# Traffic Engineering approaches using Multicriteria Optimization Techniques

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3 2 Optimizing OSPF Routing Configurations 2. Problem Definition The optimization framework proposed in this work aims to provide network administrators with efficient OSPF link weights, taking into account the users demands, the network topology and other features of the network domain. In OSPF, all links are associated with an integer weight. Every node uses these weights as an input to the Dijkstra algorithm [3] to calculate the shortest paths to all other nodes. All the traffic from a given source to a destination travels along the shortest path, except when two or more paths have the same length, in that case, traffic is divided among the arcs in these paths (load balancing) [2]. The framework assumes that client demands are mapped into a matrix summarizing, for each source/destination edge router pair, a given required bandwidth and, if also defined, a target edge-to-edge delay to be supported by the network domain. Network Scenario Example Solution A [00Mbps,50ms] [Mbps,0ms] [00Mbps,70ms] [00Mbps,00ms] [0Mbps,80ms] [00Mbps,50ms] [2Mbps,5ms] [50Mbps,5ms] [0Mbps,50ms] [Mbps,0ms] [0Mbps,60ms] B Network Optimization Tool weight weight weight weight weight weight weight weight Network Administrator weight PATH PATH 2 Fig.. Example of a network scenario. As an illustrative example, consider the network scenario included in Figure, involving only a single demand between the network node A and node B. If such demand reflects only a delay target, the administrator should be able to use OSPF weights that result in a data path with the minimum delay between such nodes, i.e path. In a different perspective, if no delay requirements are assumed, and the unique constraint between such nodes is a given bandwidth target, the administrator would try to minimize the network congestion and assign OSPF weights to force a data path inducing the lowest level of losses in the traffic (path 2 ). These two distinct optimization aims would result in two distinct sets of OSPF weights. Additionally, also considering that a given demand may have simultaneously bandwidth and delay constraints, then it is expected that the OSPF weight optimization process try to find a data path representing There are several techniques to obtain traffic demand matrices which provide estimations regarding the overall requirements within a given domain (e.g. [6] [7]).

4 a trade-off between such requirements. The example of Figure is, intentionally, extremely simple and only one demand was considered in the network domain. Assuming now that each router pair of a given Internet Service Provider (ISP) may have specific multi-constrained QoS requirements (i.e. traffic demands vs. delay restrictions), it is easy to understand how complex the problem can get, with the need of obtaining OSPF settings able to optimize multiple parameters. The formulation model sustaining the proposed optimization framework follows the traditional mathematical networking model, representing routers and transmission links by a set of nodes (N) and arcs (A), respectively, in a directed graph G = (N, A) [9], with each arc having a specific bandwidth capacity and a propagation delay, both intrinsic in the network topology 2. Additionally, a demand matrix is available (D), where each element represents the traffic demand between a pair of nodes, allowing to calculate the total load on each arc. This value is used to define a congestion measure for each link, that can be used to compute a penalty function that exponentially penalizes high values of congestion (e.g. a function such the one used in [2]). The framework was also enriched with the possibility of including delay requirements for each pair of routers in the network. These are modeled as a matrix (DR) that, for each pair of nodes, gives the delay target for traffic between the origin and destination. In a similar way, a cost function was defined to evaluate the delay compliance for each scenario. This, in turn, allowed the definition of a delay minimization cost function. One illustrative example of the type of optimization problems addressed in our framework is to find the set of OSPF weights that simultaneously minimizes the cost functions associated with network congestion and with the edge-to-edge delay penalties of the network domain, making the problem addressed in this work clearly multi-objective. In the proposed model, given a specific network topology, a traffic demand matrix (D) and a delay requirements matrix (DR), the objective is to achieve a set of OSPF weights (w) that simultaneously minimize the functions Φ (w) and γ (w), which are the penalty functions for congestion and edge-to-edge delays, respectively 3. In this context, the cost of associated with a given weight solution w is evaluated using functions Φ (w) for congestion and γ (w) for delays, with both functions normalized in the same range. The theoretical minimum value for the functions is ; acceptable values for such network functions are in the range [, 0] meaning that the traffic demands and delays restrictions (D, DR matrices) are accomplished by the routing configuration. 2.2 Multi-objective Evolutionary Algorithms This section explains how multi-objective Evolutionary Algorithms () are adapted to be used in this work. The multi-objective nature of this problem suggests are good candidates for algorithms in the multi-objective optimization area, i.e. that return a set of solutions with distinct trade-offs between 2 It was considered that the delay in each path is dominated by propagation delays. However, if required, queuing delays are also easily incorporated in the framework. 3 Details of these cost functions can be found in similar model formulations (e.g. [4]).

6 randomly generated solutions are analyzed and the best is selected; and Unit - sets every link weight to one. These heuristic are used for comparative terms, i.e. to assess the order of magnitude of the improvements obtained by the. 3 Performance Analysis BRITE Topology Generator Traffic Demands Delay Constraints Multi Objective Evolutionary Algorithms Solutions Pareto Front Fig. 2. Testbed for performance evaluation of the proposed framework. Figure 2 shows the experimental testbed used to assess the performance of the devised link weight setting optimization solution. The BRITE [3] topology generator was used to create distinct synthetic networks. The optimization results presented in this section were taken from two networks with N {30, 50} nodes, with a node average degree of m = 4, resulting in topologies with 0 and 90 links, respectively. The capacity of the links varies in the interval [, 0] Gbits and the topology generation follows the Barabasi-Albert model 4. In order to generate the traffic demands and delay constraints matrices two parameters (each one with three distinct values) were used, D p {0., 0.2, 0.3} and DR p {3, 4, 5}, allowing to tune the difficulty levels of traffic demands and delay requirements, respectively. The precise values of D p and DR p parameters were selected in accordance with the overall congestion and delay constraints levels which are intended to be imposed to each network instance, given their particular characteristics. In the devised test methodology, scenarios assuming higher values for the D p parameter and, simultaneously, lower values of the DR p parameter are the ones harder to comply 5. Based on the network topology, the demand matrices and on an initial weight assignment to the network links, a proprietary OSPF simulator will distribute the traffic along the paths, turning possible the computation of the Φ (w) and γ (w) values. The optimization module of Figure 2 will then resort to the MOEA optimization approach explained before to find the solution for the optimization problem. In the following sections the results were obtained with the optimization module operating with the NSGA-II algorithm. 4 A heavy-tail distribution was used along with an incremental grow type (the parameters HS and LS have values of 000 and 00, respectively). 5 Higher values of D p mean that higher traffic demands are being considered, being harder to comply. In counterpoint, higher values for the DR p mean that higher values for edge-to-edge delays requirements are being considered, being easier to comply.

7 3. Illustrative Analysis of Performance Congestion vs. Delay Cost Values ( and Heuristics) 000 Random Unit L2 InvCap 5 4 example of a feasible solution for the link weight setting problem 00 0 Solutions Solutions from the Pareto Front Fig. 3. a) Comparative perspective of the and heuristics results (logarithmic scale); b) results (i.e. only the white area from Fig. 3 a)). As an initial illustrative example of the optimization capabilities we select one particular instance of a network with 30 nodes and 0 links, with D p = 0. and DR p = 3. In this context, a brief analysis of the Pareto front returned by the MOEA is presented, along with comparative analysis of the performance obtained from the use of commonly used heuristics. This example will be complemented, in the next section, with additional optimization results for other network instances. However, in general terms, the conclusions drawn for this particular instance are representative of the overall performance capabilities of the proposed optimization framework. Figure 3 a) shows a particular subset of the solutions obtained by the in the selected scenario and, for comparative terms, the ones obtained by common heuristics described before. Figure 3 a) has two distinct areas, the first one corresponds to solutions assuming routing configurations able to obey the considered traffic and delay demands (i.e. the white area, where cost function values are lower than 0), and a second area were the routing solutions lead to quality degradation of the network, with overloaded links or with the target delays requests not being assured by the network (gray filled area) 6. As observed in Figure 3 a) the MOEA available in the proposed solution is able to provide the network administrator with a set of near-optimal routing configuration solutions for the network domain. In opposition, it is also noticeable that all the results of the heuristics for this instance lie outside the admissible range (i.e. outside the white area), and some of them with penalties which are one or two orders of magnitude higher than the ones obtained by. 6 Note that in the dark gray filled area none of the requests are accomplished.

8 This means that none of the heuristics is able to provide acceptable routing configurations 7. Figure 3 b) magnifies the white area of Figure 3 a) and now only the solutions are plotted. As observed, the administrator achieves a set of nearoptimal configuration solutions resulting from the Pareto front of the optimization process, all lying inside of the white area. Each one of such points (solutions) is associated with a routing weights table able to be used by the administrator according with the desired trade-off between the optimization objectives. 3.2 Optimization Results This section analyzes the optimization results for ten distinct network scenarios. The examples where taken from two networks with N {30, 50} nodes and using five distinct combination of (D p, DR p ) parameters, in this case the set {(0., 3), (0., 5), (0.2, 4), (0.3, 3), (0.3, 5)}. In the considered scenarios, the behavior of the heuristics is similar to the describe before, i.e. they are not capable of achieving acceptable performance, meaning that these solutions are completely outside of the white area of the graphs. For that reason, such results are not included in the following analysis. Figure 4 shows the Pareto fronts obtained for each of the considered scenarios. It is important to note that results were obtained in the first runs of the MOEA optimization procedures, i.e. only a single run of the optimization algorithm has been performed for each of the network instances. As observed in Figure 4, for most of the scenarios the first run of the MOEA was sufficient to find acceptable results i.e. Pareto fronts with solutions (i.e. weight settings) in the white area of the figures. The administrator is then able to select these solutions in order to reach near-optimal routing configurations obeying to the imposed constraints. As expected, the harder optimization scenarios are the ones imposing higher requirements regarding both the traffic demands and delay restrictions (e.g. D p = 0.3, DR p = 3). In such scenarios, the Pareto front patterns returned by the are not so close to the graph origin as in other network configurations. As observed in Figure 4, the first run of the MOEA was not sufficient to find near-optimal configurations for the last two scenarios with and (D p, DR p ) values of (0.3, 3) and (0.3, 5). To improve such preliminary results additional runs of the could be used to generate other weight setting configurations overcoming the performance obtained in previous runs. In order to illustrate the previous reasoning, Figures 5 a), b) and c) plot additional optimization results obtained in other runs of the for three specific scenarios (including the instances with lower quality results in the first run). The new Pareto fronts depicted in Figures 5 a), b) and c) are compared with the values obtained in the first runs (observed before in Figure 4). The analysis clearly shows an improvement of the Pareto front patterns for each scenario, containing now several points in the white regions of the figures. This 7 Note that in Fig. 3 a) a logarithmic scale is used, meaning that points outside the white area represent, in fact, extremely poor quality routing solutions.

9 N = 30 Dp= 0. DRp= N = 30 Dp= 0. DRp= N = 30 Dp= 0.2 DRp= N = 30 DRp= N = 30 DRp= Dp= 0. DRp= Dp= 0. DRp= Dp= 0.2 DRp= DRp= DRp= Fig. 4. MOEA optimization results - Pareto fronts - for two synthetic networks (N = 30, 50) with distinct combinations of D p and DR p parameters (first runs). behavior is visible in Figures 5 a), b) and c) and corresponds to a generalized displacement of the Pareto fronts to the feasible configuration area. 3.3 Single-objective vs Multi-objective Evolutionary Algorithms This section compares the proposed framework approach with other approaches in the area which assume this problem under a single objective optimization perspective. In such works, a linear weighting scheme could be used to denote the overall cost of the solution, as expressed in Equation. f(w) = αφ (w) + ( α)γ (w), α [0, ] ()

10 00 (st run) (improved results) (st run) (improved results) 0 N = 30 DRp= DRp= 3 5 Congestion vs. Delay Cost Values ( and Single Objective EAs) 0 (st run) (improved results) DRp= SO EAs Fig. 5. a) b) c) Improved results for three particular network instances of Figure 4 (in runs 2, 23 and 6, respectively); d) and single objective algorithm results. When using a single objective evolutionary algorithm, the user specifies the parameter (α) defined above, that determines the importance that is given to each objective (congestion and delays). Examples of performance analysis of this approach can be found in [4], for a large set of distinct QoS constrained scenarios. Although this strategy has obtained acceptable results, it suffers from one main drawback, since it assumes that there is one single trade-off that is optimum. Therefore, the algorithms typically return one single solution that has to be implemented by the administrator. To be able to analyze several distinct trade-offs between the two objectives, the user needs to execute different runs of the algorithm using different values of the parameter α. Moreover, for specific network configurations several tradeoffs between the congestion and delays requirements are not possible to be achieved, and the administrator will have the doubt about which values are admissible to tune the α parameter. For comparative analysis, in addition to the MOEA used in the example of Figure 3 also a single objective evolutionary algorithm was run using the objective function of Equation. The single-objective algorithm was run with three distinct values of the parameter α (0.25, 0.5 and 0.75). Figure 5 d) shows the results obtained, showing a set of selected solutions obtained by the MOEA and also the best solution obtained by each of the single-objective evolutionary algorithms. It is important to note that all the solutions shown for the multi-objective optimization are obtained in a single run, while the solutions for the single objective need three distinct runs. Looking at the Figure 5 d), and although a direct comparison of the results obtained by the alternative approaches is not

12 contribution for the traffic engineering research efforts, the proposed framework integrates efficient multi-objective optimization algorithms from the evolutionary computation area. The presented results corroborate the idea that this optimization solution brings important advantages and enlarges the set of available options to network administrators, in shorter computation times, increasing the capacity of making informed decisions regarding the trade-offs between the different factors at stake. The supporting framework is currently under rapid development and additional functionalities may be also target of the MOEA optimization perspective. The class-based [5] and multicast [4] optimization mechanisms are two examples of developments which are suitable to be improved taking advantage of the presented MOEA based optimization approach. References. Z. Wang. Internet QoS: Architectures and Mechanisms for Quality of Service. Morgan Kaufmann Publishers, B. Fortz and M. Thorup. Internet Traffic Engineering by Optimizing OSPF Weights. In Proceedings of IEEE INFOCOM, pages , E. W. Dijkstra. A note on Two Problems in Connexion with Graphs. Numerische Mathematik, (269-27), P. Sousa, M. Rocha, M. Rio, and P.Cortez, Efficient OSPF Weight Allocation for Intra-domain QoS Optimization in 6th IEEE Intern. Workshop on IP Operations and Management, IPOM 2006, LNCS 4268, pages 37-48, Springer-Verlag, M. Rocha, P. Sousa, P. Cortez and M. Rio, Quality of Service Constrained Routing Optimization using Evolutionary Computation, Applied Soft Computing, (), pages , Elsevier, A. Medina et al. Traffic matrix estimation: Existing techniques and new directions. Computer Communication Review, 32(4):6 76, A. Davy et al. An Efficient Process for Estimation of Network Demand for Qosaware IP Networking Planning. 6 th IEEE Intern. Workshop on IP Operations and Management, IPOM 2006, LNCS 4268, pages Springer-Verlag, Anders Gunnar, Mikael Johansson, Thomas Telkamp. Traffic matrix estimation on a large IP backbone: a comparison on real data In IMC 04: Proceedings of the 4th ACM SIGCOMM conference on Internet measurement, pp , R. Ahuja, T. Magnanti, and J. Orlin, Network Flows. Prentice Hall, J. Moy. RFC 2328: OSPF version 2, April Z. Michalewicz. Genetic Algorithms + Data Structures = Evolution Programs, 3rd ed.. USA: Springer-Verlag, J. Moy. OSPF, Anatomy of an Internet Routing Protocol. Addison Wesley, A. L. A. Medina, I. Matta, and J. Byers. BRITE: Universal Topology Generation from a Users Perspective, Tech. Rep , Jan P. Sousa, M. Rocha, P. Cortez and M. Rio. Multiconstrained Optimization of Networks with Multicast and Unicast Traffic. Management of Converged Multimedia Networks and Services, Springer, LNCS 5274, pages 39-50, P. Sousa, M. Rocha, M. Rio and P. Cortez. Class-Based OSPF Traffic Engineering Inspired on Evolutionary Computation, WWIC Wired/Wireless Internet Communications, pp. 4-52, Springer-Verlag, C. Coello. A Comprehensive Survey of Evolutionary-Based Multiobjective Optimization Techniques Knowledge and Information Systems (3):29-56, 999.

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