Topology Reconfiguration of an IP Network Embedded over an by t8929128

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									IEICE TRANS. COMMUN., VOL. E84-B, No.11 NOVEMBER 2001
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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.
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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
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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.
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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

								
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