Two-dimensional Mesh Networks Research Articles

A novel heterogeneous congestion criterion for mesh-based networks-on-chip

In recent years, congestion in Networks-on-chip (NoC) has emerged as an important research topic due to the increasing number of processing cores. To solve the congestion, all the methods that have been proposed require a congestion criterion to detect whether a node is congested or not. All the congestion criteria that have been developed so far have similar behavior for all nodes in the network. In this paper, for the first time, a heterogeneous congestion criterion is proposed for a two-dimensional mesh network that is determined for each node based on its betweenness centrality. This criterion can be generalized to the other topology such as torus easily. This criterion is calculated before the network starts up and does not have any overhead in run time. Using this criterion will reduce the average latency of any congestion-aware method, such as congestion-aware routing algorithms. The evaluation section shows that the use of this criterion in three famous routing algorithms reduces the average latency up to 48% (21% on average for all algorithms and traffic patterns) in both real and synthetic traffics. In addition, the usage of this criterion reduces the power consumption in all simulation conditions because of reducing the average latency and lack of overhead. It is also shown at the end of the evaluation section that an increase in the network size will result in better performance of this criterion.

Programmable photonic signal processor chip for radiofrequency applications

Integrated microwave photonics, an emerging technology combining radio frequency (RF) engineering and integrated photonics, has great potential to be adopted for wideband analog processing applications. However, it has been a challenge to provide photonic integrated circuits with equal levels of function flexibility as compared with their electronic counterparts. Here, we introduce a disruptive approach to tackle this need, which is analogous to an electronic field-programmable gate array. We use a grid of tunable Mach–Zehnder couplers interconnected in a two-dimensional mesh network, each working as a photonic processing unit. Such a device is able to be programmed into many different circuit topologies and thereby provide a diversity of functions. This paper provides, to the best of our knowledge, the first ever demonstration of this concept and shows that a programmable chip with a free spectral range of 14 GHz enables RF filters featuring continuous, over-two-octave frequency coverage, i.e., 1.6–6 GHz, and variable passband shaping ranging from a 55 dB extinction notch filter to a 1.6 GHz bandwidth flat-top filter.

Adaptive Fault-Tolerant Routing in 2D Mesh with Cracky Rectangular Model

This paper mainly focuses on routing in two-dimensional mesh networks. We propose a novel faulty block model, which is cracky rectangular block, for fault-tolerant adaptive routing. All the faulty nodes and faulty links are surrounded in this type of block, which is a convex structure, in order to avoid routing livelock. Additionally, the model constructs the interior spanning forest for each block in order to keep in touch with the nodes inside of each block. The procedure for block construction is dynamically and totally distributed. The construction algorithm is simple and ease of implementation. And this is a fully adaptive block which will dynamically adjust its scale in accordance with the situation of networks, either the fault emergence or the fault recovery, without shutdown of the system. Based on this model, we also develop a distributed fault-tolerant routing algorithm. Then we give the formal proof for this algorithm to guarantee that messages will always reach their destinations if and only if the destination nodes keep connecting with these mesh networks. So the new model and routing algorithm maximize the availability of the nodes in networks. This is a noticeable overall improvement of fault tolerability of the system.

Fully adaptive routing algorithms and region‐based approaches for two‐dimensional and three‐dimensional networks‐on‐chip

Network congestion has negative impact on the performance of networks-on-chip (NoC). In traditional congestion-aware techniques, congestion is measured at a router level and delivered to other routers, either local or non-local. One of the contributions of this study is to show that performance can be improved if the congestion level is measured for a group of routers, called cluster, and propagated over the network, rather than considering the congestion level of a single router. The presented approach is discussed in both two-dimensional (2D) and three-dimensional (3D) mesh networks. To collect and propagate the congestion information of different clusters, a distributed approach is presented. The gathered information is utilised at routing units to deliver packets through the less congested regions. To distribute packets over the network without forming deadlock, routing algorithms should be carefully designed. The authors take advantage of fully adaptive routing algorithms, providing the maximum degree of adaptiveness for distributing packets. For 2D NoCs, a conventional fully adaptive routing algorithm, named dynamic XY (DyXY), is utilised. However, for 3D NoCs a fully adaptive routing algorithm is proposed and this method is called 3D-FAR. On top of each fully adaptive routing algorithm, a region-based approach is developed.

A New Worst-Case Throughput Bound for Oblivious Routing in Odd Radix Mesh Network

1/2 network capacity is often believed to be the limit of worst-case throughput for mesh networks. However, this letter provides a new worst-case throughput bound, which is higher than 1/2 network capacity, for odd radix two-dimensional mesh networks. In addition, we propose a routing algorithm called U2TURN that can achieve this worst-case throughput bound. U2TURN considers all routing paths with at most 2 turns and distributes the traffic loads uniformly in both X and Y dimensions. Theoretical analysis and simulation results show that U2TURN outperforms existing routing algorithms in worst-case throughput. Moreover, U2TURN achieves good average-throughput at the expense of approximately 1.5x minimal average hop count.

Combining stochastic geometry and statistical mechanics for the analysis and design of mesh networks

We consider a two-dimensional mesh network comprising several source-destination pairs, each communicating wirelessly in a multihop fashion. First, we introduce a novel transmission policy for multihop networks according to which all the buffering in the network is performed at source nodes while relays just have unit-sized buffers. We demonstrate that incorporating this buffering scheme in conjunction with minor amendments to the medium access control (MAC) layer yields several benefits such as keeping packet delays small and helping regulate the traffic flow in a completely distributed fashion. Second, we employ a novel combination of tools from stochastic geometry and statistical mechanics to characterize the throughput and end-to-end delay performances of multihop wireless networks for two different channel access mechanisms, Carrier Sense Multiple Access (CSMA) and ALOHA. Our study also offers valuable insights from a system design stand-point such as determining the optimum density of transmitters or the optimal number of hops along a flow that maximizes the system’s throughput performance. We corroborate our theoretical analyses via simulations.

The Implementation of a Low Cost Single-cycle On-chip Router Based on Multiple Virtual Output Queuing

Network-on-Chip (NoC) is becoming a popular solution for communication on System-on-Chips. A router is a major component of NoC which is responsible for handling the communication. Its architecture significantly impacts on the performance of NoC. In this paper, we propose a low latency router architecture based on virtual output queuing (VOQ). The number of pipeline stages of a packet transfer can be reduced to one stage, by using VOQ buffers and speculatively performing switch allocation and switch traversal in parallel. This paper also proposes a multiple VOQ architecture for which each input port maintains multiple queues for each output channel to improve the throughput of the router. We have implemented the proposed router on FPGA and evaluated in terms of communication latency, throughput and hardware amount. The experimental results show that in a 4 × 4 two-dimensional mesh network, the proposed multiple VOQ router reduces the communication latency by 25% and cost of area by 15.6% as compared to the look-ahead speculative virtual channel router.

Near-Optimal Worst-Case Throughput Routing for Two-Dimensional Mesh Networks

Minimizing latency and maximizing throughput are important goals in the design of routing algorithms for interconnection networks. Ideally, we would like a routing algorithm to (a) route packets using the minimal number of hops to reduce latency and preserve communication locality, (b) deliver good worst-case and average-case throughput and (c) enable low-complexity (and hence, low latency) router implementation. In this paper, we focus on routing algorithms for an important class of interconnection networks: two dimensional (2D) mesh networks. Existing routing algorithms for mesh networks fail to satisfy one or more of design goals mentioned above. Variously, the routing algorithms suffer from poor worst case throughput (ROMM [13], DOR [23]), poor latency due to increased packet hops (VALIANT [31]) or increased latency due to hardware complexity (minimaladaptive [7, 30]). The major contribution of this paper is the design of an oblivious routing algorithm - O1TURN - with provable near-optimal worst-case throughput, good average-case throughput, low design complexity and minimal number of network hops for 2D-mesh networks, thus satisfying all the stated design goals. O1TURN offers optimal worst-case throughput when the network radix (k in a kxk network) is even. When the network radix is odd, O1TURN is within a 1/k2 factor of optimal worst-case throughput. O1TURN achieves superior or comparable average-case throughput with global traffic as well as local traffic. For example, O1TURN achieves 18.8%, 0.7% and 13.6% higher average-case throughput than DOR, ROMM and VALIANT routing, respectively when averaged over one million random traffic patterns on an 8x8 network. Finally, we demonstrate that O1TURN is well suited for a partitioned router implementation that is of similar delay complexity as a simple dimension-ordered router. Our implementation incurs a marginal increase in switch arbitration delay that is completely hidden in pipelined routers as it is not on the clock-critical path.

On the design of efficient ATM routing schemes

In this paper we deal with the problem of designing virtual path layouts in ATM networks when the hop-count is given and the load has to be minimized. We first prove a lower bound for networks with arbitrary topology and arbitrary set of connection requests. This result is then applied to derive lower bounds for the following settings: (i) one-to-all (one node has to be connected to all other nodes of the network) in arbitrary networks; (ii) all-to-all (each node has to be connected to all other nodes in the network) in several classes of networks, including planar and k-separable networks and networks of bounded genus. We finally study the all-to-all setting on two-dimensional meshes and we design a virtual path layout for this problem. When the hop-count and the network degree are bounded by constants, our results show that the upper bounds proposed in this paper for the one-to-all problem in arbitrary networks and for the all-to-all problem in two-dimensional mesh networks are asymptotically optimal. Moreover, the general lower bound shows that the algorithm proposed in Gerstel (Ph.D. Thesis, Technion-Haifa, Israel, 1995) for the all-to-all problem in k-separable networks is also asymptotically optimal. The upper bound for mesh networks also shows that the lower bound presented in this paper for the all-to-all problem in planar networks is asymptotically tight.

Fault-tolerant wormhole routing in two-dimensional mesh networks with convex faults

Faulty blocks are expanded, by disabling nodes, to form rectangular faults in many existing works to facilitate the designing of deadlock-free routing schemes for meshes recently. In this paper, faulty blocks are diffused to be rectangular faults, which are composed of faulty and fault-diffused nodes. These rectangular faults are then shrunk, by recovering fault-diffused nodes, to form convex faults for reducing the number of nodes disabled. Simulation results show that up to 70% of the disabled nodes, which are needed to form rectangular faults, can be recovered if the number of faulty nodes is less than 10% of the total network nodes. Both non-adaptive and adaptive fault-tolerant routing algorithms are proposed to handle these resulted convex faults. The adaptive routing algorithm is enhanced from the non-adaptive counterpart by utilizing the virtual channels that are not used in the non-adaptive algorithm; hence, the number of virtual channels per physical channel used in the adaptive algorithm is the same to that used in the non-adaptive algorithm.

Planar-optical mesh-connected tree interconnects: a feasibility study

The mesh-connected tree is a two-dimensional interconnect topology that combines aspects of a conventional tree network and a two-dimensional nearest-neighbor mesh network. Because of its topological features, a mesh-connected tree has the potential to be implemented with planar optoelectronic interconnect concepts. We examine the feasibility of employing vertical-to-surface-transmissionelectro-photonic optical array switches together with planar micro-optical components for the future implementation of an optoelectronic mesh-connected tree interconnect.

Oceanographics

We consider a two-dimensional mesh network comprising several source-destination pairs, each communicating wirelessly in a multihop fashion. First, we introduce a novel transmission policy for multihop networks according to which all the buffering in the network is performed at source nodes while relays just have unit-sized buffers. We demonstrate that incorporating this buffering scheme in conjunction with minor amendments to the medium access control (MAC) layer yields several benefits such as keeping packet delays small and helping regulate the traffic flow in a completely distributed fashion. Second, we employ a novel combination of tools from stochastic geometry and statistical mechanics to characterize the throughput and end-to-end delay performances of multihop wireless networks for two different channel access mechanisms, Carrier Sense Multiple Access (CSMA) and ALOHA. Our study also offers valuable insights from a system design stand-point such as determining the optimum density of transmitters or the optimal number of hops along a flow that maximizes the system’s throughput performance. We corroborate our theoretical analyses via simulations.