonblocking ${\rm log}_{d}(N, 0, p)$ Multicast Switching Networks

Wide-sense nonblocking (WSNB) log2(N, 0, p) switching networks under the fixed-size blocking window algorithm have been proposed by Tscha and Lee. We have generalized this approach to the variable-size blocking window algorithm and shown that the minimum number of planes depends on the window size and the number of stages. We have also generalized this concept to log2(N, m, p) switching networks. Later, Hwang and Lin have proved that for m > 2, the number of required planes for WSNB operation under the blocking window algorithm is always greater than for m les 2, and determined the optimal window size and optimal m. In this paper, we further generalized these results to logd(N, 0, p) switching networks. In the paper, we prove that the minimum number of planes for any d is reached also for different sizes of blocking window depending on d and n.

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.

A Unifying Approach to Determine the Necessary and Sufficient Conditions for Nonblocking Multicast 3-Stage Clos Networks

The 3-stage Clos network is the most-studied switching network. However, exact conditions on the strictly nonblocking multicast three-stage Clos network under various models are difficult to get, due to the messy detail and because each case employs a different argument. Hwang and Liaw (2000) made the latest attempt and pointed out errors in previous attempts. However, they made errors, too. In this paper, we propose a unifying approach to study those models systematically (which also applies to some wide-sense nonblocking (WSNB) networks). We also propose a new routing algorithm, and use the unifying approach to derive a necessary and sufficient condition for WSNB.

Wide-sense nonblocking for symmetric or asymmetric 3-stage Clos networks under various routing strategies

Beneš established the notion of wide-sense nonblocking by constructing an example on the symmetric 3-stage Clos network under packing which requires less hardware compared to strict nonblocking. This has remained the only example of a wide-sense non-blocking 3-stage Clos network which is not strictly nonblocking. In this paper, we study packing as well as several other routing strategies which have been studied in the literature and proved that no other example exists for the symmetric 3-stage Clos network. We then extend the study to asymmetric 3-stage Clos network for the first time. In particular, we extend Beneš example to asymmetric 3-stage Clos network and show that these are the only two possible examples for the strategies under study.

Cyclic crossbar network for photonic switching

Feature Issue on Optical Interconnection Networks (OIN). The rectangular crossbar network is commonly used in switching networks because it has the advantages of easy connection-path rebuilding, wide-sense nonblocking, and no crossover in its interconnection lines. However, this kind of network has two major disadvantages: one is that it has nonzero differential loss, and the other is that its signal-to-noise ratio (SNR) is decreased by both the increase of the network dimension and the insertion loss of switches. Here the cyclic crossbar network structure is presented. The cyclic crossbar network is similar to the rectangular crossbar network. For both types of network, an N×N network is constructed by N columns, and each column consists of N switches. The major difference is that construction with N backslash lines and N slash lines is used for the cyclic crossbar network. For every backslash line to have its crosspoint on the right side, the network structure is designed into a circle shape. In this type of network, the differential loss is eliminated and SNR is independent on insertion loss of switches, but the original advantages are maintained.

Lower bounds for wide-sense nonblocking Clos network

The 3- stage Clos network is generally considered the most basic multistage interconnecting network (MIN). The nonblocking property of such network has been extensively studied in the past. However, there are only a few lower bound results regarding wide-sense nonblocking. We show that in the classical circuit switching environment, to guarantee wide-sense nonblocking for large r, 2n−1 center switches are necessary, where r is the number of input switches and n is the number of inlets of each input switch. For the multirate environment, we show that for large r, any 3-stage Clos network needs atleast 3n−2 center switches to guarantee wide-sense nonblocking. Our proof works even for the two-rate environment.