Strategies for optimal logical topology design and traffic grooming

Traffic grooming techniques are used to combine low-speed data streams onto high-speed lightpaths with the objective of minimizing the network cost, or maximizing the network throughput. In this article, we present a complete suite of efficient Integer Linear Program (ILP) formulations for logical topology design and traffic grooming on mesh WDM networks. Our formulations can be easily modified to implement different objective functions and, contrary to previous formulations, our ILP formulation can be used to generate optimal solutions for practical sized networks with hundreds of requests. Our first set of formulations addresses the complete logical topology design traffic grooming problem, including RWA and traffic routing. The second set uses the simplifying assumption that RWA is not an issue. The last two sets address optimal traffic grooming alone, where the logical topology is already specified. We have studied these formulations, using simulation with networks having up to 30 nodes, and with hundreds and, in some cases, over a thousand low-speed data streams and have shown that the formulations are able to generate optimal solutions within a reasonable amount of time.     

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.     

IP/ MPLS over WDM网中考虑QoS的VPN业务设计

本文研究了在IP／MPLS over WDM网络中支持不同QoS要求的VPN业务的逻辑拓扑设计问题。对于给定的网络物理拓扑和业务需求矩阵，本文提出，基于不同时延要求的VPN业务逻辑拓扑设计可以运用两种方法加以解决。一为基于迭代的线性规划方法，适合于规模较小的网络。另一个为启发式算法，可运用于网络规模较大的环境。对比仿真结果表明，启发式算法不但较好地解决了不同QoS要求的VPN业务的选路和波长分配问题，还较好地降低了链路的最大负载。     

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     

Virtual Topology Design and Reconfiguration of Virtual Private Networks (VPNs) over All-Optical WDM Networks

This paper studies the virtual topology design and reconfiguration problem of virtual private networks (VPNs) over all-optical WDM networks. To support VPN service, a set of lightpaths must be established over the underlying WDM network to meet the VPN traffic demands and this set of lightpaths must also be dynamically reconfigurable in response to changing VPN traffic. To achieve good network performance and meet the service requirements of optical virtual private networks (oVPNs), we formulate the problem as an integer programming problem with multi-objectives and present a general formulation of the problem. In the formulation, we take into account the average propagation delay over a lightpath, the maximum link load, and the reconfiguration cost with objectives to minimize the three metrics simultaneously. The formulated problem is NP-hard and is therefore not practical to have exact solutions. For this reason, we use heuristics to obtain approximate optimal solutions and propose a balanced alternate routing algorithm (BARA) based on a genetic algorithm. To make the problem computationally tractable, we approximately divide BARA into two independent stages: route computing and path routing. At the route computing stage, a set of alternate routes is computed for each pair of source and destination nodes in the physical topology. At the path routing stage, an optimal route is decided from a set of alternative routes for each of the lightpaths between a pair of source and destination nodes. A decision is subject to the constraints and objectives in the formulation. To improve the computational efficiency, we use a genetic algorithm in BARA. Through simulation experiments, we show the effectiveness of BARA and the evolution process of the best solution in a population of solutions produced by the genetic algorithm. We also investigate the impact of the number of alternative routes between each pair of source and destination nodes on the optimized solutions.     

Survivable lightpath routing: a new approach to the design ofWDM-based networks

Network restoration is often done at the electronic layer by rerouting traffic along a redundant path. With wavelength-division multiplexing (WDM) as the underlying physical layer, it is possible that both the primary and backup paths traverse the same physical links and would fail simultaneously in the event of a link failure. It is, therefore, critical that lightpaths are routed in such a way that a single link failure would not disconnect the network. We call such a routing survivable and develop algorithms for survivable routing of a logical topology. First, we show that the survivable routing problem is NP-complete. We then prove necessary and sufficient conditions for a routing to be survivable and use these conditions to formulate the problem as an integer linear program (ILP). Due to the excessive run-times of the ILP, we develop simple and effective relaxations for the ILP that significantly reduces the time required for finding survivable routings. We use our new formulation to route various logical topologies over a number of different physical topologies and show that this new approach offers a much greater degree of protection than alternative routing schemes such as shortest path routing and a greedy routing algorithm. Finally, we consider the special case of ring logical topologies for which we are able to find a significantly simplified formulation. We establish conditions on the physical topology for routing logical rings in a survivable manner     

Design of virtual topologies for large optical networks through an efficient MILP formulation

In this paper we propose a Mixed-Integer Linear Programming (MILP) formulation for designing virtual topologies of wavelength-routed optical networks, considering as objective function the minimization of the traffic electronically forwarded at the network nodes. Our goal is twofold. Firstly, to reduce packet router processing requirements of the electronic routers, and secondly, to get the most transparent traffic distribution for a given traffic matrix, using the available optical resources at the nodes. The proposed formulation was applied successfully to reasonable sized networks yielding optimal solutions in a few minutes. To the best knowledge of the authors, this is the first report on optimizing virtual topology and traffic routing of large optical networks with a low computational cost MILP formulation.     

Network coding for multiple unicast sessions in multi-channel/interface wireless networks

Throughput limitation of wireless networks imposes many practical problems as a result of wireless media broadcast nature. The solutions of the problem are mainly categorized in two groups; the use of multiple orthogonal channels and network coding (NC). The networks with multiple orthogonal channels and possibly multiple interfaces can mitigate co-channel interference among nodes. However, efficient assignment of channels to the available network interfaces is a major problem for network designers. Existing heuristic and theoretical work unanimously focused on joint design of channel assignment with the conventional transport/IP/MAC architecture. Furthermore, NC has been a prominent approach to improve the throughput of unicast traffic in wireless multi-hop networks through opportunistic NC. In this paper we seek a collaboration scheme for NC in multi-channel/interface wireless networks, i.e., the integration of NC, routing and channel assignment problem. First, we extend the NC for multiple unicast sessions to involve both COPE-type and a new proposed scheme named as Star-NC. Then, we propose an analytical framework that jointly optimizes the problem of routing, channel assignment and NC. Our theoretical formulation via a linear programming provides a method for finding source–destination routes and utilizing the best choices of different NC schemes to maximize the aggregate throughput. Through this LP, we propose a novel channel assignment algorithm that is aware of both coding opportunities and co-channel interference. Finally, we evaluate our model for various networks, traffic models, routing and coding strategies over coding-oblivious routing.     

A generalized service deployment framework for OSPF networks using multi‐topology routing: Modeling and methodology

The exponential growth of various applications requires deploying an ever‐growing number of network services. A generalized service deployment framework for Open Shortest Path First (OSPF) networks is proposed in this paper. The framework includes placing programmable routers, distributing different types of services on these routers, and leading traffic flow through them according to the predetermined sequence order requirement. However, it is not possible to direct all the traffic flows through the required service nodes along the shortest path with a single and suitable set of link weights. To address the issue, multiple topology routing (MTR) technique is incorporated to have various logical topologies with multiple sets of link weights. Correspondingly, the problem of jointly optimizing Placement of programmable routers, Distribution of different types of services among these routers, and Link Weights setting based on MTR (shortened to PD‐LW‐MTR) and its mixed integer linear programming formulation are presented in this paper. A novel decomposition algorithm is also proposed to address this problem efficiently. Experiment results validate the correctness and feasibility of our algorithm. It is also shown that the optimization algorithm can obtain near‐optimal solution and just only a few logical topologies over multiple sets of link weights are necessary for traffic flows to guarantee service order requirements.     

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     

Capacity dimensioning and routing for hybrid satellite and terrestrial systems

Satellite network architecture plays an important role in the success of a satellite business. For future commercial broadband data satellite networks integrated with the terrestrial network, satellite network topology, link capacity, and routing have major impacts on the cost of the network and the amount of revenue the network can generate. To find the most cost-effective satellite network topology, we propose a unified mathematical framework using a two-stage stochastic programming formulation. The solution to the stochastic programming formulation gives optimal link capacities and an optimal routing strategy for different network topologies, taking into account uncertainties in long-term aggregate traffic statistic estimation. Using a simple satellite network example, we show the feasible topology regions for three different satellite topologies and show that, for some parameter values, the hybrid topology is more cost effective than nonhybrid topologies. In the limit of high traffic rejection cost, stochastic dimensioning reduces to static dimensioning. We study worst case static dimensioning for a general geosynchronous earth orbit satellite network and show the feasible topology regions, as well as effective cost comparisons for different topologies. We conclude with a discussion on network cost and architectural flexibility relating to satellite network design.     

Reconfiguration of Logical Topologies with Minimum Traffic Disruptions in Reliable WDM-Based Mesh Networks

A wavelength division multiplexing (WDM) network offers a flexible networking infrastructure by assigning the route and wavelength of lightpaths. We can construct an optimal logical topology, by properly setting up the lightpaths. Furthermore, setting up a backup lightpath for each lightpath improves network reliability. When traffic demand changes, a new optimal (or sub-optimal) topology should be obtained by again applying the formulation. Then, we can reconfigure the running topology to the logical topology obtained. However, during this reconfiguration, traffic loss may occur due to the deletion of older lightpaths. In this paper, we consider reconfiguring the logical topology in reliable WDM-based mesh networks, and we propose five procedures that can be used to reconfigure a running lightpath to a new one. Applying the procedures one by one produces a new logical topology. The procedures mainly focus on utilizing free wavelength resources and the resources of backup lightpaths, which are not used usually for transporting traffic. The results of computer simulations indicate that the traffic loss is remarkably reduced in the 14-node network we used as an example.     

A novel robust routing algorithm for multi-granularity connection requests in wavelength division multiplexing mesh networks

In this paper, we propose a novel robust routing algorithm based on Valiant load-balancing under the model of polyhedral uncertainty (i.e., hose uncertainty model) for WDM (wavelength division multiplexing) mesh networks. Valiant load-balanced robust routing algorithm constructs the stable virtual topology on which any traffic patterns under the hose uncertainty model can be efficiently routed. Considering there are multi-granularity connection requests in WDM mesh networks, we propose the method called hose-model separation to solve the problem for the proposed algorithm. Our goal is to minimize total network cost when constructing the stable virtual topology that assures robust routing for the hose model in WDM mesh networks. A mathematical formulation (integer linear programming, ILP) about Valiant load-balanced robust routing algorithm is presented. Two fast heuristic approaches are also proposed and evaluated. We compare the network throughput of the virtual topology constructed by the proposed algorithm with that of the traditional traffic grooming algorithm under the same total network cost by computer simulation.     

Enhanced Optimal and Heuristic Solutions of the Routing Problem in Light-Trail Networks

Light-trail is an efficient and feasible technology for IP transport over all-optical networks. The proposition of light-trails for all-optical networks has demonstrated a number of advantages over other paradigms such as Wavelength Routing (WR), Optical Burst Switching (OBS) and Optical Packet Switching (OPS). This article tackles the routing problem of light-trails with the solution objective of minimizing the number of needed light-trails to accommodate an offered traffic matrix. We present two enhancements to the Integer Linear Programming (ILP) formulation of the routing problem. We also propose a computationally efficient routing heuristic for use with static and incremental traffic models. The heuristic is based on routing flows one-by-one. This is done by assigning a set of attributes to each flow and to each network path. The flow attributes are used to determine the order in which flows are presented to the routing algorithm. The path attributes are used to determine which path is selected to route the flow at hand. The efficiency of the proposed heuristic is confirmed using example problems of different network topologies.     

A Lagrangian-Relaxation Based Network Profit Optimization For Mesh SONET-Over-WDM Networks

In Wavelength Division Multiplexing (WDM) networks, the huge capacity of wavelength channels is generally much larger than the bandwidth requirement of individual traffic streams from network users. Traffic grooming techniques aggregate low-bandwidth traffic streams onto high-bandwidth wavelength channels. In this paper, we study the optimization problem of grooming the static traffic in mesh Synchronous Optical Network (SONET) over WDM networks. The problem is formulated as a constrained integer linear programming problem and an innovative optimization objective is developed as network profit optimization. The routing cost in the SONET and WDM layers as well as the revenue generated by accepting SONET traffic demands are modelled. Through the optimization process, SONET traffic demands will be selectively accepted based on the profit (i.e., the excess of revenue over network cost) they generate. Consiering the complexity of the network optimization problem, a decomposition approach using Lagrangian relaxation is proposed. The overall relaxed dual problem is decomposed into routing and wavelength assignment and SONET traffic routing sub-problems. The subgradient approach is used to optimize the derived dual function by updating the Lagrange multipliers. To generate a feasible network routing scheme, a heuristic algorithm is proposed based on the dual solution. A systematic approach to obtain theoretical performance bounds is presented for an arbitrary topology mesh network. This is the first time that such theoretical performance bounds are obtained for SONET traffic grooming in mesh topology networks. The optimization results of sample networks indicate that the roposed algorithm achieves good sub-optimal solutions. Finally, the influence of various network parameters is studied.     

Algorithms for the global design of WDM networks including the traffic grooming

In this paper, we propose a model and algorithms for the global design problem of wavelength division multiplexing (WDM) networks including the traffic grooming. This problem consists in finding the number of fibres between each pair of nodes (i.e. the physical topology), finding the number of transponders at each node, choosing the set of lightpaths (i.e. the virtual topology), routing these lightpaths over the physical topology and, finally, grooming and routing the traffic over the lightpaths. Since this problem is NP-hard, we propose two heuristic algorithms and a tabu search metaheuristic algorithm to find solutions for real-size instances within a reasonable amount of computational time.     

Toward energy‐proportional Internet core networks: an energy‐minimized routing and virtual topology design for Internet protocol layer

With the exponential growth of Internet traffic, the energy consumption issue of core networks is increasingly becoming critical. Today's core networks are highly underutilized most of the time because of the over‐provisioning and redundancy dimensioning, which results in severe energy inefficiency. In previous work, many non‐deterministic polynomial‐time hard mathematics formulation models have been proposed to minimize the energy consumption of core networks. However, effective heuristics are needed to solve these models in medium/large‐size networks. This work studies the energy‐minimized routing and virtual topology design problem of the power‐hungry Internet protocol (IP) layer in core networks, aiming to achieve an energy‐proportional IP layer by exploiting the variation of traffic with hours to reconfigure virtual topology and reroute traffic. We formulate energy‐minimized routing and virtual topology design as an Integer linear programming problem and propose a LR algorithm, a heuristic based on the Lagrangian relaxation, to solve this problem in a polynomial‐time. The simulation results indicate that the LR algorithm outperforms the best previous algorithm and can achieve a near energy‐proportional IP layer with significant power saving. Furthermore, a detailed analysis of simulation results is conducted, which suggests a design principle of network equipment to facilitate the power saving. Copyright © 2013 John Wiley & Sons, Ltd.     

Comparison of ILP formulations for the RWA problem

We present a review of the integer linear programming (ILP) formulations that have been proposed for the routing and wavelength assignment problem in WDM optical networks assuming asymmetrical traffic. We show that all formulations proposed under asymmetrical traffic assumptions, both link and path formulations, are equivalent in terms of the upper bound value provided by the optimal solution of their linear programming relaxation, although their number of variables and constraints widely differ. We propose improvements for some of the formulations that result in further reductions in the number of variables and constraints.Under the objective of minimizing the blocking rate, we propose an experimental comparison of the best lower and upper bounds that are available. We then discuss the easiness of exact ILP solution depending on the formulations. We observe that LP relaxation bounds often provide solutions with a value very close to the optimal ILP one. We solve exactly for the first time several RWA (Routing and Wavelength Assignment) realistic instances, including those proposed by Krishnaswamy and Sivarajan [R. Krishnaswamy, K. Sivarajan, Algorithms for routing and wavelength assignment based on solutions of LP-relaxation, IEEE Communications Letters 5 (10) (2001) 435–437], with a proof of the optimality.     

Optimal Link Weights for IP-Based Networks Supporting Hose-Model VPNs

From traffic engineering point of view, hose-model VPNs are much easier to use for customers than pipe-model VPNs. In this paper we explore the optimal weight setting to support hose-model VPN traffic in an IP-based hop-by-hop routing network. We try to answer the following questions: (1) What is the maximum amount of hose-model VPN traffic with bandwidth guarantees that can be admitted to an IP-based hop-by-hop routing network (as opposed to an MPLS-based network), and (2) what is the optimal link weight setting that can achieve that? We first present a mixed-integer programming formulation to compute the optimal link weights that can maximize the ingress and egress VPN traffic admissible to a hop-by-hop routing network. We also present a heuristic algorithm for solving the link weight searching problem for large networks. We show simulation results to demonstrate the effectiveness of the search algorithm.