Logical topology design for linear and ring optical networks

The design of logical topologies in wavelength-routing multihop optical networks is a well-studied problem. We consider logical topology (LT) design over the popular ring and linear topologies. Our objective is the minimization of the electronic processing delay for the worst case traffic flow. For uniform traffic between nodes, this delay minimization corresponds to minimizing the number of hops on a shortest path between the farthest two nodes in the logical topology (the diameter of the logical topology). The simple structure of the physical topologies enables us to present a rigorous analysis of the problem. We present lower bounds for the achievable diameter wherever possible and propose practical logical topology design algorithms and corresponding upper bounds. We also present an application of the LT designs in the linear topology to the survivability of ring networks     

GEMNET: a generalized, shuffle-exchange-based, regular, scalable,modular, multihop, WDM lightwave network

GEMNET is a generalization of shuffle-exchange networks and it can represent a family of network structures (including ShuffleNet and de Bruijn graph) for an arbitrary number of nodes. GEMNET employs a regular interconnection graph with highly desirable properties such as small nodal degree, simple routing, small diameter, and growth capability (viz. scalability). GEMNET can serve as a logical (virtual), packet-switched, multihop topology which can be employed for constructing the next generation of lightwave networks using wavelength-division multiplexing (WDM). Various properties of GEMNET are studied     

Graph-theoretic analysis of structured peer-to-peer systems: routing distances and fault resilience

This paper examines graph-theoretic properties of existing peer-to-peer networks and proposes a new infrastructure based on optimal-diameter de Bruijn graphs. Since generalized de Bruijn graphs exhibit very short average distances and high resilience to node failure, they are well suited for distributed hash tables (DHTs). Using the example of Chord, CAN, and de Bruijn, we study the routing performance, graph expansion, clustering properties, and bisection width of each graph. Having confirmed that de Bruijn graphs offer the best diameter and highest connectivity among the existing peer-to-peer structures, we offer a very simple incremental building process that preserves optimal properties of de Bruijn graphs under uniform user joins/departures. We call the combined peer-to-peer architecture optimal diameter routing infrastructure.     

Design of logical topologies: a linear formulation forwavelength-routed optical networks with no wavelength changers

We consider the problem of constructing logical topologies over a wavelength-routed optical network with no wavelength changers. We present a general linear formulation which considers routing traffic demands, and routing and assigning wavelengths to lightpaths, as a combined optimization problem. The formulation also takes into account the maximum number of hops a lightpath is permitted to take, multiple logical links in the logical topology, multiple physical links in the physical topology, and symmetry/asymmetry restrictions in designing logical topologies. The objective is to minimize congestion. We show by examples how equality and inequality logical degree constraints have a bearing on congestion. We prove that, under certain conditions, having equality degree constraints with multiple edges allowed in the design of logical topologies does not affect congestion. This helps in reducing the dimensionality of the search space and hence speeds up the search for an optimal solution of the linear formulation. We solve the linear formulation for small examples and show the tradeoff between congestion, number of wavelengths available and the maximum number of hops a lightpath is allowed to take. For large networks, we solve the linear formulation by relaxing the integer constraints. We develop topology design algorithms for large networks based on rounding the solutions obtained by solving the relaxed problem. Since the whole problem is linearizable, the solution obtained by relaxation of the integer constraints yields a lower bound on congestion. This is useful in comparing the efficiency of our heuristic algorithms. Following Bienstock and Gunluk (1995), we introduce a cutting plane which helps in obtaining better lower bounds on congestion and also enables us to reduce the previously obtained upper bounds on congestion     

Design of logical topology with K‐connected constraints and channel assignment for multi‐radio wireless mesh networks

In multi‐radio multi‐channel wireless mesh networks, the design of logical topology is different from that in single channel wireless mesh networks. The same channel assignment algorithm used for various logical topologies will lead to diverse network performance. In this paper, we study the relationship between k ‐connected logical topology and the maximum number of assigned channels. Meanwhile, we analyze the issues affecting channel assignment performance, and present the lower and upper bounds of the maximum allowable number of assigned channels for k ‐connected logical topology. We then develop a k ‐connected logical topology design algorithm based on shortest disjoint paths and minimum interference disjoint paths for each node‐pair. In addition, we propose a static channel assignment algorithm according to minimum spanning tree search. Extensive simulations show that our proposed algorithm achieves higher throughput and lower end‐to‐end delay than fault tolerant topology control algorithms, which validates the involved trade‐off between path length and nodal interference. Moreover, numerical results demonstrate that our proposed channel assignment further improves network performance under the context of limited radio interfaces. Copyright © 2014 John Wiley & Sons, Ltd.     

一种计算缩减级型广义洗牌网络平均跳距的算法

简单介绍了广义洗牌网络（ＧＳＮ）的结构和分类,着重分析缩减级型ＧＳＮ的平均跳距性能,并提出一种计算平均跳距的算法     

Rearrangeable multihop lightwave networks: congestion minimization on regular topologies

We address the design of rearrangeable multihop lightwave networks having regular connectivity topology (such as Perfect Shuffle (PS), de Bruijn (dB) graph, GEneralized shuffleexchange Multihop NETwork (GEMNET) and Manhattan Street Network (MSN)). We propose a new formulation of the combined station assignment/flow routing problem with the congestion minimization objective. The formulation is applicable to any regular topology. We then develop a heuristic solution strategy based on tabu search. Given our objective, we want to assess the merit of a regular versus an arbitrary topology, as well as compare different regular topologies across several data instances. In terms of achieving small congestion (as obtained heuristically), the results suggest that with increased problem sizes, regular topologies become more attractive. In such cases the benefit of having less restricted arbitrary network topology might not be fully utilized. Equivalently, having regular topology for larger instances will still provide a large enough search space to (heuristically) obtain good throughput (i.e., small congestion). Moreover, such design will implicitly offer benefits associated with management and operations of regular topologies.     

The forwarding index of communication networks

A network is defined as an undirected graph and a routing which consists of a collection of simple paths connecting every pair of vertices in the graph. The forwarding index of a network is the maximum number of paths passing through any vertex in the graph. Thus it corresponds to the maximum amount of forwarding done by any node in a communication network with a fixed routing. For a given number of vertices, each having a given degree constraint, we consider the problem of finding networks that minimize the forwarding index. Forwarding indexes are calculated' for cube networks and generalized de Bruijn networks. General bounds are derived which show that de Bruijn networks are asymptotically optimal. Finally, efficient techniques for building large networks with small forwarding indexes out of given component networks are presented and analyzed.     

The Role of Network Topologies in the Optical Core of IP-over-WDM Networks with Static Wavelength Routing

In this paper, we present a performance analysis of network topologies for the optical core of IP-over-WDM networks with static wavelength routing. The performance analysis is focused on regular degree four topologies, and, for comparison purposes, degree three topologies are also considered. It is shown that the increase of the nodal degree from three (degree three topology with smallest diameter) to four (degree four topology with smallest diameter) improves the network performance if a larger number of wavelengths per link is available. However, the influence of wavelength interchange on the nodal degree gain is small. The performance of regular degree four topologies with smallest diameter is also compared with the performance of mesh–torus topologies (which are also degree four topologies), and it is shown that the blocking probability of degree four topologies with smallest diameter is about two orders of magnitude lower than the blocking probability of mesh–torus topologies. It is also presented a performance comparison of WDM-based networks with nodal degrees ranging from two to five and it is shown that the increase of the nodal degree from two to three leads to high nodal degree gains, while de increase of the nodal degree from four to five leads to low nodal degree gains. These results show that degree three and degree four topologies are very attractive for use in the optical core of IP-over-WDM networks.     

WDM-based local lightwave networks. II. Multihop systems

For pt.I see ibid., vol.6, no.3, p.12-27, 1992. A survey of wavelength-division-multiplexing (WDM)-based local lightwave networks is presented. The general characteristics of multihop systems are discussed, and various multihop approaches are reviewed. The construction of optimal structures based on minimizing the maximum link flow and optimizations based on minimization of the mean network packet delay are also reviewed. Regular topologies that have been studied as candidates for multihop lightwave networks, including the perfect shuffle, the de Bruijn graph, the toroid, and the hypercube, are discussed. Near-optimal node placement algorithms and shared-channel multihop systems are also discussed     

A new architecture and a new metric for lightwave networks

The notion of a logically routed network was developed to overcome the bottlenecks encountered during the design of a large purely optical network. In the last few years, researchers have proposed the use of torus. Perfect shuffle, hypercube, de Bruijn graph, Kautz graph, and Cayley graph as an overlay structure on top of a purely optical network. All these networks have regular structures. Although regular structures have many virtues, it is often difficult in a realistic setting to meet these stringent structural requirements. In this paper, we propose generalized multimesh (GM), a semiregular structure, as an alternate to the proposed architectures. In terms of simplicity of interconnection and routing, this architecture is comparable to the torus network. However, the new architecture exhibits significantly superior topological properties to the torus. For example, whereas a two-dimensional (2-D) torus with N nodes has a diameter of Θ(N^0.5), a generalized multimesh network with the same number of nodes and links has a diameter of Θ(N^0.25). In this paper, we also introduce a new metric, flow number, that can be used to evaluate topologies for optical networks. For optical networks, a topology with a smaller flow number is preferable, as it is an indicator of the number of wavelengths necessary for full connectivity. We show that the flow numbers of a 2-D torus, a multimesh, and a de Bruijn network, are Θ(N^1.5), Θ(N^1.25), and Θ(N log N), respectively, where N is the number of nodes in the network. The advantage of the generalized multimesh over the de Bruijn network lies in the bet that, unlike the de Bruijn network, this network can be constructed for any number of nodes and is incrementally expandable     

Design of logical topologies for wavelength-routed optical networks

The problem of designing a logical topology over a wavelength-routed all-optical network (AON) physical topology is studied. The physical topology consists of the nodes and fiber links in the network. On an AON physical topology, we can set up lightpaths between pairs of nodes, where a lightpath represents a direct optical connection without any intermediate electronics. The set of lightpaths along with the nodes constitutes the logical topology. For a given network physical topology and traffic pattern, our objective is to design the logical topology and the routing algorithm so as to minimize the network congestion while constraining the average delay seen by a source-destination pair and the amount of processing required at the nodes (degree of the logical topology). Ignoring the delay constraints can result in fairly convoluted logical topologies with very long delays. On the other hand, in all our examples, imposing it results in a minimal increase in congestion. While the number of wavelengths required to imbed the resulting logical topology on the physical all optical topology is also a constraint in general, we find that in many cases of interest this number can be quite small. We formulate the combined logical topology design and routing problem described above as a mixed integer linear programming problem which we then solve for a number of cases of a six-node network. This programming problem is split into two subproblems: logical topology design, and routing. We then compare the performance of several heuristic topology design algorithms against that of randomly generated topologies, as well as lower bounds     

Valiant load-balancing and regionalized routing scheme

Valiant load-balancing(VLB)routing scheme has drawbacks of logical full mesh,intermediate nodes(networks)and single application of topology.To address these,the authors propose a novel routing scheme called regionalized VLB(R-VLB).Based on ideas of VLB and regionalizing,R-VLB divides the nodes of backbone network into several regions whose topological structure is logical full mesh,and combines shortest-path routing scheme and VLB routing scheme.R-VLB also achieves logical local interconnection,non-central nodes(networks)and a wide range of application of topology.The relevant theoretical analysis and simulation results show that R-VLB achieve good throughput and failure performance close to that of VLB,and it even has better delay performance.R-VLB provides an idea for the application of VLB routing scheme.     

Efficient routing and wavelength assignment for reconfigurable WDMnetworks

Through the use of configurable wavelength-division-multiplexing (WDM) technology including tunable optical transceivers and frequency selective switches, next-generation WDM networks will allow multiple virtual topologies to be dynamically established on a given physical topology. For N node P port networks, we determine the number of wavelengths required to support all possible virtual topologies (PN lightpaths) on a bidirectional ring physical topology. We show that if shortest path routing is used, approximately N wavelengths are needed to map N lightpaths. We then present novel adaptive lightpath routing and wavelength assignment strategies that reduce the wavelength requirements to [(N/2)] working wavelengths per port for protected networks and [(N/3)] wavelengths in each direction per port for unprotected networks. We show that this reduced wavelength requirement is optimal in the sense that it is the minimum required to support the worst case logical topology. Furthermore, we prove that a significant number of logical topologies require this minimum number of wavelengths. We also develop joint routing and wavelength assignment strategies that not only minimize the number of wavelengths required to implement the worst case logical topologies but also reduce average wavelength requirements. Finally, methods for extending these routing and wavelength assignment results to general two-connected and three-connected physical topologies are presented     

A general approach for all-to-all routing in multihop WDM optical networks

WDM optical networks provide unprecedented high speed and reliability for message transfer among the nodes. All-to-all routing is a fundamental routing problem in such networks and has been well studied on single hop WDM networks. However, the number of wavelengths to realize all-to-all routing on the single hop model typically is very large. One way to reduce the number of wavelengths is to use k-hop routing, in which each routing path consists of k segments and each segment is assigned a different wavelength, where k usually is a small constant. Because of the complexity of design and analysis for such a routing problem, only few papers discussed and proposed all-to-all routing by k/spl ges/2 hops. However, the proposed algorithms are usually exceeding complicated even for ring topologies. Often, an ad hoc approach is employed to deal with each individual topology. In this paper we propose a generic method for all-to-all routing in multi-hop WDM networks, which aims to minimize the number of wavelengths. We illustrate the approach for several optical networks of commonly used topology, including lines, rings, tori, meshes, and complete binary trees. For each case an upper bound on the number of wavelengths is obtained. The results show that this approach produces clear routing paths, requires less wavelengths, and can easily incorporate load balancing. For simple topologies such as lines and rings, this approach easily produces the same bounds on the number of wavelengths that were hard-obtained previously. Moreover, this general approach provides a unified routing algorithm for any d-dimensional torus, which seems impossible to obtain by the previous approach.     

无线ad hoc网络多性能指标基本性能边界

在无线ad hoc网络中,基本性能边界对路由算法和资源分配协议的分析和评价具有重要的意义。对无线ad hoc网络多性能指标基本性能边界进行了研究,包括理论上最优的性能边界和实际可以得到的性能边界。提出了一种稳定状态(steady state)下的网络基本性能指标分析模型。该模型考虑了无线网络广播特性和无线信道干扰,可同时分析多个性能指标,包括：吞吐量、端到端延迟和能量消耗。基于该模型,针对ad hoc网络中最常见的多流—单/双中继拓扑分析基本性能指标,求解多目标优化问题得到基本性能边界。仿真结果验证了模型的准确性,均方根误差小于10-3量级。     

Enhancing peer-to-peer systems through redundancy

Peer-to-peer systems can share the computing resources and services by directly communicating within a widely distributed network. It is important that these systems can efficiently locate, in as few hops as possible, the node storing the desired data in a large system. Thus, it is worth consuming some extra storage to obtain better routing performance. In this paper, we propose redundant strategies to improve the routing performance and data availability on Chord and De Bruijn topologies. Hybrid-Chord combines multiple chord rings and successors, and Redundant D2B maintains successors, to improve the routing performance. The proposed systems can reduce the number of lookup hops significantly (by as much as 50%) compared to the original ones, and have better fault tolerance capabilities, with a small storage overhead     

Chord上拓扑不匹配的研究和改进

Chord系统中没有考虑到逻辑网络拓扑和物理网络拓扑不相匹配而导致的路由效率低下,由此提出了一种利用节点IP地址信息使节点得以聚类从而达到系统逻辑网络拓扑与物理网络拓扑在一定程度上的匹配,对Chord系统改进得到了TChord系统模型,通过仿真实验证明了TChord系统在路由延迟和覆盖网络路由跳数方面比Chord系统有明显的改进,从而效提高路由效率.