A Lagrangean relaxation and subgradient framework for the routing and wavelength assignment problem in WDM networks

Unlike traditional heuristics, we provide in this paper an optimization framework for the routing and wavelength assignment (RWA) problems with the objective of minimizing the rejection penalty of the connection demands in an all-optical wavelength-division-multiplexing (WDM) network. Our new link-based formulation takes the fairness issue and the limited wavelength conversion into consideration. The framework employs a decomposition approach to decide on the rejection/selection of the route and wavelength assignment for a semilightpath, by appropriately relaxing some of the constraints in the Lagrangean relaxation (LR) method. At the higher level, we update Lagrange multipliers iteratively with the subgradient method. At the lower level, we propose the modified minimum cost semilightpath (MMCSLP) algorithm to solve all the subproblems. A heuristic algorithm is also proposed to generate a feasible RWA scheme based on the solution to the dual problem. When compared with some latest methodology in the literature, we demonstrate that our framework can achieve better performance in terms of the computation time and the number of connection demands rejected. The much shorter computation time is due to the polynomial time complexity of our framework. In addition to achieving a very good (near-optimal) solution, the influence from the change of the number of converters is studied. Finally, we demonstrate that our framework produces fairer routing decisions by adjusting some design parameters in our framework.     

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.     

A RWA Algorithm for Differentiated Services with QoS Guarantees in the Next Generation Internet based on DWDM Networks

A major challenge in next generation Internet (NGI) backbone networks based on dense-wavelength division multiplexing (DWDM) is the provision of guaranteed quality-of-service (QoS) for a wide variety of multimedia applications. This paper proposes a new routing algorithm called multi-wavelength minimum interference path routing (MW-MIPR) to provide more reliable QoS guarantees by consideration of the potential future network's congestion status. This improves wavelength utilization by choosing a route that does not interfere too much with potential future connection requests. Moreover, we introduce a differentiated routing and wavelength assignment (RWA) mechanism combined with recovery strategy and the proposed MW-MIPR algorithm based on the differentiated service model in the NGI. Simulation results show that the proposed MW-MIPR algorithm achieves a smaller blocking probability than dynamic routing (DR) that yields the best performance among previous RWA algorithms. And we prove that a differentiated RWA combined with a recovery capability together with the proposed routing scheme provides satisfied QoS assurance for each service class in terms of signal quality and survivability.     

Routing and wavelength assignment in optical networks

The problem of routing and wavelength assignment (RWA) is critically important for increasing the efficiency of wavelength-routed all-optical networks. Given the physical network structure and the required connections, the RWA problem is to select a suitable path and wavelength among the many possible choices for each connection so that no two paths sharing a link are assigned the same wavelength. In work to date, this problem has been formulated as a difficult integer programming problem that does not lend itself to efficient solution or insightful analysis. In this work, we propose several novel optimization problem formulations that offer the promise of radical improvements over the existing methods. We adopt a (quasi-)static view of the problem and propose new integer-linear programming formulations, which can be addressed with highly efficient linear (not integer) programming methods and yield optimal or near-optimal RWA policies. The fact that this is possible is surprising, and is the starting point for new and greatly improved methods for RWA. Aside from its intrinsic value, the quasi-static solution method can form the basis for suboptimal solution methods for the stochastic/dynamic settings.     

Routing and wavelength assignment strategies in optical networks

We consider the routing and wavelength assignment (RWA) problem on wavelength division multiplexing (WDM) networks without wavelength conversion. When the physical network and required connections are given, RWA is the problem to select a suitable path and wavelength among the many possible choices for each connection such that no two paths using the same wavelength pass through the same link. In WDM optical networks, there is need to maximize the number of connections established and to minimize the blocking probability using limited resources. This paper presents efficient RWA strategies, which minimizes the blocking probability. Simulation results show that the performance of the proposed strategies is much better than the existing strategy.     

On the routing and wavelength assignment in multifiber WDM networks

This paper addresses the problem of routing and wavelength assignment (RWA) in multifiber WDM networks with limited resources. Given a traffic matrix, the number of fibers per link, and the number of wavelengths a fiber can support, we seek to maximize the carried traffic of connections. We formulate the problem as an integer linear program (ILP), and show that the lightpaths selected by this formulation can indeed be established by properly configuring the optical switches. An upper bound on the carried traffic can be computed by solving the linear programming (LP)-relaxation of the ILP formulation. It is shown that this bound can be also computed exactly, and in polynomial-time, by solving a significantly simplified LP which considers only one wavelength. The bound can, thus, easily scale to an arbitrarily large number of wavelengths. Furthermore, we demonstrate that any instance of the RWA problem is also an instance of the more general maximum coverage problem. This allows us to take a greedy algorithm for maximum coverage and obtain an algorithm which provides solutions for the RWA problem that are guaranteed to be within a factor of (1-(1/e)) of the optimal solution. Each iteration of the greedy algorithm selects a set of lightpaths that realizes, using one wavelength, the maximum number of connection requests not previously realized. Computational results confirm the high efficiency of our proposed algorithm.     

Routing and Wavelength Assignment in Optical Networks Using Logical Link Representation and Efficient Bitwise Computation

In this paper, we propose and evaluate a new approach for implementing efficient routing and wavelength assignment (RWA) in wavelength division multiplexing (WDM) optical networks. In our method, the state of a fiber is given by the set of free wavelengths in this fiber and is efficiently represented as a compact bitmap. The state of a multiple-fiber link is also represented by a compact bitmap computed as the logical union of the individual bitmaps of the fibers in this link. Likewise, the state of a lightpath is represented by a similar bitmap computed as the logical intersection of the individual bitmaps of the links in this path. The count of the number of 1-valued bits in the bitmap of the route from source to destination is used as the primary reward function in route selection. A modified Dijkstra algorithm is developed for dynamic routing based on the bitmap representation. The algorithm uses bitwise logical operations and is quite efficient. A first-fit channel assignment algorithm is developed using a simple computation on the bitmap of the selected route. The resulting bitwise routing algorithm combines the benefits of least loaded routing algorithms and shortest path routing algorithms. Our extensive simulation tests have shown that the bitwise RWA approach has small storage overhead, is computationally fast, and reduces the network-wide blocking probability. The blocking performance of our RWA method compares very favorably with three routing methods: fixed alternate routing, shortest path using flooding, and Dijkstra’s algorithm using mathematical operations. Our simulation experiments have also evaluated the performance gain obtained when the network access stations are equipped with finite buffers to temporarily hold blocked connection requests.     

Dynamic Routing and Wavelength Assignment in Survivable WDM Networks

Dense wavelength division multiplexing (DWDM) networks are very attractive candidates for next generation optical Internet and intelligent long-haul core networks. In this paper we consider DWDM networks with wavelength routing switches enabling the dynamic establishment of lightpaths between each pair of nodes. The dynamic routing and wavelength assignment (RWA) problem is studied in multifiber networks, assuming both protection strategies: dedicated and shared. We solve the two subproblems of RWA simultaneously, in a combined way using joint methods for the wavelength selection (WS) and wavelength routing (WR) tasks. For the WS problem in contrast to existing strategies we propose a new, network state based selection method, which tries to route the demand on each wavelength, and selects the best one according to different network metrics (such as available channels, wavelengths per fiber and network load). For the WR problem we propose several weight functions for using in routing algorithms (Dijkstra or Suurballe), adapting dynamically to the load of the links and to the length of the path. The combination of different wavelength selection and routing (WS&WR) methods enables wide configuration opportunities of our proposed algorithm allowing good adaptation to any network state. We also propose the extension of the RWA algorithm for dedicated and shared protection and a new method for applying shared protection in dynamic WDM environment. The detailed analysis of the strategies demonstrate that our RWA algorithm provides significantly better performance than previous methods in terms of blocking probability whether with or without protection methods.     

A proof of wavelength conversion not improving the lagrangian bound of the static RWA problem

The fact that wavelength conversion hardly improves the performance of static routing and wavelength assignment (RWA) in Wavelength Division Multiplexing (WDM) networks has been observed in many previous studies. However, other than simulation results, until now there was no formal proof of such fact. In this paper, we formally prove that wavelength conversion does not improve the Lagrangian bound of the static RWA problem.     

A practical approach for routing and wavelength assignment in largewavelength-routed optical networks

We consider large optical networks in which nodes employ wavelength-routing switches which enable the establishment of wavelength-division-multiplexed (WDM) channels, called lightpaths, between node pairs. We propose a practical approach to solve routing and wavelength assignment (RWA) of lightpaths in such networks. A large RWA problem is partitioned into several smaller subproblems, each of which may be solved independently and efficiently using well-known approximation techniques. A multicommodity flow formulation combined with randomized rounding is employed to calculate the routes for lightpaths. Wavelength assignments for lightpaths are performed based on graph-coloring techniques. Representative numerical examples indicate the accuracy of our algorithms     

WDM光网络中基于传输损伤的公平RWA算法

在WDM光网络中,物理层上存在使信号传输质量恶化的因素,当信号质量劣化到一定程度会导致连接失败,因此有必要在选路和波长分配RWA（Routing and Wavelength Assignment）算法中考虑物理层的传输损伤。连接公平性问题是指网络中长路径连接请求的阻塞率表现比短路径差,文中分析传输损伤约束的引入对连接公平性的影响,提出基于传输损伤的动态RWA算法：固定波长配额FWQ（Fixed Wavelength Quota）算法和非固定波长配额UFWQ（UnFixed Wavelength Quota）算法。     

智能光网络中的路由和波长分配问题

随着下一代智能光网络概念的提出，应用于传统光网络的路由和波长分配方法面临着许多新的挑战。本以自动交换光网络为代表，分析了智能光网络中不同类型连接的特点和实现路由和波长分配的控制软件模块，并着重从路由模式、多粒度分层选路、路由和波长分配算法、信令路由协议等几个方面出发，对智能光网络中的路由和波长分配问题进行了深入的探讨。同时提出了相应的解决方案。     

Dynamic circuit provisioning in all-optical WDM networks using lightpath switching

In this paper we investigate the problem of provisioning holding-time-aware (HTA) dynamic circuits in all-optical wavelength division multiplexed (WDM) networks. We employ a technique called lightpath switching (LPS) wherein the data transmission may begin on one lightpath and switch to a different lightpath at a later time. Lightpath switches are transparent to the user and are managed by the network. Allowing LPS creates a number of segments that can use independent lightpaths. We first compare the performance of traditional routing and wavelength (RWA) assignment to routing and wavelength assignment with LPS. We show that LPS can significantly reduce blocking compared to traditional RWA. We then address the problem of routing dynamic anycast HTA dynamic circuits. We propose two heuristics to solve the anycast RWA problem: anycast with continuous segment (ACS) and anycast with lightpath switching (ALPS). In ALPS we exercise LPS, and provision a connection request by searching for the best candidate destination node is such a way that the network resources are utilized efficiently. In ACS we do not allow a connection request to switch lightpaths. The lightpaths to each candidate destination node of a request are computed using traditional RWA algorithms. We first compare the performance of ACS to ALPS and observe that ALPS achieves better blocking than ACS. Furthermore, we also compare the performance of these two anycast RWA algorithms to the traditional unicast RWA algorithm. We show that the anycast RWA algorithms presented here significantly outperform the traditional unicast RWA algorithms.     

QoS aware traffic grooming and integrated routing on IP over WDM networks

In this article, we consider traffic grooming and integrated routing in IP over WDM networks. The challenges of this problem come from jointly considering traffic grooming, IP routing, and lightpath routing and wavelength assignment (RWA). Due to the high bandwidth of optical fiber, there exists a mismatch between the capacity needed by an IP flow and that provided by a single lightpath. Traffic grooming is therefore used to increase the network utilization by aggregating multiple IP flows in a single lightpath. However, traffic grooming incurs additional delays that might violate Quality-of-Service (QoS) requirements of IP users. In this work, the tradeoff between traffic grooming and IP QoS routing is well-formulated as a mixed integer and linear optimization problem, in which the revenue from successfully provisioning IP paths is to be maximized. Problem constraints include IP QoS, routing, optical RWA, and the WDM network capacity. We propose a novel Lagrangean relaxation (LGR) algorithm to perform constraint relaxation and derive a set of subproblems. The Lagrangean multipliers are used in the proposed algorithm to obtain a solution in consideration of grooming advantage and resource constraints simultaneously. Through numerical experiments and comparisons between the proposed algorithm and a two-phase approach, LGR outperforms the two-phase approach under all experimental cases. In particular, the improvement ratio becomes even more significant when the ratio of IP flow to the wavelength capacity is smaller.     

波长路由光网络中RWA算法的设计分析

文章通过对波长路由光网络中路由与波长分配(RWA)问题的研究,介绍了求解路由子问题和波长分配子问题的常用方法,总结了3种类型的RWA问题的优化解决方法,最后对目前RWA算法设计中存在的问题进行了分析并阐述了解决此类问题的重要性.     

Resource efficient network design and traffic grooming strategy with guaranteed survivability

In WDM networks, path protection has emerged as a widely accepted technique for providing guaranteed survivability of network traffic. However, it requires allocating resources for backup lightpaths, which remain idle under normal fault-free conditions. In this paper, we introduce a new design strategy for survivable network design, which guarantees survivability of all ongoing connections that requires significantly fewer network resources than protection based techniques. In survivable routing, the goal is to find a Route and Wavelength Assignment (RWA) such that the logical topology remains connected for all single link failures. However, even if the logical topology remains connected after any single link fault, it may not have sufficient capacity to support all the requests for data communication, for all single fault scenarios. To address this deficiency, we have proposed two independent but related problem formulations. To handle our first formulation, we have presented an Integer Linear Program (ILP) that augments the concept of survivable routing by allowing rerouting of sub-wavelength traffic carried on each lightpath and finding an RWA that maximizes the amount of traffic that can be supported by the network in the presence of any single link failure. To handle our second formulation, we have proposed a new design approach that integrates the topology design and the RWA in such a way that the resulting logical topology is able to handle the entire set of traffic requests after any single link failure. For the second problem, we have first presented an ILP formulation for optimally designing a survivable logical topology, and then proposed a heuristic for larger networks. Experimental results demonstrate that this new approach is able to provide guaranteed bandwidth, and is much more efficient in terms of resource utilization, compared to both dedicated and shared path protection schemes.     

Application of Petri Nets and Lagrangian Relaxation to Scheduling Automatic Material-Handling Vehicles in 300-mm Semiconductor Manufacturing

This paper deals with vehicle-scheduling problem (VSP) in an automatic material-handling environment in 300-mm semiconductor wafer manufacturing. We adopt Petri nets (PNs) modeling techniques to model the complicated coupling dynamics among transport jobs and overhead hoist transport (OHT) vehicles in a 300-mm OHT loop. The congestion phenomenon among OHT vehicles is captured. With help of the PN models, we formulate the OHT VSP as an integer programming problem whose objective is to schedule OHT vehicles to transport jobs such that average job completion time is minimized. Instead of solving for the optimal solution, we develop a solution methodology to generate a feasible schedule efficiently. A Lagrangian relaxation step is first taken to decompose the PN-based, integer programming problem into individual job-scheduling subproblems. To reduce computation efforts in solving each subproblem optimally, we develop an approximation method to solve each job subproblem by utilizing a reduced PN model of the job. Lagrangian multipliers are then optimized by a surrogate subgradient method. A heuristic algorithm is developed to adjust the dual solution to a feasible schedule. Numerical results demonstrate that our solution methodology can generate good schedules within a reasonable amount of computation time for realistic problems. Compared to a popular vehicle-dispatching rule, our approach can achieve in average 32% improvements on the average delivery time in our realistic test cases.     

MC-BRM: A distributed RWA algorithm with minimum wavelength conversion

There are two strategies for solving Routing and Wavelength Assignment (RWA) in wavelength-routed networks: centralized and distributed. Centralized approaches are appropriate for small networks with light traffic, whereas distributed approaches are suitable for large networks with heavy traffic. Solving RWA problem in distributed algorithms can be generally divided into two phases: routing phase and wavelength assignment phase. Allocating a wavelength over a physical path for a connection request can be performed by one of two major strategies: Backward Reservation Method (BRM) and Forward Reservation Method (FRM). In this work, we assume that every node in the network can be equipped with a number of wavelength converters. Wavelength converters are usually chosen in a free policy. However, we propose a distributed algorithm, called Minimum-Conversion Backward Reservation Method (MC-BRM), that attempts to establish light-paths with minimum number of wavelength conversions. The MC-BRM algorithm can efficiently reduce the number of required wavelength conversions in the network. Besides improving blocking probability, MC-BRM can lead to better fairness in establishing light-paths with different number of hops. Finally, we make the worst case analysis for estimating wavelength conversion usages in individual nodes.     

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.

Binary quadratic programming formulation for routing and wavelength assignment problem in all-optical WDM networks

Routing and wavelength assignment (RWA) is the most concern in wavelength routed optical networks. This paper proposes a novel binary quadratic programming (BQP) formulation for the static RWA problem in order to balance traffic load among a network links more fairly. Subsequently, a greedy heuristic algorithm namely variable-weight routing and wavelength assignment (VW-RWA) is proposed to solve the developed BQP problem. In this method, the weight of a link is proportional to the link congestion. Performance evaluation results for different practical network topologies show that our proposed algorithm can decrease the number of required wavelengths in the network, blocking rate and variance of used wavelengths in each link. Besides, it is shown that the number of required wavelengths to establish call requests for a given network topology can be reduced at lower cost compared to other heuristics.