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IEICE TRANS. COMMUN., VOL. E84-B, No.11 NOVEMBER 2001 1 PAPWE Special Section on the APCC Proceedings Topology Reconfiguration of an IP Network Embedded over an ATM Network Sang Ahn†, Meejeong Lee‡, and Tatsuya Suda† Summary between the current network topology and the traffic If IP networks are embedded over the facility networks flowing over the network. such as ATM or DWDM, link addition or removal is The flexibility to dynamically reconfigure an overlaid easily accomplished by setting up or tearing down network has been well recognized and exploited for digital switched virtual circuits. Exploiting the flexibility of this cross-connect systems, facility networks for an ATM light-overhead reconfiguration, we propose a dynamic network connectivity [1,6]. More recently, this issue has topology reconfiguration scheme to improve network been extensively studied in the context of WDM networks, utilization and the quality of services. The proposed where a network topology is updated on the fly [3,5]. dynamic topology reconfiguration scheme alleviates Most existing efforts, however, deal with reconstructing a transient surge of traffic or congestion by temporarily topology entirely, instead of partially reconfiguring the adding IP links to the underlying IP network topology network. However, reconfiguring an entire network (built based on long-term traffic predictions). Identifying topology suffers from a large overhead. A more practical locations for additional IP links and deciding the amount and cost effective way of performing dynamic topology of bandwidth to allocate to such additional IP links is a reconfiguration is to partially modify an existing topology NP-hard optimization problem, and thus, in our research, to improve network’s ability to accommodate temporal Genetic Algorithm is adopted, a widely accepted traffic changes. technique for searching near-optimal solutions in a large The proposed scheme specifically targets at the cases search space. The numerical results show that the where the initial topology is kept on a long time basis. proposed scheme effectively alleviates the transient This is often required in the real world since the initial congestion and that the computation overhead is moderate network is usually designed based on the average long such that the proposed technique is applicable to short/mid term traffic requirements. In order to facilitate this term traffic fluctuations. objective, we propose a reconfiguration scheme that only Key words: allows addition of links to the current topology keeping topology reconfiguration, dynamic reconfiguration, the links of the original topology as they are. The total embedded network, Genetic Algorithm amount of added bandwidth is assumed to be limited to a certain value in order to reflect real world cost constraint. The proposed scheme deals with a local congestion 1.Introduction incurred by temporary traffic fluctuation effectively by not only ameliorating temporary mismatches efficiently but Compared to the cost (time and management overhead) of also providing the recovery process to the original reconfiguring traditional physical long-haul links, it is topology as simple as possible. rather inexpensive to add or remove IP links using We specifically aim at the IP network built on top of an switched virtual circuits over the facility network such as ATM network, where ATM VCs are used to provide ATM. This flexibility of light-overhead reconfiguration connectivity between IP routing nodes. Although the makes it feasible to dynamically adapt the network proposed scheme is aiming at the IP over ATM topology according to the traffic fluctuations to improve environment, the same technique can be applied to any the network utilization. Through reconfiguration, environment with a packet switching network provisioned topologies of the network may evolve to accommodate on top of any type of connection-oriented underlying increasing traffic or to solve temporary mismatches networks such as DWDM and Frame Relay. Manuscript revised March 1, 2001. † Information and Computer Science, University of California Irvine; ‡Department of Computer Science, Ewha Womans University *This work was supported by the NSF through grants ANI-0083074 and ANI-9903427, by DARPA through Grant MDA972-99-1-0007, by AFOSR through Grant MURI FA9620-00-1-0330, by grants from the University of California MICRO Program Hitachi, Hitachi America, Novell, NTT, NTT Docomo, Fujitsu, and ENICOM, and by the Basic Research Program of the Korea Science & Engineering Foundation through grant 2000-0-303-001-3. IEICE TRANS. COMMUN. VOL. E84 , NO.11 NOVEMBER 2001. 2 2. Problem Formulation Variables: The location of and capacity of the added links There are several different choices with respect to the Constraints: ∑f w∈W w ≤ ∑C w∈W w and ∑A w∈W w ≤X, objective function. In previous works [1, 2], the average where Aw is the amount of the added link capacity for the packet delay is used as the objective function to be minimized. In this paper, we take the average packet loss link, w. When w is not an added new link, Aw = 0 rate, which we think is a more direct indicator of This type of multi-commodity optimization problem is congestion. To compute the average loss rate at each IP known as a NP hard problem [7]. Due to the NP-hardness, link, we modeled each IP node with M/M/1/K queuing we take an approximation approach instead of providing a system to account for packet losses. To get the closed rigid optimal solution. Specifically, we adopt genetic form of packet loss rate in M/M/1/K model, we borrow the algorithm (GA), which is known to be applicable to and result of analysis from [4] as summarized in the following. efficient for finding optimal solutions from a large Let w be an ordered pair of source and destination solution space, mostly in combinatorial problems. GAs are nodes, and W be the set of all the possible pairs. If the known to converge on optimal results faster and more amount of path flow for a source/destination pair w is efficiently than can other search methods [8]. The denoted by rw, the total traffic demand γ fed into the applicability of GA in network planning problems that are network is represented as γ = ∑r w∈W w . Under a certain typical examples of combinatorial problems, was first attempted in [2,8]. GA is applicable only when there is a routing scheme, the link flow on a link w, denoted by fw, closed form objective function available for evaluating the can be estimated from the path flow matrix R = {rw | w ∈ quality of a potential solution. W }, assuming that there is no loss. For the routing scheme, we specifically assume the shortest path routing for a given IP network topology in this paper. The total 3. Topology Optimizer Using Genetic number of packet losses is estimated as a function of the Algorithm link flow fw and the capacity of the link Cw as follows, Each candidate solution in GA is represented in the form 1− ρw Lw ( f w ) = C w ρ ww , ρ w = f w C b of a ‘chromosome’, which is a series of genetic encoding 1− ρwbw +1 w of the specific attributes. Usually it is a sequence or multi- dimensional array of binary numbers. After deciding a , where bw is the buffer capacity of a link w. suitable format, a group of chromosomes constituting the If there is no link between a node pair w, Lw, Cw, ρw , fw, initial population are generated. A GA has to go through a and bw are all defined to be 0. The average loss rate is repetitive process called a generation. A typical steps are then computed as follows. as follows: 1. Preparing a set of candidate chromosomes 1 L= γ ∑L w∈W w ( fw ) 2. Evaluating each of the chromosomes performance 3. Choosing a couple of parent chromosomes With these definitions, we formulate the problem that 4. Applying genetic operators to the two parent the proposed scheme deals with as a topology chromosomes selected in step 3 reconfiguration, where a congestion measure based on the 5. Repeating step 2, 3 and 4 to generate the entire average packet loss is minimized, subject to the constraints population of a new generation of the bandwidth amount added as well as the capacity of 6. Reproduce generations until a certain condition is the underlying facility network. The variables in this met or for a given number of times problem are the selection of the node pairs (temporary Selection process (step 3) is the first step to prepare links) to be directly connected, and the allocation of new chromosomes. After selecting two parent capacity to such links. The topology reconfiguration chromosomes with good genes, genetic operators such as problem that we will deal with can be precisely stated as crossover and mutation are applied. Through crossover follows. operation, a certain number of bits in the parent Given: The initial topology and link capacities of chromosomes are mutually exchanged. After crossover, underlying ATM network, the initial topology and mutation operator is applied with mutation rate. Mutation capacities of the embedded IP network, path flow matrix R, is an operation of toggling some portion of a chromosome, the maximum of the total amount of bandwidth increment resulting in mutated chromosomes that are not directly X, inheriting the genetic codes from its parent chromosomes. Objective: Minimize the average packet loss probability, Mutation increases the variability of the population and L of the IP network, IEICE TRANS. COMMUN. VOL. E84 , NO.11 NOVEMBER 2001 3 reduces the possibility of falling down to local minimum random topologies with 7 nodes, (b) 2 different random in the process of searching a solution. topologies with 40 nodes We assume that the underlying ATM network deploys homogeneous ATM switching nodes, where every switch 4. The Illustration of Topology is assumed to have the same given capacity for the Reconfiguration convenience of discussion. For the IP level topologies, we assume that a specific amount out of the total capacity of To give an intuitive example, Fig. 1 shows the original each ATM node is reserved for the IP traffic. The rest of topology with 7 nodes and the new topology suggested by the capacity of an ATM node is assumed assigned to the the proposed scheme. Those added temporary links are other types of traffic. The proposed scheme will exploit denoted as dotted lines. Below these graphical illustration this capacity assigned for other purposes when additional of the topologies, there are also presented the chromosome links are required. representation of each proposed topology. Table 1 shows We also varied traffic flow requirement imposed on those the amount of link flow and the capacity of each link. topologies. Traffic flow requirements are given as the values of the average flow rate incurred between all the source/ destination pairs at the time instance when the this optimizer is executed. The values of the average traffic flow rate between source/destination pairs have uniformly distributed random values. These traffic flow requirements are given to the optimizer as inputs of two-dimensional array. We applied three different types of average flow 0000000000000000000000 000001000010000010000 matrices for each topology, with total capacity/total flow (a) Initial topology (b) Improved topology ratio of 1: 0.5, 1:1, 1:2, respectively. 1:2 ratio represents overloaded situation by twice than the network’s Fig 1 Graphical representation and chromosome representation maximum capacity in average. Link Flow / Cap Link Flow / Cap 5.1 Convergence of GP topology optimizer link[1][2] 3.3967 / 5 link[1][2] 2.0910 / 5 When solving a problem using genetic algorithm, the link[1][3] 3.5943 / 5 link[1][3] 2.6923 / 5 selection of suitable number of generation to get a link[1][4] 1.9845 / 5 link[1][4] 1.9845 / 5 reasonable data is very crucial. In our experiment, 50 link[1][5] 4.0507 / 5 link[1][5] 2.0213 / 5 generations are selected. In Fig. 2, we present a typical numerical results from our experiment. It shows the link[1][6] 3.3782 / 5 link[1][6] 2.2508 / 5 number of generations for the proposed GA-based link[1][7] 3.6146 / 5 link[1][7] 2.3090 / 5 optimizer to go through to reach a near-optimal solution. link[2][6] 1.6666 / 8 link[2][6] 1.6666 / 8 The performance indicator monotonically increases only link[3][6] 0.4197 / 8 link[3][6] 0.4197 / 8 until reaching 5th generation and keeps almost flat after 5th link[4][6] 1.6666 / 8 link[4][6] 1.6666 / 8 generation until the termination of a whole session of 3000 generations. Typically, taking 50 generations leads to a link[4][7] 1.6666 / 10 link[4][7] 1.6666 / 10 local minimum with less than a certain amount (for link[2][7] 1.3056 / 8 example 2%) of errors compared to the results of last link[3][5] 0.9020 / 4 generation. (3000th generation). link[5][6] 1.1274 / 4 Convergence of optimization result in 7 Table 1. Table of each link and its link flow/capacity node topology 30 abs(log(Avg. 25 Loss Rate)) 5. Numerical Result and Justification 20 15 To present the effectiveness and efficiency of the 10 proposed GP-based topology optimizer, we applied it to IP 5 networks of two different scales. For each scale, several 0 - 2 Number of Generations 4 6 8 10 12 different random topologies are tried. Specifically, our Fig. 2 Convergence of topology optimizer experiments include the following cases; (a) 4 different IEICE TRANS. COMMUN. VOL. E84 , NO.11 NOVEMBER 2001. 4 5.2 Performance Improvement 6. Conclusion In Table 2, the performance indicators of the original Exploiting the reconfiguration flexibility of an embedded topologies and those of the new topologies obtained by the IP networks over a switched facility network, we proposed GA-based optimizer are compared for all the cases that we a dynamic topology reconfiguration scheme to cope with included in our experiments. Due to the observation in Fig. transient congestion. We formulate the problem as a 2, all the performance indicator values for the new reduced topology optimization problem to minimize the topology in this table are the ones taken after 50th degree of congestion. GA is adopted as the solution to the generation. problem. The proposed topology reconfiguration scheme is applied to various network topologies and traffic load distributions to test its validity and applicability. Flow 1 Flow 2 Flow 3 Numerical results show that the proposed topology IT GT IT GT IT GT reconfiguration may effectively alleviate the temporary T1 3.680 19.448 18.591 43.437 31.276 51.738 congestion, and the computation time may allow the T2 4.720 19.306 21.790 38.641 34.554 51.589 proposed topology reconfiguration to be performed T3 11.365 26.844 30.299 45.703 43.183 58.694 several times a day as traffic flow requirements fluctuate. T4 17.526 45.569 36.833 65.309 49.776 78.363 T5 9.302 29.462 33.876 54.561 48.640 69.368 T6 10.326 30.880 36.186 58.234 53.544 76.201 References [1] M. Gerla, J. A. S. Monteiro, and R. Pazos, “Topology Table 2. Performance (throughput) Improvement design and bandwith allocation in ATM nets,” IEEE J. Select. Areas Commun., vol. 7, pp. 1253-1262, Oct 1989 The performance values indicated in this table are [2] K. S. Tang, K. T. Ko, K. F. Man, S. Kwong, represented by the absolute values of the natural logarithm “Topology Design and Bandwidth Allocation of of the average loss, log( averageloss) . Thus the larger Embedded ATM Networks Using Genetic Algorithm,” the result value is, the smaller the average loss is. The IEEE Commun. Letters, vol. 2, no. 6, June 1998. [3] Rajiv Ramaswami and Kumar N. Sivarajan, “Design of acronym, IT, stands for Initial Topology, which is given to Logical topologies for WaveLength-Routed Optical the optimizer as input. The values under IT are the Networks,” performance measures when IT is fed up with three [4] W.K. Tsai, G Huang and Wulun Dai, “Joint Routing different traffic matrixes respectively. T1 ~ T6 refers to 6 and Rate Assignment for Multi-class QoS different topologies. Second acronym, GT refers to the Provisioning for ATM networks,” result from the GA-based topology optimizer, and it shows [5] Joseph A. Bannister and Luigi Fratta and Mario Gerla, the achievable average loss rate of the reconfigured “Topological Design of the Wavelength-Division topology. Optical Network,” 1990 [6] Mario Gerla and Leonard Kleinrock, “On the 5.3 Scalability Topological Design of Distributed Computer Networks,” Trans. On Communication, Vol. Com-25, To show genetic algorithm can give us a locally optimal No. 1, Jan. 1977 solution in a scalable way, we apply the proposed [7] Robert R. Boorstyn and Howard Frank, “Large-scale optimizer for randomly generated topologies with Network Topological Optimization,” Trans. On different number of nodes (from 5 to 40). As a comparing Communication, Vol. Com-25, No.1, Jan 1997 metric, time to reach 50th generation is measured in the [8] Samuel Pierre and Gisele Legault, “A Genetic unit of second is used. The results are summarized in Algorithm for Designing Distributed Computer tabular format in Table 3. The computation time increases Network Topologies,” Trans. On Systems, Man, and fairly sharply as the number of nodes in the network Cybernetics, Vol.28, No.2, April 1998 increases. Even for the 40-node case, however, it still remains under 2 minutes, which is in an affordable range for an online topology reconfiguration. 5 nodes 10 15 20 25 30 35 40 nodes nodes nodes nodes nodes nodes nodes 2.8sec 3.2sec 4.5sec 8.3sec 11.2sec 27.1sec 20.1sec 95sec Table 3. Time to reach 50 generations