Rearrangeable Nonblocking Research Articles

Making Path Selection Bright: A Routing Algorithm for On-Chip Benes Networks

Making Path Selection Bright: A Routing Algorithm for On-Chip Benes Networks

Rearrangeable Nonblocking Conditions for Four Elastic Optical Data Center Networks

Four variants of elastic optical data center network (DCN) architectures based on optical circuit switching were proposed in an earlier study. The necessary and sufficient values of frequency slot units (FSUs) per fiber required for these four DCNs in the sense of there being strictly nonblocking (SNB) were derived, but no results in the sense of being rearrangeable nonblocking (RNB) were presented. In reality, only limited bandwidths are available, and reducing the value of FSUs per fiber has become a critical task to realize nonblocking optical DCN architectures in practice. In this paper, we derive the sufficient value of FSUs per fiber required for the four DCNs to be RNB by two multigraph approaches. Our results show that the proposed RNB conditions in terms of FSUs per fiber for a certain two of the four DCNs reduce their SNB results down to at least half for most cases, and even down to one-third.

Rearrangeable and Repackable S-W-S Elastic Optical Networks for Connections with Limited Bandwidths

Elastic optical networks flexibly allocate bandwidth to a connection for improving utilization efficiency. The paper considers an optical node architecture that is similar to a three-stage Clos network for elastic optical networks. The architecture, which employs space switching in the first and the third stages and wavelength switching in the second stage, is called an S-W-S switching fabric. In this paper, we propose a graph-theoretic approach and different routing algorithms to derive the sufficient conditions under which an S-W-S switching fabric will be rearrangeable nonblocking and repackable nonblocking. The proposed rearrangeable and repackable nonblocking S-W-S switching fabrics for connections with limited bandwidths consume around half the number of middle wavelength switches compared to strictly nonblocking S-W-S switching fabrics.

Rearrangeable W-S-W Elastic Optical Networks Generated by Graph Approaches: erratum

In elastic optical networks, a connection uses different spectrum widths that spread over adjacent frequency slot units (FSUs) to improve utilization efficiency. A three-stage wavelength-space-wavelength (W-S-W) optical node architecture for elastic optical networks employs wavelength switching in the first and third stages and space switching in the second stage. This paper considers twoW-S-Warchitectures, calledWSW1andWSW2networks. In an earlier study, a matrix decomposition approach was used to derive a condition that was sufficient for rearrangeable nonblocking (RNB), but only for a WSW1 network with a limited number of connection rates. In this paper, instead of using a matrix decomposition approach, we use a graph approach to derive the same result. Furthermore, we adopt different graph approaches to derive two sufficient conditions, which benefit limited connection rates and limited input/output fibers of an RNB WSW1 (or WSW2) network. Specifically, the former is better than the latter if the number of connection rates is less than the minimum ceiling value of half the number of 1) input/output switches and 2) FSUs in each input and output fiber, and vice versa if the number of input/output switches is less than the minimum value of 1) twice the maximum FSUs occupied by a single connection and 2) FSUs in each input and output fiber. Note that limited input/output switches lead to limited input/output fibers. The graph approaches proposed in this paper can be applied to various other elastic optical networks for further study

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.

Compact InGaAsP/InP nonblocking 4 × 4 trench-coupler-based Mach-Zehnder photonic switch fabric.

The existing photonic switch matrices usually show the drawbacks of either a large footprint or high cross talk. Here, we propose a compact InGaAsP/InP rearrangeable nonblocking 4×4 photonic switch fabric based on 2×2 Mach-Zehnder interferometer (MZI) switch elements in a Benes architecture. Each switch element consists of two frustrated total internal reflection (TIR) couplers and TIR mirrors serving as 90° waveguide bends, forming the square layout configuration of the 2×2 MZI switches. We investigate the design parameters of the switch element and 4×4 photonic switch matrix by using FDTD and transfer matrix methods, respectively. Our analysis results show that the proposed device exhibits an ultracompact chip size of ∼340 μm×120 μm, the minimum cross talk of -23 dB in the 1.5∼1.6 μm wavelength range, the total insertion loss of ∼3.9 dB, the low electrical energy of ∼0.4 pJ/bit, and an operation speed up to 50GHz. Experimentally, we can demonstrate the feasibility of fabricating 2×2 MZI switches and an operational low-loss trench-coupler. The enabling component of the 2×2 MZI switch can scale its pattern in the 2D directions. This as-formed compact 4×4 switch fabric can be potentially applied in large-scale InP-based photonic integrated circuits.

Nonblocking Multirate 2-Stage Networks

A 2-stage network is the most compact multistage interconnection network (MIN) for interconnecting small switches to form a large one. For larger networks, the switches in each stage can be replaced with 2-stage networks to reduce crosspoint cost. The 2-stage network preserves only conditional nonblockingness, while a multirate 2-stage network preserves nonblockingness. Multirate MINs have been exploited in many prior works, but multirate 2-stage networks have not previously been studied. In this letter, we prove the necessary and sufficient conditions for strictly nonblocking, rearrangeable nonblocking, and re-packable nonblocking multirate 2-stage networks. The results can be directly applied to the architecture design of elastic optical networks which allocate a flexible use of the spectrum to each connection, as each space switch is replaced with a bandwidth-variable waveband-converting switch, which has full-range conversion capability.

New Class of Rearrangeable Nonblocking Multicast Free-Space Optical Switches

In this paper, we propose N × N rearrangeable nonblocking multicast free-space optical switches. Our design exploits nonmovable tri-state switching elements (T-SEs) that support signal splitting and switching simultaneously and seamlessly, and thus, separate splitting stages used in the conventional multicast switches are not needed. It follows that the propagation loss that may be encountered by an optical beam passing through a splitting stage followed by a crossbar (e.g., splitter-and-delivery-based switches) can be avoided in the proposed switch, since the beam passes through only a single stage. The proposed switch exhibits an optimal hardware complexity, as it requires only N(N + 1) /2 T-SEs. The switch is analyzed and compared to existing optical multicast switches in terms of hardware complexity, power loss, and cost. Comparison results show that the proposed switch provides multicast capability with a lower hardware complexity and a comparable performance. Cost analysis shows that for N = 4, the overall cost of the new design is lower than that of existing strictly nonblocking switches, even if the T-SE is 3.5 to 10 times the cost of typical microelectromechanical systems mirrors. In addition, we present a simple routing algorithm that systematically establishes connections over the new switch.

Nonblocking 4×4 silicon electro-optic switch matrix with push–pull drive

A compact rearrangeable nonblocking 4×4 silicon electro-optic switch matrix based on a Spanke-Beneš network is proposed and fabricated by a 0.18 μm standard commercial complementary metal-oxide semiconductor line. By respectively modulating the two modulation arms with a push-pull drive, a cross talk (CT) of less than -18 dB is obtained for the switching element with 150-μm-long modulation arms. The total steady-state power consumption of the switch matrix ranges from 4.46 to 35.92 mW for different routing states. The CT values of the routing state with the minimum and maximum power consumptions are less than -19 dB and less than -12 dB, respectively.

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.

Rearrangeable Nonblocking Optical Interconnection Network Fabrics With Crosstalk Constraints

In this paper, we studied the necessary and sufficient conditions for Banyan-type networks, which are rearrangeable nonblocking (RNB) by considering all possible degrees of crosstalk constraints. To the best of our knowledge, this paper is the first one to propose a comprehensive solution that takes into account of all the possible crosstalk constraints for optical interconnection network fabrics. Therefore, the necessary and sufficient RNB conditions for optical interconnection networks under various crosstalk constraints are defined completely. Moreover, we found the conditions are independent from the degree of crosstalk constraint. It means the number of needed planes will not increase due to a stricter constraint by allowing a lower degree of crosstalk unless it goes down to zero crosstalk. It also signifies that a much stricter degree of crosstalk constraint could be imposed without changing the hardware fabrics. These conditions provide the useful tips for a cost-effective design of such optical interconnection networks.

ALGORITHM-HARDWARE CODESIGN OF A FAST PARALLEL ROUTING ARCHITECTURE FOR CLOS NETWORKS

Clos networks are an important class of switching networks due to their modular structure and much lower cost compared with crossbars. For routing I/O permutations of Clos networks, sequential routing algorithms are too slow, and all known parallel algorithms are not practical. We present the algorithm-hardware codesign of a unified fast parallel routing architecture called distributed pipeline routing (DPR) architecture for rearrangeable nonblocking and strictly nonblocking Clos networks. The DPR architecture uses a linear interconnection structure and processing elements that performs only shift and logic AND operations. We show that a DPR architecture can route any permutation in rearrangeable nonblocking and strictly nonblocking Clos networks in [Formula: see text] time. The same architecture can be used to carry out control of any group of connection/disconnection requests for strictly nonblocking Clos networks in [Formula: see text] time. Several speeding-up techniques are also presented. This architecture is designed for Clos-based packet and circuit switches of practical sizes.

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.

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.

Rearrangeable Nonblocking 8×8 Matrix Optical Switches Based on Extended Banyan Network

Based on the CROSSBAR network (CN) and the BANYAN network (BN), two new rearrangeable nonblocking constructions of extended BANYAN network (EBN) are proposed for implementing 8×8 optical matrix switch. The interconnection characteristics of these two types of rearrangeable nonblocking EBN were studied, and the logic program for driving switching units was provided. The calculated insertion loss was 3.3 dB for 8×8 optical matrix switch. Silica waveguide 8×8 matrix optical switch was designed and fabricated according to the calculated results. The silica waveguide propagation loss of 0.1dB/cm and waveguide-fiber coupling loss of 0.5dB/point were measured. With the fabricated 8×8 matrix optical switch, optical insertion loss of 4.6 dB, cross-talk of -38 dB, polarization dependent loss of 0.4 dB, averaged switching power of 1.6 W, and switching time of 1 ms were achieved. A basic agreement between experimental results and theoretical calculated values was achieved.

Demonstration for rearrangeable nonblocking 8×8 matrix optical switches based on extended banyan networks

Based on the CROSSBAR network (CN) and the BANYAN network (BN), two new rearrangeable nonblocking constructions of extended BANYAN network (EBN) were proposed for implementing 8x8 optical matrix switch. The interconnection characteristics of these two types of rearrangeable nonblocking EBN were studied, and the logic program for driving switching units was provided. The calculated insertion loss is 3.3 dB for 8x8 optical matrix switch. Silica waveguide 8x8 matrix optical switch was designed and fabricated according to the calculated results. The silica waveguide propagation loss of 0.1dB/cm and waveguide-fiber coupling loss of 0.5dB/point were measured. With the fabricated 8x8 matrix optical switch, optical insertion loss of 4.6 dB, cross-talk of -38 dB, polarization dependent loss of 0.4 dB, averaged switching power of 1.6 W, and switching time of 1 ms were obtained. A basic agreement between experimental results and theoretical calculated values was achieved.

Rearrangeable Nonblocking 8×8 Matrix Optical Switch based on Silica Waveguides and Extended Banyan Network

Based on the CROSSBAR network (CN) and the BANYAN network (BN), two new rearrangeable nonblocking constructions of extended BANYAN network (EBN) were proposed for implementing 8×8 optical matrix switch. The interconnection characteristics of these two types of rearrangeable nonblocking EBN were studied, and the driver logic program of switching units was provided. The calculated insertion loss is 3.3 dB for 8×8 optical matrix switch. Silica waveguide 8×8 matrix optical switch was designed and fabricated according to the calculated results. The silica waveguide propagation loss of 0.1dB/cm and waveguide- fiber coupling loss of 0.5dB/point were measured out. With the fabricated 8×8 matrix optical switch, optical insertion loss of 4.6 dB, cross-talk of -38 dB, polarization dependent loss of 0.4 dB, averaged switching power of 1.6 W, and switching time of 1 ms were achieved. A basic agreement between experimental results and theoretical calculated values was achieved.

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.

Design of Optical Rearrangeable Nonblocking MINs Under Various Crosstalk Constraints

Optical interconnection networks suffer from the intrinsic crosstalk problem that should be overcome to make them work properly. Vertical stacking of optical banyan networks is a novel scheme for constructing nonblocking optical multistage interconnection networks (MINs). Rearrangeable nonblocking optical MINs are feasible since they have lower complexity than their strictly nonblocking counterparts. In this paper, we determine the sufficient condition for these MINs to be rearrangeable nonblocking under various crosstalk constraints. We show how the crosstalk constraint affects the design of rearrangeable nonblocking MINs and demonstrate that these networks can tolerate a stricter crosstalk constraint without increasing their hardware complexity significantly. The results in the paper will be useful in designing optical MINs with reasonable hardware cost and crosstalk level.

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.