Routing and wavelength assignment in optical networks from edgedisjoint path algorithms

Routing and wavelength assignment (RWA) problems in wavelength-routed optical networks are typically solved using a combination of integer programming and graph coloring. Such techniques are complex and make extensive use of heuristics. We explore an alternative solution technique in the well-known maximum edge disjoint paths (EDP) problem which can be naturally adapted to the RWA problem. Maximum EDP is NP-hard, but now it is known that simple greedy algorithms for it are as good as any of the more complex heuristic solutions. In this paper we investigate the performance of a simple greedy maximum edge disjoint paths algorithm applied to the RWA problem and compare it with a previously known solution method     

A new approach for routing and wavelength assignment for permanent and reliable wavelength paths in wide all-optical WDM networks

This article proposes a new approach for routing and wavelength assignment (RWA) for permanent and reliable wavelength paths (WP) in wide all-optical WDM networks with wavelength continuity constraint. Given a number of available wavelengths on each optical fiber, for each simple link failure of the network, we seek to maximize the number of satisfied requests for connections. This is known as RWAP problem. In our algorithm, called RWA with Minimum Loaded Link for Permanent and Reliable wavelength paths (MLL-PR), routing is based on the search for the optimal path while trying to minimize the maximum load on the links of the network in order to minimize the maximum link capacity and then minimize the number of dropped lightpaths after any link failure. The wavelength assignment is based on a graph coloring method using tabu-search. A series of experiments using two well-known networks (ARPANET and NSFNET) have been carried out in order to evaluate the performance of our approach, in terms of the number of blocked demands, for different failure scenarios. Generally, our results are better than those provided by the current solving approaches taken as reference.

Dynamic routing and wavelength assignment with optical bypass using ring embeddings

We consider routing and wavelength assignment in ring, torus, and tree topologies with the twin objectives of minimizing wavelength usage and maximizing optical bypass. The P-port dynamic traffic assumption is used, which allows each node to send and receive at most P calls. For rings we show that PN/4 wavelengths are necessary and sufficient, and provide a four-hub ring architecture that requires only half of these wavelengths to be locally processed. We extend this approach to develop RWA and bypass algorithms for both tori and trees by embedding virtual rings within these topologies and applying the ring algorithms. For an R×C torus, we embed R+C rings onto the torus and provide an approach to RWA and banding based on solving disjoint RWA/banding problems for each ring. Our RWA algorithm is more wavelength efficient than any currently known algorithm and uses the minimum number of wavelengths for R≥2C. Our subsequent banding algorithm allows half of these wavelengths to bypass all but 4R hub nodes. Finally, we give a RWA for trees that embeds a single virtual ring and uses the ring to obtain a RWA that requires no more than PN/2 total wavelengths; this figure is shown to be optimal for balanced binary trees. A banding algorithm follows that allows half these wavelengths to bypass all non-hub nodes.     

Dynamic Establishment of Segmented Protection Paths in Single and Multi-Fiber WDM Mesh Networks

Wavelength division multiplexed (WDM) networks are matured to provide, scalable data centric infrastructure, capable of delivering flexible, value added, high speed and high bandwidth services directly from the optical (WDM) layer. But, providing fault-tolerance at an acceptable level of overhead in these networks has become a critical problem. This is due to the size of the current and future networks and diverse quality of service (QoS) requirements for multimedia and mission critical applications. Several distributed real-time applications require communication services with fault-tolerance apart from guaranteed timeliness at acceptable levels of overhead. Several methods exist in the literature which attempt to guarantee recovery in a timely and resource efficient manner. These methods are centered around a priori reservation of network resources called spare resources along a protection path. This protection path is usually routed from source to destination along a totally link disjoint path from primary path. This paper considers the problem of routing and wavelength assignment (RWA) in wavelength routed WDM optical networks. In particular, we propose an efficient algorithm to select routes and wavelengths to establish dependable connections (D-connections), called segmented protection paths. Our algorithm does not insist on the existence of totally disjoint paths to provide full protection. We present experimental results which suggest that our scheme is attractive enough in terms of average call acceptance ratio, spare wavelength utilization, and number of requests that can be satisfied for a given number of wavelengths assuming that the requests come one at time, and wavelengths are assigned according to fixed ordering. Furthermore, the results suggest that our scheme is practically applicable for medium and large sized networks, which improves number of requests that can be satisfied and helps in providing better QoS guarantees such as bounded failure recovery time and propagation delays without any compromise on the level of fault-tolerance for a given number of wavelengths and fibers. We conduct extensive simulation experiments to evaluate the effectiveness of the proposed scheme on different networks and compare with existing methods.This work was supported by the Department of Science and Technology, New Delhi, India. An earlier version of this paper was presented at Opticomm 2002 conference, July 29-August 2, Boston, USA.     

Restoration performance study of k-shortest disjoint paths in WDM optical networks

Many researchers have proposed restoration techniques incorporating the concept of k-shortest disjoint paths in survivable WDM (Wavelength Division Multiplexing) optical networks, but without considering network performance and network costs simultaneously. In this paper we need to carefully look into how well the concept of shortest disjoint paths is incorporated for given objective functions. Seven objective functions and four algorithms are presented to evaluate the concept of k-shortest disjoint paths for the design of a robust WDM optical network. A case study based on simulation experiments is conducted to illustrate the application and efficiency of k-shortest disjoint paths in terms of following objective goals: minimal wavelengths, minimal wavelength link distance, minimal wavelength mileage costs, even distribution of traffic flows, average restoration time of backup lightpaths, and physical topology constraints. Sungwoo Takis an assistant professor in the Department of Computer Science and Engineering at Pusan National University. He is also a research member at Research Institute of Computer Information and Communication at Pusan National University. He received a Ph.D. degree in Computer Science from the University of Missouri Kansas City. He has served as a TPC member for the IEEE ICCCN (International Conference on Computer Communications and Networks) since 2004. His research interests include Computer Networks, Wireless Networks, Software Architecture, WDM Optical Networks, Real-time Systems, and SoC (System on Chips) based Communication Chip Design. E. K. Park is a Professor of Computer Science at the University of Missouri at Kansas City. He received a Ph.D. degree in Computer Science from the Northwestern University. His research interests include software engineering, software architectures, software agents, distributed systems, object-oriented methodology, software tolerance and reliability, computer networks and management, optical networks, database/data mining, and information/knowledge management.     

适用于波长交换光网络（WSON）的波长旋转图模型设计

将网络虚拓扑链路及关联波长均匀分布到旋转球体的表面,建立了新型的波长交换光网络(WSON)的波长旋转图模型,并基于旋转图模型提出了路由波长分配(RWA)新策略及算法.仿真结果表明,每条链路的总波长数分别为4和8时,新策略算法的阻塞率平均降低5.03%和9.71%,资源利用率平均提高3.3%和1.54%.该模型用于解决具有波长转换能力的RWA问题效果明显.     

Graph-theoretic construction of low-density parity-check codes

This article presents a graph-theoretic method for constructing low-density parity-check (LDPC) codes from connected graphs without the requirement of large girth. This method is based on finding a set of paths in a connected graph, which satisfies the constraint that any two paths in the set are either disjoint or cross each other at one and only one vertex. Two trellis-based algorithms for finding these paths are devised. Good LDPC codes of practical lengths are constructed and they perform well with iterative decoding.     

Heuristic and Hybrid Methods for Solving Optimal Multiple Multicast Problem on WDM Ring Network

The Optimal Multiple Multicast Problem (OMMP) on wavelength division multiplexing (WDM) ring networks without wavelength conversion is considered in this paper. When the physical network and the set of multicast requests are given, OMMP is the problem that selects a suitable path (or paths) and wavelength (or wavelengths) among the many possible choices for each multicast request such that not any pair of paths using the same wavelength pass through the same link. In this paper, a formulation of OMMP is given; this problem is NP-hard since the famous RWA problem which has been proved NP-hard is a special case of OMMP. In this paper, the OMMP is divided into two subproblems: path routing and wavelength assignment subproblems. For each subproblem, two heuristic algorithms are proposed to solve it. Moreover, a hybrid method which combines heuristic and simulated annealing algorithm is proposed to find the near optimal solution. Experimental results indicate that these algorithms are efficient.     

Solving the routing and wavelength assignment problem in WDM networks for future planning - [Topics in optical communications]

In this article we define and analyze the routing and wavelength assignment problem by applying a virtual topology for both the optical network and the light paths. We introduce our developed algorithm to solve offline RWA problem. First the light path requests are constrained to repeated uniform distributed traffic. The reason is that this constraint permits us to study and analyze the behavior of the RWA problem. In addition, this constraint could be used as a benchmark to compare different algorithms. Then we relax the requests constraint to be non-uniform traffic. We show that the maximum number of assigned wavelengths depends on the number of traversed links, not on the shortest path length. Theorems are derived with proof to justify our algorithm. The effect of adding supplementary links to the WDM optical network is also explained to show how this approach could be used in the future planning for online operation. Finally, the result shows significant different in the number of wavelengths used compared to a recent backbone implemented network.     

The most congested cutset: deriving a tight lower bound for the chromatic number in the RWA problem

Routing and wavelength assignment (RWA) is an important issue in the design of routing protocols in an all-optical network. A solution for the RWA problem should determine the least possible number of wavelengths, also known as the chromatic number. In this letter, we introduce the concept of cutset congestion, and show that the congestion of the most congested cutset of a graph representing the network is a tight lower bound for the chromatic number in the RWA problem. In contrast to other existing techniques, our method can be applied to any network and any traffic pattern.     

An algorithm for optimal assignment of a wavelength in a tree topology and its application in WDM networks

In this paper, we present a polynomial time algorithm that gives an optimal solution to the routing and wavelength assignment (RWA) problem in a tree topology. One of the major design issues in wavelength-division multiplexed networks is the assignment of the limited number of wavelengths among network stations so that greater capacity can be achieved. The problem of RWA is known to be NP-hard problem. Many researchers have tackled the problem of RWA with a number of efficient heuristic algorithms. This paper presents an algorithm that optimally assigns a single wavelength to maximize one-hop traffic in a tree topology. The algorithm uses dynamic programming and is shown to be optimal with a time complexity of O(N/sup 4/). We also propose a heuristic scheme to use our optimal algorithm for wavelength assignment in a general graph. The heuristic works on the tree subgraphs of a given graph and the remaining spare wavelengths can be assigned with an existing RWA policy.     

Topology and analysis of an N-stage cascaded polymer eight-port microring optical router with 7N channel wavelengths

Eight-port optical routers are widely used in cluster-mesh photonic networks-on-chip(No C). By using 24 groups of cross-coupling two-ring resonators, a 1-stage 8-port polymer optical router is proposed, which can optically route 7 channel wavelength data streams along definite path in two-dimensional(2D) plane. Under the selected 7 channel wavelengths, the insertion losses along all routing paths are within 0.02-0.58 d B, the maximum crosstalk of all routing operations is less than-39 d B, and the device footprint size is about 0.79 mm2. Then, a universal novel structure and routing scheme of N-stage cascaded 8-port optical router are presented, which contains 7N channel wavelengths. Because of the good scalability in wavelength, this device shows potential application of wideband signal routing in optical No C.     

节点不完全可靠无向网络k-端可靠度计算

可靠性是保障网络系统正常运行的必要条件,k-端可靠性问题是网络可靠性的最一般问题.通过对已有的计算2-端可靠度的方法进行扩展和改进,提出了一种计算节点不可靠无向网络k-端可靠度的方法.先将图的边定义为链路及其端点,然后通过矩阵变换运算,得到不相交的k-端路径,在此基础上,利用条件概率对k-端路径的概率进行求解以得到网络...     

A new approach for fast segment‐based protection in WDM mesh networks

We propose a new approach for developing segment‐based schemes for protection against single link/node failure in wavelength division multiplexing (WDM) mesh networks. In the proposed approach, every request is allocated a pair of link disjoint but most coupled primary and backup paths. Two paths are said to be most coupled if they share the maximum number of end nodes of some existing requests. Coupled paths reduce the total number of hops need to be traversed by a failure signal and, hence, potentially reduces the overall recovery time. We show that the problem of finding a pair of disjoint and most coupled paths is NP‐complete. Accordingly, we propose an efficient and fast protection algorithm called SPXP—Segment Pre‐Cross‐Connected Protection, to allocate disjoint and most coupled paths. The proposed SPXP algorithm reduces the recovery time by ensuring that backup resources are pre‐configured along each backup segment and, hence, is readily available upon a failure. Simulation results for different incremental traffic models and network topologies show that, for most cases, the proposed SPXP exhibits better performance in terms of blocking probability, resource usage, and recovery time compared with existing protection schemes. Copyright © 2010 John Wiley & Sons, Ltd.     

Routing and wavelength assignment in all-optical networks

Considers routing connections in a reconfigurable optical network using WDM. Each connection between a pair of nodes in the network is assigned a path through the network and a wavelength on that path, such that connections whose paths share a common link in the network are assigned different wavelengths. The authors derive an upper bound on the carried traffic of connections (or equivalently, a lower bound on the blocking probability) for any routing and wavelength assignment (RWA) algorithm in such a network. The bound scales with the number of wavelengths and is achieved asymptotically (when a large number of wavelengths is available) by a fixed RWA algorithm. The bound can be used as a metric against which the performance of different RWA algorithms can be compared for networks of moderate size. The authors illustrate this by comparing the performance of a simple shortest-path RWA (SP-RWA) algorithm via simulation relative to the bound. They also derive a similar bound for optical networks using dynamic wavelength converters, which are equivalent to circuit-switched telephone networks, and compare the two cases. Finally, they quantify the amount of wavelength reuse achievable in large networks using the SP-RWA via simulation as a function of the number of wavelengths, number of edges, and number of nodes for randomly constructed networks as well as de Bruijn networks. They also quantify the difference in wavelength reuse between two different optical node architectures     

The k-Diameter of a Kind of Circulant Graph

The diameter of a graph G is the maximal distance between pairs of vertices of G. When a network is modeled as a graph, diameter is a measurement for maximum transmission delay. The k-diameter dk(G) of a graph G, which deals with k internally disjoint paths between pairs of vertices of G, is a extension of the diameter of G. It has widely studied in graph theory and computer science. The circulant graph is a group-theoretic model of a class of symmetric interconnection network. Let Cn(i, n/2) be a circulant graph of order n whose spanning elements are i and n/2, where n4 and n is even. In this paper, the diameter, 2-diameter and 3-diameter of the Cn(i, n/2) are all obtained if gcd(n,i)=1, where the symbol gcd(n,i) denotes the maximum common divisor of n and i.     

异构传感器网络的一种生存期可延长的可调节拓扑结构

目前,大多数的拓扑控制算法采用的能耗模型不符合实际,仅仅只考虑了发送能耗,忽略了不同接收能耗对底层拓扑结构的影响。其次,通过构建最小能耗拓扑子图的拓扑控制算法并不能最大化网络生存期。基于真实的能耗模型主要研究异构传感器网络的拓扑控制问题,提出了一种适用于异构传感器网络生存期可延长的可调节结构（ALPH）来控制网络拓扑。理论和仿真实验表明：通过ALPH构造的拓扑图保持了网络的连通性和双向性;在不同的射频模块下,ALPH以最小能耗保留了任意节点对之间的最大生存期路径;ALPH可以依据不同电路能耗参数P R0进行调整,使得所生成的拓扑图在DRNG与MaxPower之间调节变化,并且允许节点有不同的路径损耗指数;基于网络设备的真实参数值,与先前的拓扑结构DRNG、DGG、EYG和MaxPower相比,ALPH可以有效地延长网络生存期。     

The k-Diameter of a Kind of Circulant Graph

The terminology and notion in this paper are similar to Ref.[1], all graphs discussed here are finite and simple. The diameter d(G) of a graph G is the maximal distance between pairs of vertices of G. The connectivity of G is the minimum number of vertices needed to be removed in order to disconnect the graph. When a network is modeled as a graph,a vertex represents a node of processor (or a station) and an edge between two vertices is the link (or connection) between those two processors. I…     

网树求解有向无环图中具有长度约束的最大不相交路径

对有向无环图中具有长度约束的最大不相交路径问题进行研究,该问题是求解图中两点间路径长度为k的最大不相交路径。为了对该问题进行求解,提出了贪婪搜索算法(GP, greedy path),该算法先将一个有向无环图转化为一棵深度为k+1的网树,然后计算每个网树节点的树根叶子路径数,并以此计算图中每个顶点的总路径数,之后从网树的第k+1层节点出发,在当前节点的双亲节点中选择未被使用且总路径数最小的双亲,以此形成一条优化的不相交路径,最后迭代这一过程,直到不再有新的不相交路径为止。GP算法的时间和空间复杂度分别为O(wkn(p+q))和O(kn(p+q)+n2)。为了测试GP算法的近似性,又建立了一种能够生成人工数据的算法,该算法能够准确地控制有向无环图中最大不相交路径的数量。通过该算法生成了大量测试用数据,实验结果表明GP算法较其他对比性算法具有良好的近似性且实际求解时间较短,验证了该方法的有效性和可行性。     

On Conflict-Free All-to-All Broadcast in One-Hop Optical Networks of Arbitrary Topologies

In this paper, we investigate the problem of all-to-all broadcast in optical networks, also known as gossiping. This problem is very important in the context of control plane design as it relates to status information dissemination. We present a routing and wavelength assignment (RWA) method to reduce the number of wavelengths such that the communication is conflict-free in a wavelength division multiplexing (WDM) optical environment without wavelength converters. Our approach utilizes the tap-and-continue capability of the optical nodes. The network topology is considered to be arbitrary as long as it is connected. Both cases of maximally and nonmaximally edge-connected graphs are studied. For the first case, we give a closed-form expression for the lower bound on the number of wavelengths, which is an elegant extension of the results in for concurrent broadcast trees in optical networks. Furthermore, we show how to achieve this bound. The second case is more involved and requires a specific procedure to achieve the minimum number of wavelengths. For this case, we provide an attractive method for the RWA algorithm that attempts to minimize the number of wavelengths. Our solution for this case is within a constant factor that is strictly less than 2 from the optimal solution. The proposed algorithm uses the concept of "cactus" representation of all minimum edge-cuts in a graph in a novel recursive approach.