Adaptive deadlock-free worm-hole routing in hypercubes

The static network performance and dynamic communication performance of the Hierarchical Torus Network (HTN) using dimension-order routing algorithm have already been evaluated and shown to be superior to the performance of other interconnection networks. However, the assessment of the dynamic communication performance improvement of HTN by the efficient use of both the physical link and virtual channels has not yet been evaluated. This paper addresses three adaptive routing algorithms - link-selection, channel-selection, and a combination of link-selection and channel-selection - for the efficient use of physical links and virtual channels of an HTN to enhance dynamic communication performance. It also proves that the proposed adaptive routing algorithms are deadlock-free with 3 virtual channels. The dynamic communication performances of an HTN is evaluated by using dimension-order routing and proposed adaptive routing algorithms under various traffic patterns. It is found that the dynamic communication performance of an HTN using these adaptive routing is better than when the dimension-order routing is used, in terms of network throughput.

Oblivious routing algorithms use only locally avail¬able information at network nodes to forward traffic, and as such, a plausible choice for distributed implementations. It is a natural desire to quantify the performance penalty we pay for this distributedness. Recently, Racke has shown that for general undirected graphs the competitive ratio is only O(log n), that is, the maximum congestion caused by the oblivious algorithm is within a logarithmic factor of the best possible congestion. And while the performance penalty is larger for directed networks (Azar gives a O(vn) lower bound), experiments on many real-world topologies show that it usually remains under 2. These competitive measures, however, are of worst-case type, and therefore do not always give adequate characterization. The more different combinations of demands a routing algorithm can accommodate in the network without congestion, the better. Driven by this observation, in this paper we introduce a new competitive measure, the volumetric competitive ratio, as the measure of all admissible demands compared to the measure of demands routed without congestion. The main result of the paper is a general lower bound on the volumetric ratio; and we also show a directed graph with O(1) competitive ratio that exhibits O(n) volumetric ratio. Our numerical evaluations show that the competitivity of oblivious routing in terms of the new measure quickly vanishes even in relatively small common-place topologies.

The performance of interconnection networks can be improved drastically by using wormhole routing and virtual channel flow control. Adaptive routing strategies, which are superior to oblivious routing, supply a set of alternative output virtual channels associated with different physical links, when a message is routed. A selection function selects a free one from the set. In this paper, we have evaluated the performance of three adaptive wormhole routing algorithms with minimum paths in 3D mesh networks: Dynamic Routing proposed by Dally and Aoki, Negative Last routing developed by Glass and Ni based on their Turn Model and Full Dynamic Routing proposed by us based on Duato’s adaptive routing theory. Three different selection functions, namely Static, Random and Greedy have been compared.

Compressionless wormhole routing: an analysis for hypercube with virtual channels

The necklace hypercube network has recently been introduced as an attractive alternative to the well-known hypercube. Previous research on this network topology has mainly focused on topological properties and VLSI aspects of this network. In this paper, we propose some adaptive routing algorithm for the necklace hypercubes. The performance of necklace hypercubes using the proposed routing algorithm is then evaluated by means of simulation experiments. Experiments are realized under different working loads and for different network factors. Moreover, a comparison between the necklace hypercube and the well-known hypercube network is conducted. The comparison has been done considering implementation constraints including constant pin-out and constant bisection band-width constraints

The past few years have seen a rise in popularity of massively parallel architectures that use fat-trees as their interconnection networks. In this paper we formalize a parametric family of fat-trees, the k-ary n-trees, built with constant arity switches interconnected in a regular topology. A simple adaptive routing algorithm for k-ary n-trees sends each message to one of the nearest common ancestors of both source and destination, choosing the less loaded physical channels, and then reaches the destination following the unique available path. Through simulation on a 4-ary 4-tree with 256 nodes, we analyze some variants of the adaptive algorithm that utilize wormhole routing with 1, 2 and 4 virtual channels. The experimental results show that the uniform, bit reversal and transpose traffic patterns are very sensitive to the flow control strategy. In all these cases, the saturation points are between 35–40% of the network capacity with 1 virtual channel, 55–60% with 2 virtual channels and around 75% with 4 virtual channels. The complement traffic, a representative of the class of the congestion-free communication patterns, reaches an optimal performance, with a saturation point at 97% of the capacity for all flow control strategies. In this case virtual channels are of little help and the average network latency experiences an increase proportional to the number of virtual channels, due to the multiplexing of several packets onto the same physical links.

Turn-model is a classical method for designing partially adaptive routing algorithms without virtual channels, and can also be the basis of fully adaptive routing algorithms. We propose a novel scheme, Selective Extension of Routing Algorithms based on turn model (SERA), which alleviates restrictions on turn and path selections if possible without adding any new buffers or virtual channels. SERA can improve adaptivity of the original routing algorithms, and maintain the deadlock-free property. Thus, SERA is an important extension of the previous turn model theory. To present the effectiveness of SERA in adaptive algorithms, we redesign two existing routing algorithms, Odd-Even and LEAR. Simulation results show that the SERA scheme achieves an average delay reduction of 6% compared to the original routing algorithms.

Adaptive routing is widely regarded as a promising approach to improving interconnection network performance. Many designers of adaptive routing algorithms have used synthetic communication patterns, such as uniform and transpose traffic, to compare the performance of various adaptive routing algorithms with each other and with oblivious routing. These comparisons have shown that the average message latency is usually lower with adaptive routing. On the other hand, when a parallel program is executed on a multiprocessor the goal is to reduce the total execution time. We explain why improving the average message latency of a routing algorithm does not necessarily lead to a lower execution time for real applications. We support this observation by reporting simulation results for both adaptive and oblivious routing using communication derived from real applications. Specifically, we report the performance of various routing algorithms for directed acyclic graphs (DAGs) derived from the Cholesky factorization of sparse matrices. Our results show that there is little correlation between average message latency and the total execution time of a parallel program. Hence, average message latency does not seem to be a useful measure of the performance of a routing algorithm. This strongly suggests that current comparisons of routing algorithms do not provide a reliable indication of the performance improvements to be realized by executing programs on a multiprocessor with such a routing algorithm. We interpret these results and suggest several alternatives for further research.

A Comparison of Router Architectures for Virtual Cut-Through and Wormhole Switching in a NOW Environment

Fault tolerant routing algorithms, are a key concern in on-chip communication. This paper examines fault tolerant communication algorithms for use in network-on-chip (NoC). We propose an improved wormhole-switched routing algorithm in 2-dimensional mesh based on f-cube3 algorithm to decrease message latency. The existing key concept is using numbers of virtual channels (VC) via a physical link. This paper proposes some improvements to make use of VCs while the numbers of them are fixed. We show that when a message is not blocked by fault, all VCs could be used; f-cube3, however, uses only one of the VCs. Furthermore, the strength of the improved algorithm is demonstrated by comparing results of simulations in both f-cube3 and the improved algorithm if-cube3.

We present a model for designing wormhole routing algorithms that are deadlock free, livelock free, minimal or nonminimal, and maximally adaptive. A unique feature of this model is that it is not based on adding physical or virtual channels to network topologies (though it can be applied to networks with extra channels). Instead, the model is based on analyzing the directions in which packets can turn in a network and the cycles that the turns can form. Prohibiting just enough turns to break all of the cycles produces routing algorithms that are deadlock free, livelock free, minimal or nonminimal, and maximally adaptive for the network. In this paper, we focus on the two most common network topologies for wormhole routing,n-dimensional mesh, just a quarter of the turns must be prohibited to prevent deadlock. The remaining three quarters of the turns permit partial adaptiveness in routing. Partially adaptive routing algorithms are described for 2D meshes,n-dimensional meshes,k-aryn-cubes, and hypercubes. Simulations of partially adaptive and nonadaptive routing algorithms for 2D meshes and hypercubes show that which algorithm has the lowest latencies and highest sustainable throughput depends on the pattern of message traffic. For nonuniform traffic, partially adaptive routing algorithms perform better than non-adaptive ones.

Direct network performance is affected by different design parameters which include number of virtual channels, number of ports, routing algorithm, switching technique, deadlock handling technique, packet size, and buffer size. Another factor that affects network performance is the traffic pattern. In this thesis, we study the effect of hotspot traffic on system performance. Specifically, we study the effect of hotspot factor, hotspot number, and hot spot location on the performance of mesh-based networks. Simulations are run on two network topologies, both the mesh and torus. We pay more attention to meshes because they are widely used in commercial machines. Comparisons between oblivious wormhole switching and chaotic packet switching are reported. Overall packet switching proved to be more efficient in terms of throughput when compared to wormhole switching. In the case of uniform random traffic, it is shown that the differences between chaotic and oblivious routing are indistinguishable. Networks with low number of hotspots show better performance. As the number of hotspots increases network latency tends to increase. It is shown that when the hotspot factor increases, performance of packet switching is better than that of wormhole switching. It is also shown that the location of hotspots affects network performance particularly with the oblivious routers since their achieved latencies proved to be more vulnerable to changes in the hotspot location. It is also shown that the smaller the size of the network the earlier network saturation occurs. Further, it is shown that the chaos router’s adaptivity is useful in this case. Finally, for tori, performance is not greatly affected by hotspot presence. This is mostly due to the symmetric nature of tori.

3-Dimensional Networks-on-Chips (3D NoCs) are proposed as the next generation interconnect infrastructure for multi/many core embedded systems due to the high performance characteristics and scalability. However the heat and thermal issues in 3D NoCs are critical. Reducing the vertical links between dies becomes can be one of the proper solutions, but the 3D NoC system performance can be harmed due to the less number of possible vertical links. In order to find the best trade-off point between the vertical links reduction and 3D NoC performance, in this paper, we demonstrate a dynamic quadrant partitioning (DQP) adaptive routing algorithm for 3D NoCs with irregular reduced vertical link density topologies, which can improve the system performance (latency max. 10.9% and energy max. 24.1%) in comparison to deterministic routing algorithm with the same vertical link number configurations. Also our DQP routing algorithm can maintain the system performance in comparison to full vertical link connection running dimension-order deterministic routing algorithm (ZXY) by reducing 40% vertical links number. The comparison results are demonstrated with different benchmark applications and random generated task graphs.

In this paper, we present an adaptive fault-tolerant wormhole routing algorithm for hypercubes by using 4 virtual networks. Each node is identified to be in one of the four states: safe, ordinarily unsafe, strongly unsafe, and faulty. Based on the concept of unsafe nodes, we design a routing algorithm for hypercubes that can tolerate at least n-1 faulty nodes and can route a message via a path of length no more than the Hamming distance between the source and destination plus four. Previous algorithms which achieve the same fault tolerant ability need at least 5 virtual channels per physical channel. Simulation results show that our algorithm outperforms previous known results.

Communication delay in hypercubes in the presence of bit-reversal traffic