A method to evaluate the a switching unit spatial extensibility of and network

Switching units and networks have been analyzed as extensible fabrics, mostly in terms of their scheduling algorithms. The traditional literature on switching extensibility has provided complexity theory only relating to the total numbers of inputs （or outputs） and exchange lines. This paper analyzes switching extensibility in terms of not only the scheduling algorithm and also the fabric itself. It is found that determining extensibility from soft complexity related to the number of inputs （or outputs） of the scheduling algorithm and the fabric extensibility in previous studies without quantization is a flawed conception. A method is thus proposed to express the spatial extensibility of a switching unit or network in terms of the connections of a switching resource and capacity. The method calculates parameter ES （the efficiency of switching） of an m x n switching unit and obtains two functions of the switching unit to describe spatial extensibility along with the number of unilateral inputs or outputs. It is found that the range of ES is （0, 1] and three types of switching unit and two types of crosspoint networks have ES = 1. ES is calculated for banyan, Clos, parallel packet, fully interconnected and recirculation switching networks. The ES value for the banyan switching network is larger than that for other networks, and switching networks are classified into three types that have absolute/linear/denied spatial extensibility according to the limES value. It is demonstrated that a switching network has the largest ES value when it contains only the five types of switching unit for which ES ---- 1. Finally, a group-switching-first self-routing banyan switching network with lower blocking probability and time delay is deduced, and the ES method is contrasted with two other methods of evaluating spatial extensibility in terms of their mathematical expressions and intuitive graphics, for the five types of switching network listed above.     

A new self-routing multicast network

In this paper, we propose a design for a new self-routing multicast network which can realize arbitrary multicast assignments between its inputs and outputs without any blocking. The network design uses a recursive decomposition approach and is based on the binary radix sorting concept. All functional components of the network are reverse banyan networks. Specifically, the new multicast network is recursively constructed by cascading a binary splitting network and two half-size multicast networks. The binary splitting network, in turn, consists of two recursively constructed reverse banyan networks. The first reverse banyan network serves as a scatter network and the second reverse banyan network serves as a quasisorting network. The advantage of this approach is to provide a way to self-route multicast assignments through the network and a possibility to reuse part of network to reduce the network cost. The new multicast network we design is compared favorably with the previously proposed multicast networks. It uses O(n log² n) logic gates, and has O(log² n) depth and O(log² n) routing time where the unit of time is a gate delay. By reusing part of the network, the feedback implementation of the network can further reduce the network cost to O(n log n)     

Algebraic analysis of the topological properties of a banyan network and its application in fault-tolerant switching networks

In this paper, we introduce abstract algebraic analysis of the topological structure of a banyan network, which has become the baseline for most switching networks. The analysis provides the following key results: (1) The switching elements of a switching stage are arranged in order, that is, each stage of a banyan network consists of a series of a cyclic group. (2) The links between switching stages implement a homomorphism relationship in terms of self-routing. Therefore, we can recover the misrouting of a detour fault link by providing adaptive self-routing. (3) The cyclic group of a stage is a subgroup of that of the next stage, so that every stage and its adjacent stage make up a factor group. Based on this analysis, we introduce a cyclic banyan network that is more reliable than other switching networks. We present mathematical analysis of the reliability of the switching network to allow quantitative comparison against other switching networks.     

Testing the dynamic full access property of a class of multistageinterconnection networks

The banyan network, and networks topologically equivalent to it, have recently been adopted as interconnection networks in multiprocessor systems. Often, a multiprocessor system is reconfigured when the banyan network becomes faulty. It is possible to avoid a complicated reconfiguration process as long as the faulty banyan network still possesses the dynamic full access (DFA) property. In this paper, we determine a necessary and sufficient condition for a faulty banyan network to possess the DFA property and design a test procedure based on the condition. The test procedure can be used to decompose a faulty banyan network into subsystems possessing the DFA property. We also evaluate the probability that a banyan network loses the DFA property, given the number of faulty switching elements. It is found that as long as faults do not occur in switching elements located in the first and last stages, this probability is very small, even when there are quite a few faulty switching elements     

高性能交换与调度仿真平台的设计与实现

仿真实验已成为交换结构和调度策略性能评价的重要手段,而目前存在的交换结构与调度策略的仿真软件在可继承性与可扩展性方面还存在缺陷.基于Crossbar交换结构,建立数学模型,引入系统级设计方法,采用面向对象技术,设计并实现了用于研究交换结构和调度策略的仿真平台——SPES(switching performance evaluation system).该平台集成了输入排队、输出排队、联合输入输出排队、联合输入交叉点排队等多种交换结构以及相应调度策略.设计上实现了业务流、交换结构和调度策略三者之间的分离,具有良好的可继承、可扩展特性.用户通过与仿真平台之间的简单交互,完成模块的添加与仿真环境参数的配置,在支持变长业务、区分服务质量模型和多交换平面仿真方面具有良好的特性.通过简单扩展。该平台还可以实现网络级性能仿真.最后给出了基于该平台,在CICQ(combined input and crosspoint queuing)交换结构下,对所提出的支持DiffServ模型的分布式调度策略DS(DiffServ supporting algorithm)在不同业务流模型下的性能测试结果,并与输入、输出排队交换结构进行了比较,展示了DS良好的性能,验证了仿真平台的合理性.     

基于时槽预定的加权公平调度策略

面向以太网的物理帧时槽交换(Ethernet-oriented physical frame timeslot switching,简称EPFTS)技术以用户域内使用最为广泛的以太网MAC(media access control)帧为运载对象、以定长物理层帧EPF(Ethernet-oriented physical frame)的传输时间为时槽,作为数据传输与交换的基础.针对EPFTS交换技术的特点,提出了一类新的调度策略--时槽加权的公平调度原则(timeslot-reservation based weighted fair scheduling,简称TRWFS),以解决EPFTS交换机中的业务数据调度问题.TRWFS以连接建立阶段各业务流预定的时槽数为基础,控制交换矩阵仲裁过程中各输入端向输出端请求转发信元的时刻,借用一般轮询算法的二相迭代机制来解决端口冲突问题.还给出了TRWFS的3种实现算法,表明TRWFS的实现复杂度可与一般Round-Robin调度算法相当.仿真实验结果进一步表明,即使在重负载条件下,TRWFS仍可有效保障EPFTS交换机各端口对上的预定时槽数,并在平均传输时延和吞吐率保障方面优于其他经典调度算法.     

The composite banyan network

A new multipath multistage interconnection network called the composite banyan network is proposed. The network incorporates both the banyan and the reverse banyan networks and is constructed by superimposing the two. The basic building blocks in the composite banyan network are 3×3 switching elements with log₂N stages. A major advantage of the composite banyan network over existing networks with 3×3 SEs is an efficient and fast control algorithm that sets up a path between any source and destination pair. Instead of complex numerical calculations, the network can easily generate a primary routing tag and alternate tags through simple binary operations. Also, the network has a lot of favorable features, including regularity, symmetry, and easy rerouting capability under faults and conflicts. It is shown that at least two totally disjoint paths exist between any source and destination pair, which increase the degree of fault-tolerance. A deterministic permutation routing algorithm is also developed for the 8×8 composite banyan network, Using a simple tabular method, it is shown that the algorithm always finds a set of conflict-free tags     

Algorithms for burst rescheduling in WDM optical burst switching networks

Wavelength division multiplexing (WDM) is a promising technology for realizing terabit networks. Optical burst switching (OBS) is a way to efficiently support bursty traffic on WDM-based optical Internet networks. In OBS networks, the control (header) and payload (data) components of a burst are sent separately with a time gap. The control packet first traverses the burst switching nodes and reserves suitable wavelengths on the links for the corresponding data burst by using a scheduling algorithm. Our work is motivated from the observation that the existing scheduling algorithms either have low computational complexity or high performance in terms of burst dropping probability, but not both simultaneously. Since the arrival of bursts is dynamic, it is highly desirable that the scheduling is done as quickly as possible. We develop scheduling algorithms which integrate the merits of both low computational complexity and high burst dropping performance. The key idea is to reschedule an existing burst by assigning a new wavelength to it keeping the burst arrival and leaving time unchanged in order to accommodate the new burst. We propose computationally simple rescheduling algorithms called on-demand burst rescheduling and aggressive burst rescheduling. The effectiveness of the proposed algorithms and the signaling overhead are studied through simulation experiments.     

一种基于输入队列的交换机快速会聚调度算法

随着网络带宽需求的增加,高性能交换机的地位日趋重要。交换机包括3个部分:(1)在输入端口保存到达此端口的信元的输入缓冲。(2)在输出端口保存将要发送的信元的输出缓冲。(3)调度输入信元到所需输出端口的调度模块。当由多个输入端口要求输出到同一输出端口的时候由此调度算法来裁决一个输入输出对。一般而言,交换机的性能很大一部分取决于这一调度算法的性能,但并不希望这一调度算法成为交换机性能的瓶颈。该文讨论了许多近年来常用的算法,在此基础上同时提出一种新的的调度算法。通过计算机模拟结果可以看出这种算法具有更高的效率,更快的会聚速度。     

A three-stage construction for multiconnection networks

Summary A multiconnection network of size N is a switching network with N inputs and N outputs which realizes multiconnections, i.e., connections between the N inputs and N outputs in such a way that every output is connected to exactly one input, but an input can be connected to an arbitrary number of outputs. That network is complete if it can realize all N ^N multiconnections. This structure generalizes the permutation network. We consider here the design of multiconnection networks by a three-stage Clos network using complete substitution networks as its building cells and we show that the resulting multiconnection network is complete if and only if the cells in the middle stage have size 2. Moreover, we describe the control algorithm for such a network. This leads to the design of cellular multiconnection networks of arbitrary size with a relatively simple control algorithm.     

互连网络拓扑等价的图分析法

提出了描述互连网络拓扑等价的图分析法。获得了全交叉网络与基准，逆基准，Ｏｍｅｇａ，ｆｌｉｐ，Ｓ＝Ｆ＝２ＳＷ榕树，简化数据变换等多级互连网络拓扑等价的逻辑名结构。阐明了用光学全交叉网络模拟实现上述网络的互连函数的原理及其多处理机，电信交换等领域的潜在应用。     

基于输入排队的高速交换调度算法研究

高速交换网络一般采用基于定长信元的交换结构,其性能决定于排队策略和信元调度算法.输入排队策略只有和一个有效的调度算法相结合,才能保证交换结构具有良好的吞吐率和时延等性能.主要阐述了基于VOQ的最大数量匹配算法,最大权重匹配算法,稳定结合算法,神经网络算法等输入排队调度算法,分别从技术特点,性能指标和实现复杂度等多个方面进行比较和分析.分析了分布式和集中式两大类调度算法的工作方式,并根据各类算法的特点提出,神经网络算法可以通过定义其优先级函数实现其余各类算法.     

Optimal Routing Algorithms for a Class of Cylindrical Banyan Multicomputers

The cylindrical banyan network is a variation of the classical banyan network in two ways: (1) each node is a processor with a switch, and (2) every pair of nodes at the two ends is merged. We present a routing algorithm for the cylindrical banyan network, and show it is optimal in terms of the path length. We also show that for the cylindrical banyan network containing L levels with 2^L processors at each level (i.e., containing L2^L processors in total), the worst case path length between any two nodes is 1.5L. We discuss a generalization of the cylindrical banyan network and an optimal routing algorithm for it. Our routing algorithms are distributed, and so can be executed locally at each processor.     

A Study of Permutation Networks: New Designs and Some Generalizations

Permutation networks have been used in the literature to model interprocessor and processor-memory interconnections in parallel computers. This paper introduces new permutation network designs and generalizes the notion of a permutation network to provide a more flexible model of such interconnections. The new designs are based concentrators and superconcentrators, and for n inputs they can be optimized to obtain self-routing permutation networks with O(n lg n) cost, O(lg n) depth, and O(lg²n) routing time. The main feature of these new network designs is that they do not require complex routing schemes such as Clos networks since they are inherently self-routing. Generalizations of these designs are also given to obtain permutation networks in which the numbers of inputs and outputs may be different, and/or the maximum number of parallel routes between inputs and outputs can be less than the number of inputs or outputs, or both. For n inputs, αn outputs, and O(n^ϵ) parallel routes, where 0 < α ≤ 1, 0 < ϵ < 1, these generalized designs can be optimized to have permutation networks with O(n) cost, O(lg n), depth, and O(lg²n) routing time. It is shown that the previously known designs, such as Clos networks, result in inferior realizations when compared with these new designs.     

Uniform minimal full-access networks

Minimal Full-Access (MFA) networks are the class of all interconnection networks for N = 2ⁿ inputs and outputs that require a minimum number of switching elements and provide full access capability. In this paper, MFA networks with 2 × 2 switching elements that use the same interconnection pattern between the stages are studied; such networks are called uniform MFA (UMFA) networks. Most of the known networks, including the Omega, the binary n-cube, and the regular (2, 2)-banyan, belong to this class. A graph-theoretic approach is used to study the class of UMFA networks, and a procedure is described to derive topologically nonequivalent networks from the Omega network. It is shown that the number of UMFA networks grow exponentially with N, and a lower bound of about 2^N/32 is obtained for N ⩾ 32. We also outline an extension of our methods to derive similar bounds for networks using k × k switches, for k ⩾ 3.     

On the complexity of computing and learning with multiplicative neural networks.

In a great variety of neuron models, neural inputs are combined using the summing operation. We introduce the concept of multiplicative neural networks that contain units that multiply their inputs instead of summing them and thus allow inputs to interact nonlinearly. The class of multiplicative neural networks comprises such widely known and well-studied network types as higher-order networks and product unit networks. We investigate the complexity of computing and learning for multiplicative neural networks. In particular, we derive upper and lower bounds on the Vapnik-Chervonenkis (VC) dimension and the pseudo-dimension for various types of networks with multiplicative units. As the most general case, we consider feedforward networks consisting of product and sigmoidal units, showing that their pseudo-dimension is bounded from above by a polynomial with the same order of magnitude as the currently best-known bound for purely sigmoidal networks. Moreover, we show that this bound holds even when the unit type, product or sigmoidal, may be learned. Crucial for these results are calculations of solution set components bounds for new network classes. As to lower bounds, we construct product unit networks of fixed depth with super-linear VC dimension. For sigmoidal networks of higher order, we establish polynomial bounds that, in contrast to previous results, do not involve any restriction of the network order. We further consider various classes of higher-order units, also known as sigma-pi units, that are characterized by connectivity constraints. In terms of these, we derive some asymptotically tight bounds. Multiplication plays an important role in both neural modeling of biological behavior and computing and learning with artificial neural networks. We briefly survey research in biology and in applications where multiplication is considered an essential computational element. The results we present here provide new tools for assessing the impact of multiplication on the computational power and the learning capabilities of neural networks.     

数据中心差异化时延满足率优化调度

光交换网络数据传输时根据数据性质不同,用户对时延要求也有所不同,如何在保证光交换调度效率的同时满足差异化时延需求,是决定网络性能的一个重要因素.目前针对光网络调度的研究主要基于逐个时隙或基于分组进行调度.前者没有考虑重配置开销的问题,无法处理大规模数据交换,后者忽略了不同延迟以及QoS保证的需要.为了解决数据中心光交换数据时延需求不同的问题,本文提出两种新的调度算法SDF (stringent delay first)和m-SDF (m-order stringent delay first),将不同数据包的差异化时延需求、配置顺序、重配置开销和加速比作为考虑因素,在流量调度时采用贪心策略,每次选择对时延最为敏感的数据包进行优先调度以满足时延需求.所提算法在保证投递率的前提下,能最大程度满足更多数据包的传输时延.仿真实验表明两个算法具有较高的时延满足率,证明了调度算法的有效性.     

一种支持变长分组的CIOQ交换结构

在分析了组合输入输出排队结构的基础上,对传统CIOQ(Combined Input—Output Queued)的输出队列进行扩展和在内部交换结构中采用并行传送的方式,实现了交换调度的分布式操作和内部无加速的CIOQ交换;又通过将输出队列的状态信息反压到输入端和在输出端采取基于整包调度的算法,实现了对变长分组的交换,减小了定长信元交换中分组切割和重组的开销。     

On ordered scheduling for optical burst switching

Optical burst switching (OBS) is a promising optical networking paradigm for efficient transport of bursty IP traffic over wavelength division multiplexing (WDM) optical Internet networks. In OBS, the header of a burst is sent in advance of the data burst to reserve a wavelength channel at each optical switching node along the path. The nodes use a scheduling algorithm to assign wavelengths to incoming bursts. Our work is motivated from the observation that existing scheduling algorithms assign a wavelength to a burst when its header arrives at the node. Thus, information about other bursts whose headers arrive later is not available when the scheduling decision is made. This leads to suboptimal scheduling decisions and unnecessary burst dropping. The key idea in our proposed algorithm, Ordered Scheduling, is to defer making the scheduling decision until just before the burst arrival in order to have full knowledge about other bursts. The effectiveness of the proposed algorithm is studied through simulation and the computational complexity and signalling overhead are analysed.