This paper addresses the problem of finding a static virtual topology design and flow routing in transparent optical WDM networks under a time-varying (multi-hour) traffic demand. Four variants of the problem are considered, using fixed or dynamically adaptable (i.e., variable) flow routing, which can be splittable or unsplittable. Our main objective is to minimize the number of transceivers needed which make up for the main network cost. We formulate the problem variants as exact ILPs (Integer Linear Programs) and MILPs (Mixed ILPs). For larger problem instances, we also propose a family of heuristics based on the concept of domination between traffic matrices. This concept provides the theoretical foundations for a set of techniques proposed to reduce the problem complexity. We present a lower bound to the network cost for the case in which the virtual topology could be dynamically reconfigured along time. This allows us to assess the limit on the maximum possible benefit that could be achieved by using optical reconfigurable equipment. Extensive tests have been conducted, using both synthetically generated and real-traced traffic demands. In the cases studied, results show that combining variable routing with splittable flows obtains a significant, although moderate, cost reduction. The maximum cost reduction achievable with reconfigurable virtual topologies was shown to be negligible compared to the static case in medium and high loads.

Abstract-In translucent optical networks the physical layer impairments degrading the optical signal are considered in the network design. In this paper we investigate the offline problem of Routing and Wavelength Assignment (RWA) and Regenerator Placement (RP) in translucent networks. Given a network topology, an estimation of the traffic demands, the objective is to minimize the cost of the regeneration equipment used, and to avoid the lightpath blocking. We formulate an optimal ILP model of the problem, to the best of the authors' knowledge, for the first time in the literature. Its simplicity allows us to test it for small and medium size networks. Despite of this merit, the problem is NP-hard. For larger problem instances we propose two heuristic methods: Lightpath Segmentation and 3-Step method. The latter guarantees that no lightpath blocking is produced by signal degradation. We also provide a lower bound for the regenerator equipment cost. The performance and the scalability of our proposals are then investigated by carrying out extensive tests, considering different network topologies, number of wavelengths per fiber, traffic load conditions and network link lengths. Results reveal that the solutions obtained by the heuristic algorithms are optimal or close-to-optimal and require low computation times. In addition, the results help to capture the trends in the regenerator equipment cost in different network instances.

Transparent optical networks are the enabling infrastructure for converged multi-granular networks in the Future Internet. The cross-layer planning of these networks considers physical impairments in the network layer design. This is complicated by the diversity of modulation formats, transmission rates, amplification and compensation equipments, or deployed fiber links. Thereby, the concept of Quality of Transmission (QoT) attempts to embrace the effects of the physical layer impairments, to introduce them in a multicriterium optimization and planning process. This paper contributes in this field by the proposal and comparative evaluation of two novel offline impairment aware planning algorithms for transparent optical networks, which share a common QoT evaluation function. The first algorithm is based on an iterative global search driven by a set of binary integer linear programming formulations. Heuristic techniques are included to limit the binary programming complexity. The second algorithm performs different pre-orderings of the lightpath demand, followed by a sequential processing of the lightpath demands. The performance and the scalability of both approaches are investigated. Results reveal great scalability properties of the global search algorithm, and a performance similar to or better than the sequential schemes.

Abstract-This paper investigates offline planning and scheduling in transparent optical networks for a given periodic traffic demand. The main objective is to minimize the number of transceivers needed which make up for the main network cost. We call this problem "Scheduled Virtual Topology Design" and consider two variants: non-reconfigurable and reconfigurable equipment. We formulate both problems as exact MILPs (Mixed Integer Linear Programs). Due to their high complexity, we propose a more scalable tabu search heuristic approach, in conjunction with smaller MILP formulations for the associated subproblems. The main motivation of our research efforts is to assess the benefits of using reconfigurable equipment, realized as a reduction in the number of required transceivers. Our results show that the achieved reductions are not very significant, except for cases with large network loads and high traffic variability.Index Terrms-All-optical networks, virtual topology design, multilayer optimization, scheduling, tabu search.

This paper investigates offline virtual topology design in transparent optical networks under a multihour traffic demand. The main problem variant addressed here designs a reconfigurable virtual topology that evolves over time to more efficiently utilize network resources (the MH-VTD-R problem). The case of designing a static non-reconfigurable virtual topology that can accommodate the time-varying traffic (the MH-VTD-NR problem) is also considered. The objectives are to minimize: 1) the number of transceivers, which make up for the main network cost; and 2) the frequency of reconfiguration (for MH-VTD-R), which incurs additional overhead and potential service disruption. We formulate this multiobjective problem as an exact mixed integer linear program (MILP). Due to its high complexity, we propose a very efficient heuristic algorithm called Greedy Approach with Reconfiguration Flattening (GARF). GARF not only solves both (non-)reconfigurable problem variants, but it allows for tuning of the relative importance of the two objectives. Exhaustive experiments on real and synthetic traffic and comparison to previous proposals and bounds reveal the merits of GARF with respectto both solution quality and execution time. Furthermore, the obtained results indicate that the maximal transceiver cost savings achieved by the fully reconfigurable case may not be enough to justify the associated increase in reconfiguration cost. However, results show that an advantageous tradeoff between transceiver cost savings and reconfiguration cost can be achieved by a allowing a small number of virtual topology reconfigurations over time.Index Terms-Multihour traffic, reconfigurable virtual topology design, transparent optical networks.

Periodic reconfiguration of the virtual topology in transparent optical networks has been recently investigated as a mechanism to more efficiently adapt the network to predictable periodic traffic variations along the day or week. The scheduling of periodic reconfigurations should consider the trade-off between a lower network cost obtained through better resource allocation, and the undesired traffic disruptions that these reconfigurations may cause. This paper presents and compares two algorithms for planning virtual topology reconfiguration suitable for exploring this trade-off. The first is based on a Lagrangian relaxation of the planning problem, and the second is based on a Tabu Search Tabu Search meta-heuristic. The merits of both algorithms are compared. Keywords: virtual topology design, network planning, multi-hour traffic, Lagrangian relaxation, Tabu search. I TRODUCTIOTransparent optical networks based on Wavelength Division Multiplexing (WDM) have become an accepted solution for new broadband backbone networks [1]. In these networks, traffic is carried through transparent alloptical connections, called lightpaths. A lightpath is established between an optical transmitter in the originating node and an optical receiver in the terminating node over a wavelength channel in each traversed fibre. Since the traffic carried over a lightpath is wavelength switched at intermediate nodes, the costs associated to the data electronic processing are saved. The set of lightpaths established onto a physical topology to support a given set of traffic demands (in Gbps) is called a virtual topology. The Virtual Topology Design (VTD) problem implies solving a two-layered routing problem: in the upper layer, it involves routing traffic flows (demands) over the virtual topology; while in the lower layer, it involves finding a Routing and Wavelength Assignment (RWA) [2] of lightpaths over the physical topology. In this work, we assume network scenarios with an over-provisioned fiber plant where a feasible RWA solution exists for almost any lightpath in the virtual topology, focusing only on the upper layer routing problem.The VTD problem under multi-hour or periodic traffic is denoted as Multi-Hour Virtual Topology Design (MH-VTD) [3]. In this case, the set of traffic demands are represented as a temporal sequence of traffic matrices, reflecting traffic variations over a period of time (e.g. a day or a week). The MH-VTD problem can be classified into: (i) the MH-VTD-NR (non-reconfigurable) problem, where a time-fixed (non-reconfigurable) virtual topology is planned to carry the traffic demand at any time; (ii) the MH-VTD-R (reconfigurable) problem where a time-varying (reconfigurable) virtual topology is designed to more efficiently adapt to known (or estimated) traffic variations. In both problems classes, we consider the number of optical transceivers in the network as the measure of the network cost to optimize. The present work is focused on the MH-VTD-R problem where, as a second optimization criterion, the ...

This paper addresses offline virtual topology design in transparent optical networks under given periodic traffic. We call this planning problem "Scheduled Virtual Topology Design". Two problem variants are considered: for a network based on non-reconfigurable equipment and for a network based on reconfigurable equipment. Two MILP (Mixed Integer Linear Program) formulations are proposed, one for each alternative. The number of transceivers in the network is the selected cost figure to minimize. Tests are performed to evaluate the benefits of using reconfigurable equipment under different traffic conditions and network sizes. The reduction in the number of transceivers obtained by allowing temporal variations in the virtual topology seems low in all cases, indicating that using reconfigurable equipment may not be cost-effective for periodic traffic. Keywords: All-optical networks, virtual topology design, multilayer optimization, scheduling. INTRODUCTIONTransparent optical networks have been proposed to decrease costs and increase capacity in the Future Internet, i.e., "converged" multi-granular network architectures [1], [2]. In transparent optical networks, traffic is carried onto lightpaths which occupy one transmission wavelength in each traversed link. The carried traffic is electronically processed at the ingress and egress nodes of the lightpath, but not at intermediate transit nodes, saving electronic switching costs, and providing the data plane with a sort of traffic format transparency.The Wavelength Switch Fabric (WSF) is the central optical part of a switching node in transparent optical networks. A WSF can have a fixed or reconfigurable structure. In non-reconfigurable switching fabrics, connections between the input and output ports of the WSF are manually hard-wired. However, if the WSF is a device implemented using reconfigurable optical add/drop multiplexers (R-OADM) or reconfigurable wavelength crossconnects (R-WXC), then connections from input to output ports can be dynamically reconfigured allowing lightpaths to change along the time.In this paper, we focus on the offline planning of transparent optical networks for a given periodic traffic demand, which changes along a sequence of time intervals. The objective of our planning problem is to find the most cost-effective (i) scheduled virtual topology design, and (ii) routing of the electronic flows on top of the virtual topology.Scheduled virtual topology design determines the number of lightpaths to be established between every inputoutput pair of nodes over time. This resolves the number of transceivers needed in the network, which is a common cost figure of interest. Naturally, in the lower layer, each lightpath in the virtual topology has to be routed over the physical topology and assigned a wavelength. This problem is called the Routing and Wavelength Assignment (RWA) problem [3]. In this paper, we assume that the network links support a sufficient number of wavelengths for any RWA scheme. Thus, the physical-layer constraints do ...

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