An Offline Hybrid IGP/MPLS Traffic Engineering Approachunder LSP Constraints

Eueung Mulyana, Ulrich Killat

Department of Communication Networks, Technical University Hamburg-Harburg

Address : BA IIA, Denickestrasse 17, 21071 Hamburg

Phone: +49-40-42878-2925, fax : +49-40-42878-2941

Email:�mulyana,killat�@tu-harburg.de

Abstract

MPLS (Multi-Protocol Label Switching) enhances the possibility to engineer the traffic on IP networks by allowing explicitroutes. Though IGP (Interior Gateway Protocol) routing has proven its scalability and reliability, effective traffic engineering(TE) has been difficult to achieve in public IP networks, because of the limited functional capabilities of conventional IP tech-nologies. Without MPLS there are in general two possibilities to perform TE in IP networks: either by improving the existingrouting protocols, or by optimizing the parameters used for routing decisions in order to obtain better load distributions. In thiswork we propose a novel hybrid IGP/MPLS traffic engineering method based on genetic algorithms, which can be considered asan offline TE approach to handle long or medium-term traffic variations in the range of days, weeks or months. In our approachthe maximum number of hops an LSP may take and the number of LSPs which are applied solely to improve the routing perfor-mance, are treated as constraints due to delay considerations and the complexity of management. We apply our method to theGerman scientific network (B-WiN) for which a traffic matrix is available and also to some other networks with a simple demandmodel. We will show results comparing this hybrid IGP/MPLS routing scenario with the result of pure IGP routing and that of afull mesh MPLS with and without flow splitting.

keywords : routing, traffic engineering, metaheuristics, evolutionary computation, IP networks, MPLS

1 IntroductionDue to rapid growth of the Internet and due to increasing requirements for service quality, some efforts have been invested byinternet service providers(ISPs), to build a more scalable network architecture or expanding network infrastructure and capacity.Another important issue is traffic engineering (TE), that could give ISPs some degree of control of the traffic distributed overthe network. In practice, TE means mapping traffic flows onto the existing physical network topology in the most effective wayto accomplish desired operational objectives. There are several approaches for deploying TE in current IP networks e.g. byoptimizing the parameters used for routing decisions, so that a better network performance will be obtained [2, 7, 8, 9, 15, 19],or by using explicit routing in an overlay model with ATM or Frame Relay technology. Recent developments in MultiprotocolLabel Switching (MPLS) open new possibilities to address some of the limitations of IP systems concerning traffic engineering. Inparticular MPLS efficiently supports origin connection control through explicit label-switched paths (LSPs). In MPLS network,it is possible to explicitly specify one or several paths for each traffic demand from a source to a destination. By using a full meshof LSPs, the traffic matrix of source to destination flows in a network can easily be obtained. Because of scalability issues in afull mesh architecture and for seamless migration from the current IP network running IGP (Interior Gateway Protocol), the ISPsmay adopt a tactical approach to MPLS, in which they create LSP-tunnels only when necessary, for example to address specificcongestion problems. Although this approach does not fully profit from the benefits of MPLS, it is an attractive alternativecompared to the traditional TE method. To the best of our knowledge, there are only a few works that consider IGP/MPLSscenarios for offline traffic engineering [1, 16, 19]. In [19] three different models are presented. In the first model (basic IGPshortcut) a packet will be forwarded to an LSP if its destination is the tail-end of the LSP. In the second model (IGP shortcut) allpackets to nodes that are the tail-ends of LSPs and to nodes that are downstream of the tail-end nodes will flow over those LSPs.In the last model LSPs are advertised in the IGP and used in the shortest path calculation as virtual interfaces. In these threemodels IGP and MPLS are working together in the same layer i.e. IGP routing is modified taking into account LSPs. Recentwork such as [1, 16] presents an overlay model where IGP and MPLS are working separately. Although from algorithmic pointof view the overlay model is less complicated and more predictable, in the sense that an LSP is used only to route traffic fromits source to its destination, in this work we consider the basic IGP shortcut scenario and leave the other scenarios for futureinvestigations. In the following we first formulate the problem and introduce some notations. In Section 3 we discuss the geneticalgorithm for solving the problem. After that in Section 4 we present some results for the core network of the German scientific

network (B-WiN) for which the traffic matrix was available and also for some other networks with a simple demand model.

2 Problem FormulationIGP/MPLS Routing. Now we will formulate the problem in mathematical notation. A directed network � � ����� is given,where � is the set of nodes representing the network’s routers and � is the set of arcs representing the network’s links. Eachlink ��� �� � � has a capacity ���� . Furthermore, we have a demand ���� for each pair �� � � � �� , giving the demand to becarried from source to destination . A set of LSPs is denoted by � and indexed by �. An LSP� consists of a loop-free nodesequence ���� � ��� where �� , �� denote the head and tail node, respectively. A real variable ������� is associated with the load

on link ��� �� resulting from flow demand ���� along shortest path routing, and �LSP��� resulting from the flow aggregate in LSP�

��LSP� �. Note that for simplicity, in this paper we do not consider ECMP (Equal Cost Multi-Path) in case that several shortestpaths exist. It means that the ECMP feature is either disabled or using optimized metrics that result in a unique shortest pathrouting pattern.

4

6

f

f2,6

1,6

LSP

2

2

2

2

2

2

1

2

f2,5

1

2

3

5

Figure 1: Basic shortcut IGP/MPLS scenario Figure 2: The B-WiN network (node 11 is a pseudonoderepresenting IP-gate for international traffic)

Consider the network in Figure 1 with a tunnel originating from node � and ending at node � (via node �). In IGP/MPLS basicshortcut scenario all packets arrive in node � with destination of node �, e.g. the flows ���� and ���� , will be forwarded to thistunnel. To route the flow ���� router at node � computes the shortest path which is the node sequence �� � � � ��, so that theflow will be forwarded to node �. Node � evaluates the destination of the flow, and notices that it is the same as the tail-end of thetunnel, so that it will be routed to the tunnel. In contrast for the flow ����, the router at node � computes the shortest path, whichis the node sequence �� � � � �. It identifies that there are no tunnels ending at node , so the flow will be forwarded to node�. Let ���� � ����� ���� � ������ ���� � ������ ����, �� � ��� � �� be defined as a set of links that belong to the shortestpath for the flow ���� , � � ���� � ��� � �����, �� � ��� � ���� as a set of all tail nodes in � and � int

��� � ���� � ����� asthe set of all intermediate nodes in the shortest path sequence for flow ���� . So the total load on the link ��� �� can be computedas follows:

���� ����

������� ��

�LSP���� (1)

where

������� �

�����������

���� if ��� �� � ���� and �� � ; orif ��� �� � ���� and � �� � � and �� �� � int

��� ; orif ��� �� � ���� and � �� � � and �� � � � � int

��� for � � ���� , � � �� , �� � ��� � ��

� else

(2)

�LSP���� �

���

�LSP� if ��� �� belongs to the LSP�

� else(3)

Note that �LSP� is defined as the flow aggregate in LSP� i.e. �LSP� � ���� for � �� and � ��. For a given traffic matrix� � ������� ��� � � � � � and a set of metrics � � ������� ���� �� � � , the problem is then to find a set of LSPs toincrease the network performance and can be formulated as :

min � �� �max ��� � (4)

���� �max , ���� �� � � (5)

where ���� ���������

is the utilization of the link ��� ��. A constant �� is used to trade between these two components. With the

Eq. 4 we prefer solutions with a low �max, which implies that the network is better utilized and a low ���, because the number ofLSPs is directly correlated with the management complexity. Furthermore, in some cases it is important to limit the number ofhops for the LSP to avoid long delay that might be introduced by a long LSP:

��LSP� � �max � , �� (6)

where �LSP� denotes the set of nodes that belong to the LSP� and �max the maximum allowable hop-count. Having the trafficmatrix, the metrics and a set of LSPs, we can compute the load distribution on the network. Every solution has a quality measureaccording to Eq. 4. Although a solution is feasible if ���� � or correspondingly �max �, the optimization is performed withno constraints to force this condition, but we simply minimize the objective function. The desired result is a set of LSPs whichcorresponds to the minimized cost function and to the certain performance parameters. Although here we treated the set � as agiven set, the method presented can be easily integrated to a metric based optimization approach to address combined problems,for example : some LSPs are created when the metric based approach fails to further improve network performance or vice versa.Note that the formulation for IGP/MPLS routing presented here is intended for the heuristic solving method will be presented inSection 3.

General Routing Problem (MPLS with flow splitting). For comparison we will now discuss the optimal routing from a so-called general routing problem (GRP) [2]. In this case, there are no limitations on how flows can be distributed along the pathsfrom source to destination, so that it can be formulated and solved in polynomial time.

min ��� �max �

���

���

���

�����������

����� , ���� �� � � (7)

���

�����������

���� �max , ���� �� � � (8)

�� �

���� ���

������ � Æ �� �

�� �����

���� �� , ������ �� � � (9)

� ������� � , ����� , ���� �� � � (10)

Equation 7 is the objective function to minimize �max and the average utilization � � ����

��� ���� , where ���� �

���

�����������

����,

���� �� � �. Since the objective functions in Eq. 4 and Eq. 7 are different, the result from GRP is theoretically not the lowerbound from IGP/MPLS routing. But by choosing a quite high value of �� in both equations (e.g. 1000), we could hope that GRPwill give an approximate lower bound. Eq. 9 describes flow conservation constraints that ensure the desired traffic flow to berouted from source to destination. The Kronecker delta ��� is defined as having the value one when � � � and zero when � �� �.The variable ������� is associated with the fraction of the ���� that flows on the link ��� ��. Furthermore, it might be necessary todiscard some nodes in Eq. 9, which introduce long delays or represent external destination networks, in case of � �� and � �� to avoid transit of the traffic on those node (e.g. the node 11 in Figure 2).

MPLS (full mesh - without flow splitting). For the second comparison, we will change the contraint in Eq. 10 to binarycondition, which implies that each flow ���� can not be split anymore.

������� �

�� if the flow ���� is routed on the link ��� ��� else

(11)

Our experiments with CPLEX 7.5 show that, although the objective function 7 implicitly contains no-loop condition for theoptimal solution, explicit no-loop constraints are needed to speed-up the computation.�

�� �����

���� �� � , �� � � , ����� (12)

����� ���

������ � , �� � � , ����� (13)

Further computation cost can be saved by using symmetrical LSPs, so that half of integer variables can be deleted.

������� � ������� , ���� �� � � , ����� (14)

A Demand Model. Obtaining a realistic traffic matrix is quite hard, because network operators have many reasons to keep itfor themselves. To test our implementation we use the B-WiN network from ERNANI project [13] for which a traffic matrix andthe set of weights are available. The B-WiN network was the German research and scientific network, which is now replacedby the more advance network G-WiN, for which unfortunately no related informations are publicly available. Because we usealso the G-WiN [10] and the SURFnet network (the scientific network in the Netherlands) [18], we will now introduce a simpledemand model, which is a formal and a generalized version of the model proposed in [17]. The model consists of two parts. Thefirst one (Eq. 15) is for local traffic i.e. traffic between nodes in the network. And the second one (Eq. 16 and 17) is for trafficto(from) outside networks.

� local��� � random [�local

min , �localmax ] (15)

�� �����down �

���

��down���

if � ��� � ��nwc and � ��

�

� else(16)

�� �����up �

���

��up

���if � ��� � ��

nwc and � ���

� else(17)

�� � random [�� �� , � �� ] (18)

where � is a set of outside traffic-types, �down is the approximate downstream traffic volume of type � i.e. traffic from outside

network, �up is the approximate upstream traffic volume of type � i.e. traffic to outside network, ��

nwc � ����� is a set of nodeswith connection to outside network for traffic type �, ��

� is a set of nodes whose traffic is routed through the node ��� . Thus thetraffic matrix can be formulated as follows :

���� � � local���

����

��� �����down �� �����up� , ��� � � � �� (19)

3 A Genetic Algorithm for Hybrid IGP/MPLS TEGenetic algorithm (GA) is a population-based search method, that is adopted from the nature. The population consists of individ-uals or chromosomes that represent solutions to the problem. So the first design challenge of the GA is how to encode a solutionin terms of a chromosome. The next step is to use this encoding method to produce an initial population by randomly generating asuitable number of chromosomes. There are no standardized rules to decide how many chromosomes should be in the population.The size of around 50 up to 200 chromosomes is typically enough, because the number of chromosomes in the population is notdirectly correlated with the quality of the solutions. After generating this intial population, all chromosomes enter the evolutionloop, consisting of selection and some processes to form new chromosomes. At the beginning of each iteration some vectors ofhigh quality are selected as parent chromosomes, which by applying the genetic mechanisms ”crossover” and ”mutation” willhopefully produce some better solutions for the next generation. The least successful chromosomes of the previous iteration willbe removed and then be substituted by the new ones. Applying the described processes in many iterations we continously improvethe average quality of the solution vectors until the exit condition is satisfied. This exit condition is ideal if the best fitness foundmatches the global optimum of the objective function. As for most cases we do not know this global optimum, the program willterminate based on a predefined number of iterations or when for a certain number of iterations there are no more improvements.In the following we will dicuss the method in more detail.

Encoding. In order to apply a genetic algorithm to the problems defined in Section 2, in general a suitable encoding of possiblesolutions in a vector (i.e. chromosome) representation is needed. In our case a chromosome is represented by a set of numbers���� ��� � ��� � �� where �� is an integer and �� � ��� �max�. Each position � is correlated with a certain flow from the trafficmatrix, so that when �� � � the flow will be routed according to shortest path computation. If �� �� �, the flow will be routedwith a certain LSP. The constant �max is defined as follows:

�max �

���

� �� if � �� �given

�given else(20)

where �given is the given upper-bound and � a set of all possible LSPs for the flow associated with the position �. To select theflows, we first route all flows according to shortest path computation and select the flows for each position from the links with

high utilization. The set of possible LSPs for flow ���� is obtained by applying Dijkstra’s algorithm to the modified networktopology : we will cut certain links on the currently available paths to find a new path. If the new path does not exist, then it willbe added to the list. This method is repeated several times to obtain more LSP candidates.

Selection. All chromosomes will be selected according to their fitness. In our case we want a fitness value as small as pos-sible. There are two selection mechanisms i.e. to select parent chromosomes for a new generation and to remove some of badchromosomes from the current population. For the first task we implement a so-called ”rank selection” to make the probabilityto be selected a little bit more balanced for all chromosomes in the population. We first rank the population and then everychromosome receives a probability value from this ranking: the probability value is measured relative to the probability value ofthe last (worst) chromosome i.e. the last but one will have twice that probability etc. Of course the total of these probabilitiesmust equal one. Hence these probability values can be mapped on corresponding non overlapping intervals in the range ��� �� anda randomly chosen number in this interval is used to select a chromosome. For the second task we simply sort the chromosomesaccording to their fitness from good to bad and then remove some of the least performing chromosomes.

Crossover and Mutation. In genetic algorithms there are two standard operators to produce new individuals. The first oneis called crossover. In general the production of new chromosomes by crossover consists of the combination of two parentchromosomes of the old population. This means that all offspring’s genes will be inherited either from the first parent or fromthe second one. The main goal of this mechanism is to get better solutions. The second method is called mutation and changesthe genes randomly. Its main goal is to lower the danger of getting stuck in local optima. Of course the implementation ofthese operators may vary depending on the problem and encoding method of the solutions. In our implementation, crossover isperformed by generating a random real number, that is randomly distributed in the interval ��� ��. If the number is lower than50% the gene ���

� of offspring � will be inherited from the gene ���� from parent �. If the number is more than 50% the gene ����

will be inherited from the gene ���� . The complementary rule exists for the gene ���� of offspring �. For mutation we generate

another real number; if this number is lower than a probability of mutation �mut the offspring’s genes will be arbitrarily mutated.

4 ResultsFor the following results we set the constant �� � � �� (Eq. 4) for the B-WiN and G-WiN networks, and �� � ��� for theSURFnet5 network. the maximum hop-count �max � � (Eq. 6), the length of the chromosomes ( = the maximum LSPs number)! � �� for the B-WiN and G-WiN networks and ! � ��� for the SURFnet5 network. The search process is terminated ifthere are no more improvements after 300 iterations. All results for GRP and MPLS scenarios are computed with CPLEX 7.5MIP optimizer. The B-WiN network topology is shown in Figure 2. Unfortunately (for space reasons) the traffic matrix, linkcapacities and metrics could not be presented here. The G-WiN and SURFnet5 networks topologies are taken from [10] and [18]respectively. The demands for these G-WiN and SURFnet5 networks are generated according to Eq. 19 and for shortest pathcomputation hop-count metric (all weights equal 1) is used.

100

102

700

800

900

1000

1100

1200

Fitness Convergence

Fit

ness

Iterations

Average FitnessBest Fitness

100

102

0.7

0.8

0.9

1

1.1

1.2

Convergence of Max. Utilization

Max

imum

Uti

lizat

ion

Iterations

Average Max. Util.Best Max. Util.

100

102

20

25

30

35

Conv. of Total Number of LSPs

Tot

al L

SPs

Iterations

Average Total LSPsBest Total LSPs

Figure 3: The convergence characteristics of the GA for the B-WiN network

Convergence. Figure 3 shows the convergence characteristic of the fitness, �max, and ��� for the B-WiN network. There arealmost no differences between the result for the fitness and that for the �max. In contrast to that, the result for ��� shows moredynamics. It can also happen that ���best " ���average. This is the influence of the constant ��, that was set to � �� . It means thatthe importance ratio for �max and ��� is 1000:1. With this setting, the algorithm will first prefer to search a good �max.

B-WiN G-WiN SURFnet5IGP IGP/MPLS MPLS GRP IGP IGP/MPLS MPLS GRP IGP IGP/MPLS MPLS GRP

# nodes 11 10 19# links 36 40 68# demands 110 90 342# Variables 3961 3961 3601 3601 23257 23257# Constraints 7716 1336 6340 940 42818 6566�max 0.706667 0.646018 0.64 0.637363 0.648 0.3776 0.3332 0.331733 0.6593 0.43335 0.39795 0.397925� 1.41509 1.54795 1.5625 1.56896 1.54321 2.64831 3.0012 3.01447 1.51676 2.3076 2.51288 2.51304� 0.370304 0.404939 0.376007 0.371432 0.22537 0.262475 0.268835 0.235474 0.183814 0.191077 0.18452 0.183814# LSP 0 22 110 118 0 24 90 103 0 36 342 343

Table 1: Some network parameters and the results (all networks)

Network Utilization. For the B-WiN network the maximum utilization �max and correspondingly the maximum scale factor# � �

�maxfound in IGP/MPLS scenario are quite close to the approximate lower bounds from general routing problem (GRP) and

MPLS (the exact parameters are shown in Table 1). But they are also not so far from the �max and # for IGP case (compared tothe results from two other networks). One possible reason for this is, that the metrics used for the B-WiN network are alreadyoptimized, while those for two other networks are not (hop-count metric).

Total Number of LSPs. Table 1 shows that the total number of LSPs varies from about 12% for the SURFnet5 network(compared to the MPLS case) to 27%(G-WiN). Our early investigations with several runs show that a factor of about 25% can beachieved on average. It can be improved by increasing �max.

5 ConclusionIn this paper we have considered the problem designing LSPs for hybrid IGP/MPLS traffic engineering scenario and proposed anovel approach based on genetic algorithms. Although in IGP/MPLS schemes an ISP does not have all features that MPLS mayoffer, for example a source destination flow measurement, the approach seems to be an attractive alternative and complement forthe traditional offline traffic engineering by optimizing IGP metrics. Our early results show that the performance obtained byconstructing a few LSPs is quite close to the performance obtained by a full-mesh LSPs configuration. Surely it should be furtherinvestigated in particular by using larger networks. This issue, the influence of several parameters and statistical characteristicsof the method are subject of our future research.

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