Complexity of Wavelength Assignment in Optical Network Optimization

We study the complexity of a set of design problems for optical networks. Under wavelength division multiplexing (WDM) technology, demands sharing a common fiber are transported on distinct wavelengths. Multiple fibers may be deployed on a physical link. Our basic goal is to design networks of minimum cost, minimum congestion and maximum throughput. This translates to three variants in the design objectives: 1) MlN-SUMFlBER: minimizing the total cost of fibers deployed to carry all demands; 2) MlN-MAXFlBER: minimizing the maximum number of fibers per link to carry all demands; and 3) MAX-THROUGHPUT: maximizing the carried demands using a given set of fibers. We also have two variants in the design constraints: 1) CHOOSEROUTE: Here we need to specify both a routing path and a wavelength for each demand; 2) FIXEDROUTE: Here we are given demand routes and we need to specify wavelengths only. The FIXEDROUTE variant allows us to study wavelength assignment in isolation. Combining these variants, we have six design problems. Previously we have shown that general instances of the problems MIN-SUMFIBER-CHOOSEROUTE and MIN-MAXFIBER-FIXEDROUTE have no constant-approximation algorithms. In this paper, we prove that a similar statement holds for all four other problems. Our main result shows that MIN-SUMFIBER-FIXEDROUTE cannot be approximated within any constant factor unless NP-hard problems have efficient algorithms. This, together with the previous hardness result of MIN-MAXFIBER-FIXEDROUTE, shows that the problem of wavelength assignment is inherently hard by itself. We also study the complexity of problems that arise when multiple demands can be time-multiplexed onto a single wavelength (as in time-domain wavelength interleaved networking (TWIN) networks) and when wavelength converters can be placed along the path of a demand.     

A framework for fiber delay‐line buffers in packet‐based asynchronous multifiber optical networks (PAMFONET)

A major challenge in packet‐based optical networks is packet contention, which occurs when two or more packets are heading to the same output at the same time. To resolve contention in the optical domain, a fundamental approach is fiber delay‐line (FDL) buffering, in which packets can be delayed for a fixed amount of time. In the literature, the performance of FDL buffering has been studied extensively. However, most existing works are based on an assumption that there is only one fiber per link in the network. In this paper, we address the architecture and performance of FDL buffers in packet‐based asynchronous multifiber optical networks (PAMFONET), in which each link in the network may consist of multiple optical fibers. We propose a framework for FDL buffers in PAMFONET, in which we provide three essential architectures and corresponding packet scheduling policies. Extensive simulation results show that, with appropriate settings, the same number of FDLs can lead to better performance in multifiber networks than in single‐fiber networks. Copyright © 2011 John Wiley & Sons, Ltd.     

A Node-Level Blocking Probability Analysis for WRONs

This work presents the blocking performance of a single node with (full or limited) wavelength conversion in wavelength routed optical networks (WRON) based on the theory of probability. A blocking probability model is proposed. Particularly, we pay more attention to investigate wavelength routing node performance improvement by using the more feasible case of limited wavelength conversion. Based on our analytical model, we calculate the blocking probability for a single wavelength routing node and then make a simulation to validate it. It is shown that a node with low conversion degrees having a small number of fiber link ports and a large number of wavelengths per link is a more realistic choice.     

Performance Analysis of Multi-Fiber WDM Network with Limited-Range Wavelength Conversion

Wavelength routed optical networks have emerged as a technology that can effectively utilize the enormous bandwidth of the optical fiber. Wavelength conversion technology and wavelength converters play an important role in enhancing fiber utilization and in reducing the overall call blocking probability of the network. In this paper, we develop a new analytical model to calculate the average blocking probability in multi-fiber link networks using limited range wavelength conversion. Based on the results obtained, we conclude that the proposed analytical model is simple and yet can effectively analyze the impact of wavelength conversion ranges and number of fibers on network performance. Also a new heuristic approach for placement of wavelength converters to reduce blocking probabilities is explored. Finally, we analyze network performance with the proposed scheme. It can be observed from numerical simulations that limited range converters placed at a few nodes can provide almost the same blocking probability as full range wavelength converters placed at all the nodes. We also show that being equipped with a multi-fiber per-link has the same effect as being equipped with the capability of limited range wavelength conversion. So a multi-fiber per-link network using limited range wavelength conversion has similar blocking performance as a full wavelength convertible network. Since a multi-fiber network using limited range wavelength conversion could use fewer converters than a single-fiber network using limited range wavelength conversion and because wavelength converters are today more expensive than fiber equipment, a multi-fiber network in condition with limited range wavelength conversion is less costly than a single fiber network using only limited range wavelength conversion. Thus, multi-fiber per-link network using limited range wavelength conversion is currently a more practical method for all optical WDM networks. Simulation studies carried out on a 14-node NSFNET, a 10-node CERNET (China Education and Research Network), and a 9-node regular mesh network validate the analysis.     

Lighting fibers in a dark network

We consider the problem of network design in transparent, or clear channel, optical networks associated with wavelength-division multiplexing (WDM). We focus on the class of traffic engineering models known as routing, wavelength, and capacity assignment problems. Here, in contrast to traditional networks, traffic flow paths must also be assigned an end-to-end wavelength. This additional requirement means that there can be an increased cost associated with optimal capacity allocations for such WDM-flows. In general, this can be arbitrarily worse than traditional network designs. We argue that in order to evaluate the benefit of different switch technologies, a good benchmark is to measure the increase in costs purely in terms of link capacity, we call this the cost of transparency. Experimental research shows that this cost is small in multifiber networks with modest switching functionality at the nodes. We present theoretical justification for why this occurs, and prove that in multiwavelength multifiber transparent networks the cost of transparency all but disappears if there is moderate traffic load. Our arguments are based on efficient heuristics that may also be useful for more complex network optimizations. This suggests that the cost savings from using wavelength converters is significant only in young networks with relatively few fibers lit. Such savings may, thus, be small relative to the initial capital expense involved in installing wavelength conversion.     

Performance analysis of multi-fiber WDM network with limited-range wavelength conversion

Wavelength routed optical networks have emerged as a technology that can effectively utilize the enormous bandwidth of the optical fiber. Wavelength conversion technology and wavelength converters play an important role in enhancing fiber utilization and in reducing the overall call blocking probability of the network. In this paper, we develop a new analytical model to calculate the average blocking probability in multi-fiber link networks using limited-range wavelength conversion. Based on the results obtained, we conclude that the proposed analytical model is simple and yet can effectively analyze the impact of wavelength conversion ranges and number of fibers on network performance. Also a new heuristic approach for placement of wavelength converters to reduce blocking probabilities is explored. Finally, we analyze network performance with the proposed scheme. It can be observed from numerical simulations that limited-range converters placed at a few nodes can provide almost the same blocking probability as full range wavelength converters placed at all the nodes. We also show that being equipped with a multi-fiber per-link has the same effect as being equipped with the capability of limited-range wavelength conversion. So a multi-fiber per-link network using limited-range wavelength conversion has similar blocking performance as a full wavelength convertible network. Since a multi-fiber network using limited-range wavelength conversion could use fewer converters than a single-fiber network using limited range wavelength conversion and because wavelength converters are today more expensive than fiber equipment, a multi-fiber network in condition with limited-range wavelength conversion is less costly than a single-fiber network using only limited-range wavelength conversion. Thus, multi-fiber per-link network using limited-range wavelength conversion is currently a more practical method for all optical WDM networks. Simulation studies carried out on a 14-node NSFNET, a 10-node CERNET (China Education and Research Network), and a 9-node regular mesh network validate the analysis.     

Analysis and design of resilient multifiber wavelength-routedoptical transport networks

Wavelength-routed optical networks (WRONs) are attracting significant attention for future high-capacity transport applications. This paper studies resilient multifiber WRONs, investigating the influence on the network performance of the maximum number of wavelengths per fiber W restoration strategies, node functionality, and physical topology. Fiber requirements are analyzed for numerous network topologies both without and with link failure restoration, considering different optical cross-connect (OXC) configurations and terminal functionalities. An integer linear program (ILP) formulation is presented for the exact solution of the routing and wavelength allocation (RWA) problem, with minimal total number of fibers, F_T (W). Lower bounds on F_T(W) are discussed, and heuristic algorithms proposed. Three restoration strategies are considered and compared in terms of capacity requirement. Different network topologies are analyzed, to evaluate the influence of physical connectivity and network size on the restoration capacity. Network evolution in terms of growth in traffic demand is investigated to study the importance of wavelength conversion within the OXC's as a function of network size and connectivity, traffic demand, and wavelength multiplicity W     

Performance Analysis of WDM Optical Networks with Wavelength Usage Constraint

Due to power considerations, it is possible that not all wavelengths available in a fiber can be used at a given time. In this paper, an analytical model is proposed to evaluate the blocking performance of wavelength-routed optical networks with and without wavelength conversion where the usable wavelengths in a fiber is limited to a certain maximum number, referred to as wavelength usage constraint. The effect of the wavelength usage constraint is studied on ring and mesh-torus networks. It is shown that the analytical model closely approximates the simulation results. We also evaluate the performance of the first-fit wavelength assignment algorithm and compare its performance with the random wavelength assignment algorithm through simulation. It is observed that increasing the total number of wavelengths in a fiber is an attractive alternative to wavelength conversion when the number of usable wavelengths in a fiber is maintained the same.     

Performance Evaluations for Dynamic Wavelength Routed All-Optical Multifiber Networks

This paper presents a study on dynamic wavelength routed all-optical networks by simulating traffic on all-optical networks. A performance study is carried out on dynamic all-optical networks for fixed and free routing. It is explained how multiple fibers correspond to limited wavelength conversion, and it is explained why the presence of wavelength converters increase the complexity of optical cross connects. We find that both free routing and wavelength conversion lowers the blocking probability significantly. The new contribution is that we determine the gain in blocking probability as function of the number of fibers per link and the offered load. We find that multiple fibers reduce the effect of wavelength converters significantly.     

An analysis of oblivious and adaptive routing in optical networkswith wavelength translation

We present an analysis for both oblivious and adaptive routing in regular, all-optical networks with wavelength translation. Our approach is simple, computationally inexpensive, accurate for both low and high network loads, and the first to analyze adaptive routing with wavelength translation in wavelength division multiplexed (WDM) networks while also providing a simpler formulation of oblivious routing with wavelength translation. Unlike some previous analyses which use the link independence blocking assumption and the call dropping (loss) model (where blocked calls are cleared), we account for the dependence between the acquisition of wavelengths on successive links of a session's path and use a lossless model (where blocked calls are retried at a later time). We show that the throughput per wavelength increases superlinearly (as expected) as we increase the number of wavelengths per link, due both to additional capacity and more efficient use of this capacity; however, the extent of this superlinear increase in throughput saturates rather quickly to a linear increase. We also examine the effect that adaptive routing can have on performance. The analytical methodology that we develop can be applied to any vertex and edge symmetric topology, and with modifications, to any vertex symmetric (but not necessarily edge symmetric) topology. We find that, for the topologies we examine, providing at most one alternate link at every hop gives a per wavelength throughput that is close to that achieved by oblivious routing with twice the number of wavelengths per link. This suggests some interesting possibilities for network provisioning in an all-optical network. We verify the accuracy of our analysis for both oblivious and adaptive routing via simulations for the torus and hypercube networks     

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.     

Design-dimensioning model for transparent WDM packet-switchedirregular networks

A detailed analytical traffic model for all-optical wavelength division multiplexing (WDM) photonic packet-switched networks is presented and the requirements for buffer size and link dimensions are analyzed. This paper shows that due to the topology, packets may generate traffic bottlenecks produced by a tendency of the routing scheme to send packets with different destinations through preferred paths. This effect increases the traffic load and, hence, the probability of blocking at the output links of specific routers in the network and, therefore, a large buffer depth or an increment in the number of fibers per link is required. Three router architectures are analyzed and it is shown that WDM all-optical router architectures with shared contention resolution resources are the best candidates to reduce hardware volume and cost of all-optical networks. It is shown that routers with a bank of completely shared wavelength converters (WCs) require a fraction of WCs compared to router architectures that use a WC per wavelength. This fraction depends on the location of the router, the network topology, and the traffic load in the network. However, in general terms, about 50% to 90% of WCs can be saved by architectures with shared wavelength-conversion resources. Also, it is shown that limited wavelength conversion degrees d=8 and d=10 in packet-switching routers with 16 and 32 wavelengths give the same probability of packet loss performance as full wavelength conversion     

Uniform waveband assignment in optical mesh networks

The cost of an optical network in wavelength division multiplexing (WDM) networks can be reduced using optical reconfigurable optical add/drop multiplexers (ROADMs), which allow traffic to pass through without the need for an expensive optical-electro-optical (O-E-O) conversion. Waveband switching (WBS) is another technique to reduce the network cost by grouping consecutive wavelengths and switching them together using a single port per waveband. WBS has attracted the attention of researchers for its efficiency in reducing switching complexity and therefore cost in WDM optical networks. In this paper, we consider the problem of switching wavelengths as non-overlapping uniform wavebands, per link, for mesh networks using the minimum number of wavebands. Given a fixed band size b _s , we give integer linear programming formulations and present a heuristic solution to minimize the number of ROADMs (number of wavebands) in mesh networks that support a given traffic pattern. We show that the number of ROADMs (or number of ports in band-switching cross-connects) can be reduced significantly in mesh networks with WBS compared to wavelength switching using either the ILP or the heuristic algorithm. We also examine the performance of our band assignment algorithms under dynamic traffic.     

Efficient routing and wavelength assignment for multicast in WDMnetworks

The next generation multimedia applications such as video conferencing and HDTV have raised tremendous challenges on the network design, both in bandwidth and service. As wavelength-division-multiplexing (WDM) networks have emerged as a promising candidate for future networks with large bandwidth, supporting efficient multicast in WDM networks becomes eminent. Different from the IP layer, the cost of multicast at the WDM layer involves not only bandwidth (wavelength) cost, but also wavelength conversion cost and light splitting cost. It is well known that the optimal multicast problem in WDM networks is NP-hard. In this paper, we develop an efficient approximation algorithm consisting of two separate but integrated steps: multicast routing and wavelength assignment. We prove that the problem of optimal wavelength assignment on a multicast tree is not NP-hard; in fact, an optimal wavelength assignment algorithm with complexity of O(NW) is presented. Simulation results have revealed that the optimal wavelength assignment beats greedy algorithms by a large margin in networks using many wavelengths on each link such as dense wavelength-division-multiplexing (DWDM) networks. Our proposed heuristic multicast routing algorithm takes into account both the cost of using wavelength on links and the cost of wavelength conversion. The resulting multicast tree is derived from the optimal lightpaths used for unicast     

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.     

On the wavelength assignment problem in multifiber WDM star andring networks

This paper studies-the off-line wavelength assignment problem in star and ring networks that deploy multiple fibers between nodes and use wavelength division multiplexing (WDM) for transmission. The results in this paper show that the ability to switch between fibers increases wavelength utilization. In particular, sharper per-fiber bounds on the number of required wavelengths are derived for the multifiber version of the assignment problem in star and ring networks. Additionally, the complexity of the problem is studied and several constrained versions of the problem are also considered for star and ring networks. A summary of contributions is provided     

波分复用波长路由节点的阻塞特性分析

利用概率统计理论的方法，从节点层次上定量分析了节点规模、复用波长数目以及波长转换对波分复用(WDM)波长路由网络中波长路由节点的影响。提出了基于概率统计的节点阻塞模型。数值结果突出表明波长转换能力越强的全光节点，其性能越优。为了提高网络资源的使用效率并增强全光网络的灵活性，必须实现全光网络中的虚波长路由波长转换器。通过数值计算找到了阻塞性能和代价的折中，研究中发现配置较低波长转换能力波长转换器的波长路由节点将会具备更强的性价比优势，当前在构建光通信系统时使用弱波长转换能力的光节点更可行。     

Multifiber Shared-Per-Wavelength All-Optical Switching: Architectures, Control, and Performance

A new wavelength converter sharing strategy for multifiber optical switches, namely shared-per-wavelength (SPW), which employs wavelength converters with fixed input wavelengths is presented. The aim is to reduce switch costs by using simpler optical components and low complexity space switching matrices. Practical implementations of both the well-known shared-per-node (SPN) and the new SPW schemes are presented, as well as the related scheduling algorithms to manage optical packet forwarding in synchronous scenario. An analytical model to evaluate blocking performance of the SPN architecture is also provided. Results show the accuracy of the model in the range of interest for switch design. The proposed architectures are compared in terms of performance and number of optical components employed. The SPW approach is shown to save a large number of semiconductor optical amplifier gates with respect to the SPN one when the number of fibers per interface is suitably not too high. In these cases, the SPW architecture requires a number of wavelength converters higher than the SPN, but simpler, being their inputs tuned on a single wavelength.     

Models,Complexity and Algorithms for the Design of Multi-fiber WDM Networks

In this paper, we study multi-fiber optical networks with wavelength division multiplexing (WDM). We extend the definition of the well-known Wavelength Assignment Problem (WAP) to the case of k fibers per link and w wavelengths per fiber, generalization that we will call (k,w)-WAP. We develop a new model for the (k,w)-WAP based on conflict hypergraphs. Furthermore, we consider two natural optimization problems that arise from the (k,w)-WAP: minimizing the number of fibers k given a number of wavelengths w, on one hand, and minimizing w given k, on the other. We develop and analyze the practical performance of two methodologies based on hypergraph coloring.     

Dynamic lightpath establishment considering four-wave mixing in multifiber WDM networks

This paper proposes a dynamic lightpath establishment scheme considering four-wave mixing (FWM) in multifiber wavelength-division multiplexed (WDM) all-optical networks. The FWM is one of the most important physical impairments to be resolved in WDM networks because the FWM induces nonlinear inter-channel crosstalk and decays the performance of WDM networks. In WDM networks, data are transmitted via lightpaths. When the effect of FWM crosstalk is large, it is highly possible that data transmission fails even if lightpaths are correctly established. The proposed scheme aims to avoid not only the blocking of lightpath establishment but also the accumulation of FWM crosstalk by means of ingenious selection of routes, wavelengths, and fibers for lightpath establishment. In the proposed scheme, a route and a wavelength are selected for each lightpath based on wavelength availability and wavelength placement of established lightpaths. Furthermore, fibers on the route are selected based on estimated FWM power. In this paper, we show the effectiveness of the proposed scheme through simulation experiments.