engenharia de tráfego na internet: entendendo o de tráfego...
TRANSCRIPT
PPGEE
Programa de Pós-Graduação em Engenharia Elétrica
Engenharia de Tráfego na Internet: Entendendo o processo de tomada de decisão para gerenciamento de tráfego na américa do sul. Internet Traffic Engineering: Understanding the decision-making process for traffic management in South America.
Márcio De Deus
Márcio De Deus
Grupo de Pesquisa Planejamento e análise de tráfego em redes
Reseach Group
Network planning and traffic analysis
Paulo H. P.Carvalho (Supervisor), Márcio A. de Deus, João Paulo Leite.
[email protected], [email protected], [email protected]
Departamento de Engenharia Elétrica
LEMOM Lab Universidade de Brasilia
Brasilia – DF
Márcio De Deus
How to assure the effecQve resource usage?
Network OperaQonà Traffic engineering?
Engineering à Capacity Planning?
SoluQon not based in a math model:
Márcio De Deus
How to assure the effecQve resource usage?
Network OperaQonà Traffic engineering?
Engineering à Capacity Planning?
SoluQon not based in a math model:
or = ??
Márcio De Deus
How to assure the effecQve resource usage?
Network OperaQonà Traffic engineering?
Engineering à Capacity Planning?
SoluQon based in a math model:
Márcio De Deus
A traffic or network model can only exists if the existence of a math model could make possible to extract basic parameters to simulate a future utilization. [Takine e Masuyama]
Math Model
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Day - Time
Mb
ps
/ n VoIPP2PE-MailBrowsing
BANDWIDTH SUM
TIMESLOT
SERVICE
Parameters PredicQon
Current ConfiguraQon
New configuraQon
Self-similar Monofractal Multifractal
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httpP2PStreamingVoIP
Márcio De Deus
Decision-‐making process
Collect and process data
Goal (Best SoluQon
Ranking)
Acquired knowledge
Decision-‐making
MulQcriteria analysis AlternaQve a0
AlternaQve a1
AlternaQve an
Criterion c0
Criterion c1
Criterion cn
Goal
D={dji} W
{w1 ,…, wn)
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Márcio De Deus
CooperaQve Inter-‐Domain Traffic Engineering using Nash Bargaining and DecomposiQon SoluQon criteria: 1. Minimum informaQon to be exchange between ASes. 2. The efficiency is based on the cooperaQon approach on a Pareto basis. 3. Fairness is the main approach for the best soluQon. 4. Based on a 50/50 usage criteria
assume that ISPs can improve their local performance bybargaining (or negotiating) about the traffic flow distributionon their peering links. Our first insight is that we can usethe well-known concept of Nash bargaining [10],[11] to doso. Under this scheme, the ISPs agree to jointly optimize asocial cost function, known as the Nash product, which isessentially the product of the utility functions of the twoISPs. The key advantage of using this approach is thatthe solution is guaranteed to provide Pareto efficiency andfairness. When the ISPs’ utilities (measures of performance,such as average delay or maximum load on a link) aredirectly comparable, this solution is min-max fair, i.e.,the gains from cooperation are equal. However, when theutilities are not comparable, it still provides a Pareto efficientsolution that is proportionally fair [12]. By this, we meanthat the gains from cooperation to individual ISPs are equalafter some (automatic) suitable scaling of the utilities. Thisscaling is endogenous to the solution and, therefore, ishighly desirable.
This leaves us with the issue of not revealing criticalinternal information. Our insight here is that we can use dualdecomposition [13] to transform the joint optimization of theNash product into a procedure with precisely this property,as follows. The global optimization problem can be decom-posed into two independent sub-problems by recognizingthe coupling flows (these are the flows crossing between ISPdomains) and introducing appropriate Lagrange multipliers(or shadow prices) [13]. These sub-problems can now beassigned to the ISPs to be solved in a decentralized manner.These have the critical feature that they are completely local– an ISP’s assigned sub-problem depends only on its ownnetwork – thus, the ISPs don’t have to share critical internalinformation. Relying on this insight, we develop an iterativeprocedure based on the sub-gradient method [14] where,given Lagrange multipliers, the ISPs independently optimizetheir local sub-problems to come up with their requiredcoupling flows. The Lagrange multipliers are then updatedusing the sub-gradient method, which uses the difference inthe two sets of required flows to determine the magnitudeof the update. The update can be done in a decentralizedmanner. After the update, the ISPs again try to optimize theirlocal sub-problems. We show that this process converges infinite time to a fair and Pareto-efficient allocation.
We evaluate the effectiveness of our approach using sim-ulations over real ISP topologies. Through simulations, weshow that our approach significantly out-performs unilateralapproaches such as the commonly used hot potato or shortestpath routing (where ISPs route to nearest peering locationin terms of link weights) as well as the Nash equilibriumsetting (where ISPs optimize local objectives while playingbest responses to each other [9]). For the case where ISPsemploy similar utilities, we compare our solution againstcentralized optimal routing (where a central arbitrator op-timizes the common objective across both ISP networks).We also confirm the proportional fairness guarantees of oursolution via simulation experiments.
ISP2ISP1
yd21
yd12
sd21 − y
d21
sd12 − y
d12
Fig. 1. The Model
II. INTER-DOMAIN TRAFFIC ENGINEERING USING NASHBARGAINING AND DECOMPOSITION
A. The ModelWe model the interaction between two ISPs: ISP1 and
ISP2 as shown in Figure 1. These ISPs are optimizingutilities u1 and u2, respectively. As mentioned in Section I,these utilities are related to some measure of performance.These utilities could mean different things to the ISPs. Forexample, for one ISP the utility could be related to theaverage delay in the network, and for the other ISP theutility could be related to the maximum load on a linkin the network. The ISPs optimize these utilities under theflow conservation constraints, i.e., flows from all sources toall destinations must be routed. To simplify exposition, inthe following description, we assume that the ISPs employMPLS-like routing. We believe the approach we describebelow can be easily modified to yield a mechanism forsetting link weights for ISPs using OSPF in a way similarto [15].We make the common assumption that the utilities are
either convex or concave functions, and that the ISPs arerespectively minimizing or maximizing these utilities. Forexample, some convex utilities are the maximum load on alink and the average delay using convex link per unit delayfunctions (e.g., the per unit delay in an M/M/1 queue).We assume that ISP1 needs to send flows sd
12 to ISP2 ona per destination basis: sd
12 is a vector of flows to be sent toeach of the destinations in ISP2 from ISP1.2 Similarly, ISP2
needs to send flows sd21 to ISP1 on a per destination basis:
sd21 is a vector of flows to be sent to each of the destinationsin ISP1 from ISP2. Even though the ISPs may have multiplepeering links, to facilitate easier understanding, we explainour model using two bi-directional peering links (Figure 1).The model generalizes readily to multiple peering links. Weassume that ISP1 splits sd
12 so that yd12 goes on the upper
link and (sd12 − yd
12) goes on the lower link. Similarly ISP2
splits sd21 so that yd
21 goes on the upper link and (sd21 − yd
21)goes on the lower link.Optimizing for the utilities would be a no-brainer if the
ISPs had no interaction. Then they could optimize theirrespective utilities independently. What makes it compli-cated is the interaction of the ISPs through flows sent be-tween each other. These flows make the ISPs utilities inter-2We make the notation precise in Section II-C.1.
2
u2
u1
Pareto frontier
breakdown point
feasibleregion
Fig. 2. The feasible region with Pareto efficient frontier.
dependent. These flows between the ISPs are sometimesreferred to as coupling flows since they cause the ISPsoptimization problems to be coupled.If the ISPs are myopic, i.e., they employ unilateral ap-
proaches towards inter-domain TE, they would optimizewithout paying attention to how the coupling flows affectthe other ISPs optimization problem. For example, yd
12 isan output of ISP1’s optimization problem and is thus underits control. However, yd
12 is an input to ISP2’s optimizationproblem and thus affects its outcome. Now, if ISP1 ismyopic, it will optimize without paying attention to howmuch it may be hurting ISP2 by determining yd
12 myopically.Similarly, ISP2 could determine yd
21 myopically. Thus, inthis process, both ISPs may end up hurting each other.When both ISPs route myopically, we denote the ISPs
utilities as umyopic1 and umyopic
2 , respectively. The questionthen arises is: Is there any way that the ISPs could somehowcooperate on determining the coupling flows and improvetheir performance, i.e., achieve u1 ≥ umyopic
1 and u2 ≥umyopic
2 such that1) The gains from cooperation are equitable (or fair)while operating at a Pareto efficient operation point?
2) ISPs don’t have to divulge any critical informationabout their networks?
The answer to the first question lies in the idea of NashBargaining [11]. The answer to the second question lies inthe idea of decomposition [13]. We explain both of theseideas next.
B. Nash BargainingThe basic idea behind Nash bargaining is as follows. We
assume that the ISP utilities are inter-dependent, concaveand cardinal, where by cardinal we mean that the actualvalues of utilities matter – as opposed to ordinal utilitieswhere only the relative ordering of outcomes matters. Figure2 shows the feasible region for the two utilities, where thefeasible region is defined as the region where both ISPswould do better off compared to the myopic outcome. Themyopic outcome is also referred to as the breakdown point.A fair and Pareto efficient outcome, also referred to
as the Nash solution can be obtained by maximizing theNash product given by u1u2. Using the axiomatic theory
of cooperative games, it can be shown that when twoplayers (ISPs for us) with equal market power bargain, usingthreat strategies, they should arrive at the Nash solution.Referring to Figure 2, these threat strategies correspond tothe breakdown point, which is the outcome if the ISPs areunable to reach an agreement.In what follows, we provide a brief summary of the prop-
erties of the Nash solution, using the axiomatic bargainingapproach. The idea here is that a good bargaining solutionshould satisfy the following four axioms, which we simplystate as follows (see [11] for a detailed discussion):Pareto efficiency. This is obviously desirable since ISPsprefer more to less.Symmetry. This says that the solution should provideequal gains from cooperation when the feasible region issymmetric, where by symmetric we mean that the feasibleregion is agnostic of the player’s identities and that it wouldlook the same even if the ISPs utility axis were swapped.Independence of affine transformations. This requires thatthe solution should be agnostic of any affine transformations(that is, shifts and scalings) applied to any of the twoutilities. So, if the solution is given by (uNB
1 , uNB2 ) for some
utilities (u1, u2), and u1 is scaled and shifted to α1u1 + β1,then the solution should change to (α1uNB
1 + β1, uNB2 ).
Independence of irrelevant alternatives. This basicallysays that addition of irrelevant alternatives should not changethe solution. That is, for feasible regions F and G, if(uNB
1 , uNB2 ) ∈ solution(F ), G ⊂ F , and (uNB
1 , uNB2 ) ∈ G
then (uNB1 , uNB
2 ) ∈ solution(G).It turns out that the Nash solution is the only solution that
satisfies these four axioms [10]. In fact, the Nash solution isthe only solution that satisfies the following problem that issimultaneously utilitarian (Pareto efficient) and egalitarian(fair) [11]. That is, the Nash solution solves
maximize α1u1 + α2u2
subject to α1u1 = α2u2
(u1, u2) ∈ U
for some α1 ≥ 0 and α2 ≥ 0, where the optimization isover the bounded set U . Note that this scaling by α’s doesnot change the Pareto efficient frontier in Figure 2, i.e., thevalues of the choice variables resulting in Pareto efficientpoints remain the same. These α’s bring the usually un-comparable u1 and u2 on a common footing so that we cantalk about fairness in the first place. In particular, the Nashsolution is proportionally fair [12]. This means that movingaway from the Nash solution causes a negative cumulativepercentage change in utilities. That is, if (uNB
1 , uNB2 ) is the
Nash solution, and we move to another point (u∗1, u
∗2), then
2!
i=1
(u∗i − uNB
i )
uNBi
≤ 0 (1)
We next describe how decomposition can be used tojointly optimize the Nash product without revealing anysensitive information.
C. DecompositionThe idea of decomposition is not new. It has been success-
fully used to solve large scale optimization problems [13]
3
U1 e U2 are the optimization functions to ISP1 e ISP2
Nash Solution: Max (U1U2)
Decomposition Max {ln(u1) + ln(u2)}
and to solve separable problems in a decentralized manner.Moreover, in our case, decomposition allows separate enti-ties in the optimization problem to hide their internal criticalinformation. In what follows, we first develop a preciseoptimization framework, and then use this framework toexplain decomposition.1) Optimization Formulation: We denote the network
topology of ISPi, i ∈ {1, 2}, by a directed graph Gi =(Ni,Li) with ni = |Ni| nodes and li = |Li| internal links.We also denote by P the set of p directed peering links.We then define the incidence matrix for ISPi as matrixAi ∈ Rni×(li+p), with Ai,jk = +1 if link k leaves nodej, Ai,jk = −1 if link k enters node j, and 0 otherwise.We consider aggregate data flows through the network,
where we identify each flow by its destination node. Wedenote by D the set of all possible destination nodes. ForISPi, we denote the nonnegative amount of flow originatingat node j and destined to node d ∈ D by sd
i,j (j = d).When j = d, sd
i,d is the negative sum of the flows destinedto the node d, thus ensuring flow conservation. We refer tosd
i ∈ Rn as the source-sink vector. Note that sdi , i ∈ {1, 2}
include sd12 and sd
21, as described in Section II-A. Similarly,for ISPi, we denote the amount of nonnegative flow destinedto node d on each internal link k ∈ Li by xd
i,k . We callxd
i ∈ Rl the internal flow vector for destination d. Finally,we denote the amount of nonnegative flow destined to noded on each peering link k ∈ P by yd
k. We call yd ∈ Rp thepeering flow vector for destination d. This yd includes yd
12and yd
21, as described in Section II-A.Now, we are ready to define the optimization problems
in various scenarios. We first present the Nash productproblem, where ISP would jointly solve
maximize u1u2
subject to A1
!
xd1
yd
"
= sd1, A2
!
xd2
yd
"
= sd2
xd1 ≥ 0, xd
2 ≥ 0, yd ≥ 0,
(2)
for all d ∈ D, where the optimization variables are xd1,
xd2, and yd. Here the two equality constraints are the flowconservation constraints for ISP1 and ISP2, respectively, andthe last set of inequality constraints ensures that the choicevariables are non-negative.3A related problem to (2) is when both ISPs route myopi-
cally. The myopic routing schemes that we are particularlyinterested in are:1. Hot potato routing: Under this approach, each ISP routesinter-domain traffic originating in its network to the closestpeering point (i.e., least OSPF-cost). In a way, this attemptsto minimize the network resources consumed by inter-domain traffic within the source ISP network. This formof inter-domain traffic exchange is commonly used today.2. Nash equilibrium: Under this approach, ISPs myopicallyoptimize local objectives while iteratively playing best re-sponse to each other. Each ISP finds the optimal way to splitinter-domain traffic across peering links, given the trafficsplits of its neighbor, until no better traffic split can be
3Other constraints such as link capacity constraints can be readilyincluded.
found. This dynamic eventually finds an equilibrium, alsoknown as the Nash equilibrium [9], from which no ISP hasan incentive to deviate.Under these routing schemes, each ISP myopically solves
an optimization problem
maximize ui
subject to Ai
!
xdi
yd
"
= sdi
xdi ≥ 0, yd ≥ 0,
(3)
for i = {1, 2} and for all d ∈ D. Here we use sdi instead
of sdi to represent the fact that the myopic routing strategies
change the original flow vectors. For example, in hot-potatorouting, since each ISP routes the inter-domain flows to thenearest exit points, the flow vector reflects the source offlows being on peering points instead of being on internalnodes. In Nash equilibrium, where the ISPs iterate over themyopic problems based on current incoming flows, the flowvector reflects a similar transformation.2) Decomposition: Now we look into how we can cast
problem (2) in separable form, allowing for a decentralizedsolution. We face two challenges: first, as it stands, theobjective is not separable, and second, the ISPs utilities arecoupled through yd.We first transform problem (2) into an equivalent problem
by taking the logarithm of the objective function. Sincethe logarithm is an increasing and concave function, thistransformation does not change the solution to the originalproblem [14]. We then get the following equivalent problem
maximize ln(u1) + ln(u2)
subject to A1
!
xd1
yd
"
= sd1, A2
!
xd2
yd
"
= sd2
xd1 ≥ 0, xd
2 ≥ 0, yd ≥ 0,
(4)
We next introduce new nonnegative variables yd1 and
yd2 , which are local versions of yd for ISP1 and ISP2,respectively. Problem (4) can then be rewritten as
maximize ln(u1) + ln(u2)
subject to A1
!
xd1
yd1
"
= sd1, A2
!
xd2
yd2
"
= sd2
xd1 ≥ 0, yd
1 ≥ 0, xd2 ≥ 0, yd
2 ≥ 0
yd1 = yd
2 .
(5)
We still have a coupling constraint yd1 = yd
2 , which we dealwith using dual (or pricing) decomposition [13], which isoutlined next.We first write the partial Lagrangian of problem (5), with
respect to the coupling constraint, as
L(xd1, y
d1 , xd
2, yd2 , λd) = ln(u1)+ln(u2)+
#
d
(λd)T (yd1−yd
2),
where λd ∈ Rp are Lagrange multipliers associated with thecoupling constraint. This is a separable function in (xd
1, yd1)
and (xd2, y
d2). We now solve the dual problem of problem (5),
given byminimize g1(λ
d) + g2(λd), (6)
4
Márcio De Deus
CooperaQve interdomain traffic engineering using Nash negoQaQon and dual decomposiQon SoluQon criteria: 1. Minimum informaQon to be exchange between ASes. 2. The efficiency is based on the cooperaQon approach on a Pareto basis. 3. Fairness is the main approach for the best soluQon. 4. Based on a 50/50 usage criteria
assume that ISPs can improve their local performance bybargaining (or negotiating) about the traffic flow distributionon their peering links. Our first insight is that we can usethe well-known concept of Nash bargaining [10],[11] to doso. Under this scheme, the ISPs agree to jointly optimize asocial cost function, known as the Nash product, which isessentially the product of the utility functions of the twoISPs. The key advantage of using this approach is thatthe solution is guaranteed to provide Pareto efficiency andfairness. When the ISPs’ utilities (measures of performance,such as average delay or maximum load on a link) aredirectly comparable, this solution is min-max fair, i.e.,the gains from cooperation are equal. However, when theutilities are not comparable, it still provides a Pareto efficientsolution that is proportionally fair [12]. By this, we meanthat the gains from cooperation to individual ISPs are equalafter some (automatic) suitable scaling of the utilities. Thisscaling is endogenous to the solution and, therefore, ishighly desirable.
This leaves us with the issue of not revealing criticalinternal information. Our insight here is that we can use dualdecomposition [13] to transform the joint optimization of theNash product into a procedure with precisely this property,as follows. The global optimization problem can be decom-posed into two independent sub-problems by recognizingthe coupling flows (these are the flows crossing between ISPdomains) and introducing appropriate Lagrange multipliers(or shadow prices) [13]. These sub-problems can now beassigned to the ISPs to be solved in a decentralized manner.These have the critical feature that they are completely local– an ISP’s assigned sub-problem depends only on its ownnetwork – thus, the ISPs don’t have to share critical internalinformation. Relying on this insight, we develop an iterativeprocedure based on the sub-gradient method [14] where,given Lagrange multipliers, the ISPs independently optimizetheir local sub-problems to come up with their requiredcoupling flows. The Lagrange multipliers are then updatedusing the sub-gradient method, which uses the difference inthe two sets of required flows to determine the magnitudeof the update. The update can be done in a decentralizedmanner. After the update, the ISPs again try to optimize theirlocal sub-problems. We show that this process converges infinite time to a fair and Pareto-efficient allocation.
We evaluate the effectiveness of our approach using sim-ulations over real ISP topologies. Through simulations, weshow that our approach significantly out-performs unilateralapproaches such as the commonly used hot potato or shortestpath routing (where ISPs route to nearest peering locationin terms of link weights) as well as the Nash equilibriumsetting (where ISPs optimize local objectives while playingbest responses to each other [9]). For the case where ISPsemploy similar utilities, we compare our solution againstcentralized optimal routing (where a central arbitrator op-timizes the common objective across both ISP networks).We also confirm the proportional fairness guarantees of oursolution via simulation experiments.
ISP2ISP1
yd21
yd12
sd21 − y
d21
sd12 − y
d12
Fig. 1. The Model
II. INTER-DOMAIN TRAFFIC ENGINEERING USING NASHBARGAINING AND DECOMPOSITION
A. The ModelWe model the interaction between two ISPs: ISP1 and
ISP2 as shown in Figure 1. These ISPs are optimizingutilities u1 and u2, respectively. As mentioned in Section I,these utilities are related to some measure of performance.These utilities could mean different things to the ISPs. Forexample, for one ISP the utility could be related to theaverage delay in the network, and for the other ISP theutility could be related to the maximum load on a linkin the network. The ISPs optimize these utilities under theflow conservation constraints, i.e., flows from all sources toall destinations must be routed. To simplify exposition, inthe following description, we assume that the ISPs employMPLS-like routing. We believe the approach we describebelow can be easily modified to yield a mechanism forsetting link weights for ISPs using OSPF in a way similarto [15].We make the common assumption that the utilities are
either convex or concave functions, and that the ISPs arerespectively minimizing or maximizing these utilities. Forexample, some convex utilities are the maximum load on alink and the average delay using convex link per unit delayfunctions (e.g., the per unit delay in an M/M/1 queue).We assume that ISP1 needs to send flows sd
12 to ISP2 ona per destination basis: sd
12 is a vector of flows to be sent toeach of the destinations in ISP2 from ISP1.2 Similarly, ISP2
needs to send flows sd21 to ISP1 on a per destination basis:
sd21 is a vector of flows to be sent to each of the destinationsin ISP1 from ISP2. Even though the ISPs may have multiplepeering links, to facilitate easier understanding, we explainour model using two bi-directional peering links (Figure 1).The model generalizes readily to multiple peering links. Weassume that ISP1 splits sd
12 so that yd12 goes on the upper
link and (sd12 − yd
12) goes on the lower link. Similarly ISP2
splits sd21 so that yd
21 goes on the upper link and (sd21 − yd
21)goes on the lower link.Optimizing for the utilities would be a no-brainer if the
ISPs had no interaction. Then they could optimize theirrespective utilities independently. What makes it compli-cated is the interaction of the ISPs through flows sent be-tween each other. These flows make the ISPs utilities inter-2We make the notation precise in Section II-C.1.
2
u2
u1
Pareto frontier
breakdown point
feasibleregion
Fig. 2. The feasible region with Pareto efficient frontier.
dependent. These flows between the ISPs are sometimesreferred to as coupling flows since they cause the ISPsoptimization problems to be coupled.If the ISPs are myopic, i.e., they employ unilateral ap-
proaches towards inter-domain TE, they would optimizewithout paying attention to how the coupling flows affectthe other ISPs optimization problem. For example, yd
12 isan output of ISP1’s optimization problem and is thus underits control. However, yd
12 is an input to ISP2’s optimizationproblem and thus affects its outcome. Now, if ISP1 ismyopic, it will optimize without paying attention to howmuch it may be hurting ISP2 by determining yd
12 myopically.Similarly, ISP2 could determine yd
21 myopically. Thus, inthis process, both ISPs may end up hurting each other.When both ISPs route myopically, we denote the ISPs
utilities as umyopic1 and umyopic
2 , respectively. The questionthen arises is: Is there any way that the ISPs could somehowcooperate on determining the coupling flows and improvetheir performance, i.e., achieve u1 ≥ umyopic
1 and u2 ≥umyopic
2 such that1) The gains from cooperation are equitable (or fair)while operating at a Pareto efficient operation point?
2) ISPs don’t have to divulge any critical informationabout their networks?
The answer to the first question lies in the idea of NashBargaining [11]. The answer to the second question lies inthe idea of decomposition [13]. We explain both of theseideas next.
B. Nash BargainingThe basic idea behind Nash bargaining is as follows. We
assume that the ISP utilities are inter-dependent, concaveand cardinal, where by cardinal we mean that the actualvalues of utilities matter – as opposed to ordinal utilitieswhere only the relative ordering of outcomes matters. Figure2 shows the feasible region for the two utilities, where thefeasible region is defined as the region where both ISPswould do better off compared to the myopic outcome. Themyopic outcome is also referred to as the breakdown point.A fair and Pareto efficient outcome, also referred to
as the Nash solution can be obtained by maximizing theNash product given by u1u2. Using the axiomatic theory
of cooperative games, it can be shown that when twoplayers (ISPs for us) with equal market power bargain, usingthreat strategies, they should arrive at the Nash solution.Referring to Figure 2, these threat strategies correspond tothe breakdown point, which is the outcome if the ISPs areunable to reach an agreement.In what follows, we provide a brief summary of the prop-
erties of the Nash solution, using the axiomatic bargainingapproach. The idea here is that a good bargaining solutionshould satisfy the following four axioms, which we simplystate as follows (see [11] for a detailed discussion):Pareto efficiency. This is obviously desirable since ISPsprefer more to less.Symmetry. This says that the solution should provideequal gains from cooperation when the feasible region issymmetric, where by symmetric we mean that the feasibleregion is agnostic of the player’s identities and that it wouldlook the same even if the ISPs utility axis were swapped.Independence of affine transformations. This requires thatthe solution should be agnostic of any affine transformations(that is, shifts and scalings) applied to any of the twoutilities. So, if the solution is given by (uNB
1 , uNB2 ) for some
utilities (u1, u2), and u1 is scaled and shifted to α1u1 + β1,then the solution should change to (α1uNB
1 + β1, uNB2 ).
Independence of irrelevant alternatives. This basicallysays that addition of irrelevant alternatives should not changethe solution. That is, for feasible regions F and G, if(uNB
1 , uNB2 ) ∈ solution(F ), G ⊂ F , and (uNB
1 , uNB2 ) ∈ G
then (uNB1 , uNB
2 ) ∈ solution(G).It turns out that the Nash solution is the only solution that
satisfies these four axioms [10]. In fact, the Nash solution isthe only solution that satisfies the following problem that issimultaneously utilitarian (Pareto efficient) and egalitarian(fair) [11]. That is, the Nash solution solves
maximize α1u1 + α2u2
subject to α1u1 = α2u2
(u1, u2) ∈ U
for some α1 ≥ 0 and α2 ≥ 0, where the optimization isover the bounded set U . Note that this scaling by α’s doesnot change the Pareto efficient frontier in Figure 2, i.e., thevalues of the choice variables resulting in Pareto efficientpoints remain the same. These α’s bring the usually un-comparable u1 and u2 on a common footing so that we cantalk about fairness in the first place. In particular, the Nashsolution is proportionally fair [12]. This means that movingaway from the Nash solution causes a negative cumulativepercentage change in utilities. That is, if (uNB
1 , uNB2 ) is the
Nash solution, and we move to another point (u∗1, u
∗2), then
2!
i=1
(u∗i − uNB
i )
uNBi
≤ 0 (1)
We next describe how decomposition can be used tojointly optimize the Nash product without revealing anysensitive information.
C. DecompositionThe idea of decomposition is not new. It has been success-
fully used to solve large scale optimization problems [13]
3
U1 e U2 are the optimization functions to ISP1 e ISP2
Nash Solution: Max (U1U2)
Decomposition Max {ln(u1) + ln(u2)}
and to solve separable problems in a decentralized manner.Moreover, in our case, decomposition allows separate enti-ties in the optimization problem to hide their internal criticalinformation. In what follows, we first develop a preciseoptimization framework, and then use this framework toexplain decomposition.1) Optimization Formulation: We denote the network
topology of ISPi, i ∈ {1, 2}, by a directed graph Gi =(Ni,Li) with ni = |Ni| nodes and li = |Li| internal links.We also denote by P the set of p directed peering links.We then define the incidence matrix for ISPi as matrixAi ∈ Rni×(li+p), with Ai,jk = +1 if link k leaves nodej, Ai,jk = −1 if link k enters node j, and 0 otherwise.We consider aggregate data flows through the network,
where we identify each flow by its destination node. Wedenote by D the set of all possible destination nodes. ForISPi, we denote the nonnegative amount of flow originatingat node j and destined to node d ∈ D by sd
i,j (j = d).When j = d, sd
i,d is the negative sum of the flows destinedto the node d, thus ensuring flow conservation. We refer tosd
i ∈ Rn as the source-sink vector. Note that sdi , i ∈ {1, 2}
include sd12 and sd
21, as described in Section II-A. Similarly,for ISPi, we denote the amount of nonnegative flow destinedto node d on each internal link k ∈ Li by xd
i,k . We callxd
i ∈ Rl the internal flow vector for destination d. Finally,we denote the amount of nonnegative flow destined to noded on each peering link k ∈ P by yd
k. We call yd ∈ Rp thepeering flow vector for destination d. This yd includes yd
12and yd
21, as described in Section II-A.Now, we are ready to define the optimization problems
in various scenarios. We first present the Nash productproblem, where ISP would jointly solve
maximize u1u2
subject to A1
!
xd1
yd
"
= sd1, A2
!
xd2
yd
"
= sd2
xd1 ≥ 0, xd
2 ≥ 0, yd ≥ 0,
(2)
for all d ∈ D, where the optimization variables are xd1,
xd2, and yd. Here the two equality constraints are the flowconservation constraints for ISP1 and ISP2, respectively, andthe last set of inequality constraints ensures that the choicevariables are non-negative.3A related problem to (2) is when both ISPs route myopi-
cally. The myopic routing schemes that we are particularlyinterested in are:1. Hot potato routing: Under this approach, each ISP routesinter-domain traffic originating in its network to the closestpeering point (i.e., least OSPF-cost). In a way, this attemptsto minimize the network resources consumed by inter-domain traffic within the source ISP network. This formof inter-domain traffic exchange is commonly used today.2. Nash equilibrium: Under this approach, ISPs myopicallyoptimize local objectives while iteratively playing best re-sponse to each other. Each ISP finds the optimal way to splitinter-domain traffic across peering links, given the trafficsplits of its neighbor, until no better traffic split can be
3Other constraints such as link capacity constraints can be readilyincluded.
found. This dynamic eventually finds an equilibrium, alsoknown as the Nash equilibrium [9], from which no ISP hasan incentive to deviate.Under these routing schemes, each ISP myopically solves
an optimization problem
maximize ui
subject to Ai
!
xdi
yd
"
= sdi
xdi ≥ 0, yd ≥ 0,
(3)
for i = {1, 2} and for all d ∈ D. Here we use sdi instead
of sdi to represent the fact that the myopic routing strategies
change the original flow vectors. For example, in hot-potatorouting, since each ISP routes the inter-domain flows to thenearest exit points, the flow vector reflects the source offlows being on peering points instead of being on internalnodes. In Nash equilibrium, where the ISPs iterate over themyopic problems based on current incoming flows, the flowvector reflects a similar transformation.2) Decomposition: Now we look into how we can cast
problem (2) in separable form, allowing for a decentralizedsolution. We face two challenges: first, as it stands, theobjective is not separable, and second, the ISPs utilities arecoupled through yd.We first transform problem (2) into an equivalent problem
by taking the logarithm of the objective function. Sincethe logarithm is an increasing and concave function, thistransformation does not change the solution to the originalproblem [14]. We then get the following equivalent problem
maximize ln(u1) + ln(u2)
subject to A1
!
xd1
yd
"
= sd1, A2
!
xd2
yd
"
= sd2
xd1 ≥ 0, xd
2 ≥ 0, yd ≥ 0,
(4)
We next introduce new nonnegative variables yd1 and
yd2 , which are local versions of yd for ISP1 and ISP2,respectively. Problem (4) can then be rewritten as
maximize ln(u1) + ln(u2)
subject to A1
!
xd1
yd1
"
= sd1, A2
!
xd2
yd2
"
= sd2
xd1 ≥ 0, yd
1 ≥ 0, xd2 ≥ 0, yd
2 ≥ 0
yd1 = yd
2 .
(5)
We still have a coupling constraint yd1 = yd
2 , which we dealwith using dual (or pricing) decomposition [13], which isoutlined next.We first write the partial Lagrangian of problem (5), with
respect to the coupling constraint, as
L(xd1, y
d1 , xd
2, yd2 , λd) = ln(u1)+ln(u2)+
#
d
(λd)T (yd1−yd
2),
where λd ∈ Rp are Lagrange multipliers associated with thecoupling constraint. This is a separable function in (xd
1, yd1)
and (xd2, y
d2). We now solve the dual problem of problem (5),
given byminimize g1(λ
d) + g2(λd), (6)
4
But… The south american traffic is unbalanced!
Márcio De Deus
Traffic Asymmetry
Path asymmetry – ASYPATH
S
I1 I2
D
Request Response
Load asymmetry – ASYin-‐out
S
I1 I2
DRequest
Response
Márcio De Deus
Long-‐range dependence processes • Memory process • Work in different scales:
• The incremental fBm -‐ Fractal Brownian MoCon –process can be defined as
• The fBm process can be used for forecasQng. • Defined with few parameters (second order) • The Poisson (Erlang e.g.) is a memory less process and is not
able to explain the Internet traffic.
Network Tra⇥c Modeling Using a Multifractal Wavelet Model 3
in the multifractal partition function T (q) , the burstiness as measured by themultifractal spectrum, the marginals, and the queueing behavior.
In this paper, we describe LRD and its relationship with fBm in section 2. Af-ter introducing the wavelet transform and describing the WIG model in section 3,we derive the MWM in section 4. Section 6 reports on the results of simulationexperiments with real data traces. We give an intuitive introduction to multifractalcascades in section 5 and close with conclusions in section 7.
2. fBm and LRD
Although we analyze fBm from a continuous-time point of view, for practicalcomputations and simulations, we often work with sampled continuous-time fBm.The increments process of sampled fBm
X[n] := B(n)�B(n� 1) (3)
defines a stationary Gaussian sequence known as discrete fractional Gaussian noise(fGn) with covariance behavior [10]
rX [k] ⇥ |k|2H�2, for |k| large . (4)
For 1/2 < H < 1, the covariance of fGn is strictly positive and decays soslowly that it is non-summable (i.e.,
⇤k rX [k] =⇤). This property is called LRD.
The LRD of fGn can be equivalently characterized in terms of how the ag-gregated processes
X(m)(n) :=1m
km⌅
i=(k�1)m+1
X(i) (5)
behave. It follows from (1) that X(n) fd= m1�HX(m)(n) .Hence, a log-log plot of the variance of X(m)(n) as a function of m —known
as a variance-time plot— will have a slope of 2H � 2. The variance-time plot cancharacterize LRD in non-Gaussian, non-zero-mean data as well [1].
3. Wavelets and LRD Processes
3.1. Wavelet transform
The discrete wavelet transform is a multi-scale signal representation of the form[11]
c(t) =⌅
k
uk 2�J0/2 ��2�J0t� k
⇥+
J0⌅
j=�⇥
⌅
k
wj,k 2�j/2 ⇥�2�jt� k
⇥, j, k ⌅ ZZ
Network Tra⇥c Modeling Using a Multifractal Wavelet Model 3
in the multifractal partition function T (q) , the burstiness as measured by themultifractal spectrum, the marginals, and the queueing behavior.
In this paper, we describe LRD and its relationship with fBm in section 2. Af-ter introducing the wavelet transform and describing the WIG model in section 3,we derive the MWM in section 4. Section 6 reports on the results of simulationexperiments with real data traces. We give an intuitive introduction to multifractalcascades in section 5 and close with conclusions in section 7.
2. fBm and LRD
Although we analyze fBm from a continuous-time point of view, for practicalcomputations and simulations, we often work with sampled continuous-time fBm.The increments process of sampled fBm
X[n] := B(n)�B(n� 1) (3)
defines a stationary Gaussian sequence known as discrete fractional Gaussian noise(fGn) with covariance behavior [10]
rX [k] ⇥ |k|2H�2, for |k| large . (4)
For 1/2 < H < 1, the covariance of fGn is strictly positive and decays soslowly that it is non-summable (i.e.,
⇤k rX [k] =⇤). This property is called LRD.
The LRD of fGn can be equivalently characterized in terms of how the ag-gregated processes
X(m)(n) :=1m
km⌅
i=(k�1)m+1
X(i) (5)
behave. It follows from (1) that X(n) fd= m1�HX(m)(n) .Hence, a log-log plot of the variance of X(m)(n) as a function of m —known
as a variance-time plot— will have a slope of 2H � 2. The variance-time plot cancharacterize LRD in non-Gaussian, non-zero-mean data as well [1].
3. Wavelets and LRD Processes
3.1. Wavelet transform
The discrete wavelet transform is a multi-scale signal representation of the form[11]
c(t) =⌅
k
uk 2�J0/2 ��2�J0t� k
⇥+
J0⌅
j=�⇥
⌅
k
wj,k 2�j/2 ⇥�2�jt� k
⇥, j, k ⌅ ZZ
Network Tra⇥c Modeling Using a Multifractal Wavelet Model 3
in the multifractal partition function T (q) , the burstiness as measured by themultifractal spectrum, the marginals, and the queueing behavior.
In this paper, we describe LRD and its relationship with fBm in section 2. Af-ter introducing the wavelet transform and describing the WIG model in section 3,we derive the MWM in section 4. Section 6 reports on the results of simulationexperiments with real data traces. We give an intuitive introduction to multifractalcascades in section 5 and close with conclusions in section 7.
2. fBm and LRD
Although we analyze fBm from a continuous-time point of view, for practicalcomputations and simulations, we often work with sampled continuous-time fBm.The increments process of sampled fBm
X[n] := B(n)�B(n� 1) (3)
defines a stationary Gaussian sequence known as discrete fractional Gaussian noise(fGn) with covariance behavior [10]
rX [k] ⇥ |k|2H�2, for |k| large . (4)
For 1/2 < H < 1, the covariance of fGn is strictly positive and decays soslowly that it is non-summable (i.e.,
⇤k rX [k] =⇤). This property is called LRD.
The LRD of fGn can be equivalently characterized in terms of how the ag-gregated processes
X(m)(n) :=1m
km⌅
i=(k�1)m+1
X(i) (5)
behave. It follows from (1) that X(n) fd= m1�HX(m)(n) .Hence, a log-log plot of the variance of X(m)(n) as a function of m —known
as a variance-time plot— will have a slope of 2H � 2. The variance-time plot cancharacterize LRD in non-Gaussian, non-zero-mean data as well [1].
3. Wavelets and LRD Processes
3.1. Wavelet transform
The discrete wavelet transform is a multi-scale signal representation of the form[11]
c(t) =⌅
k
uk 2�J0/2 ��2�J0t� k
⇥+
J0⌅
j=�⇥
⌅
k
wj,k 2�j/2 ⇥�2�jt� k
⇥, j, k ⌅ ZZ
Márcio De Deus
MulQfractal Spectrum (Parameters) fBm Fraclab H=0,7 Holder = Hurst em x0
fBm f periodic Holder
fBm f log Holder
Márcio De Deus
Parameter: h(t) = (0,1 + 0,8t) v 4096 samples
H(t) -‐ Hölder
Synthesized
Spectrum
SyntheQc traffic
Márcio De Deus
USàVenezuela/Colombia -‐ CharacterizaQon
Tráfego Original
Espectro de Legendre Função Hölder Interpolada
T1 T2 T3
Márcio De Deus
Internet Traffic: The real issue
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01/19/2012"01:00:00"
01/19/2012"05:00:00"
01/19/2012"09:00:00"
01/19/2012"13:00:00"
01/19/2012"17:00:00"
01/19/2012"21:00:00"
01/20/2012"01:00:00"
01/20/2012"05:00:00"
01/20/2012"09:00:00"
01/20/2012"13:00:00"
01/20/2012"17:00:00"
01/20/2012"21:00:00"
Ingress"to"Venezuela/Colombia" Egress"from"Venezuela/Colombia"
Colombia and Venezuela 80% is Inbound: Asymmetric – ASYin-‐out
Source: N.D.A.
Márcio De Deus
Internet Traffic: The real issue
Brazil 60ì70% is Inbound: Asymmetric ASYin-‐out
0"
200"
400"
600"
800"
1000"
1200"
01/13/2012"00:00:00"
01/13/2012"04:00:00"
01/13/2012"08:00:00"
01/13/2012"13:00:00"
01/13/2012"17:00:00"
01/13/2012"21:00:00"
01/14/2012"01:00:00"
01/14/2012"05:00:00"
01/14/2012"09:00:00"
01/14/2012"13:00:00"
01/14/2012"17:00:00"
01/14/2012"21:00:00"
01/15/2012"01:00:00"
01/15/2012"05:00:00"
01/15/2012"09:00:00"
01/15/2012"13:00:00"
01/15/2012"17:00:00"
01/15/2012"21:00:00"
01/16/2012"01:00:00"
01/16/2012"05:00:00"
01/16/2012"09:00:00"
01/16/2012"13:00:00"
01/16/2012"17:00:00"
01/16/2012"21:00:00"
01/17/2012"01:00:00"
01/17/2012"05:00:00"
01/17/2012"09:00:00"
01/17/2012"13:00:00"
01/17/2012"17:00:00"
01/17/2012"21:00:00"
01/18/2012"01:00:00"
01/18/2012"05:00:00"
01/18/2012"09:00:00"
01/18/2012"13:00:00"
01/18/2012"17:00:00"
01/18/2012"21:00:00"
01/19/2012"01:00:00"
01/19/2012"05:00:00"
01/19/2012"09:00:00"
01/19/2012"13:00:00"
01/19/2012"17:00:00"
01/19/2012"21:00:00"
01/20/2012"01:00:00"
01/20/2012"05:00:00"
01/20/2012"09:00:00"
01/20/2012"13:00:00"
01/20/2012"17:00:00"
01/20/2012"21:00:00"
Ingress"to"Brazil" Egress"from"Brazil"
Source: N.D.A.
Márcio De Deus
Planning & traffic engineering soluQons
Because: The South America problems are unique. Obviously: The decision-‐making must be supported by local data. The specific math models must match the real network behavior.
Márcio De Deus
AS 1st rule: no external control
“This is especially true for the inbound direc+on as the flow of traffic depends on the forwarding decision made at other routers in other Autonomous Systems. In other words, in order to engineer the way traffic enters a network, the route selec+on process at other routers has to be influenced remotely.” Explicitly Accommoda7ng Origin Preference for Inter-‐Domain Traffic Engineering Rolf Winter, ACM Symposium on Applied CompuQng, 2012
Márcio De Deus
Improving the prepend decision-‐making Process Start
Network CharacterizaQon
Internet full rouQng
Prepend CharacterizaQon
Internet full rouQng
Success Probability to use Prepend
Over 50%
Resource ForecasQng
BGP ModificaQon 2nd Plane opQon or Man2Man negoQaQon
Traffic CharacterizaQon
A
A
UQlizaQon ForecasQng
Best Path SelecQon
Network Change TentaQve
Monitoring results
End
y
n
Stable ?
y
n Wait
Next Window
Stability Window
Márcio De Deus
1st – Can I use the prepend as a T.E. tool?
0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99
1
0 5 10 15 20 25 30 35
CD
F
Difference in prepended ASN num. for same prefix
0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99
1
0 5 10 15 20 25 30 35
CD
F
Difference in prepended ASN num. for same prefix
routing tablerouting updates
Fig. 8. Difference in number of prependedASNs for the same prefix
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
CD
F
Fraction of routes with prepending paths per prefix
Fig. 9. Fraction of routes with prependingAS paths for the same prefix
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
CD
F
Fraction of monitors select routes with ASPP
Fig. 10. Fraction of monitors adopting routeswith ASPP.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
CD
F
first hop distribution among all routes
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
CD
F
first hop distribution among all routes
prefixorigin AS
Fig. 11. First hop distribution among neighbors
the prepending AS paths are likely to be longer than otherpaths, thus less preferable. However, there are 20% of theroutes are still adopted by most of the monitors. With furtherinvestigation, we found that it’s the origin AS that prependsits ASNs multiple times consistently for announcements to allits neighbors. Therefore, even the prepending increases the ASpath length, it is an equal inflation for all monitors.
ASPP can be used to balance the traffic among all neighborsor to provision a backup route. We categorize routes from allmonitors for the same prefix at any time according to their firsthop ASes. We then calculate the fraction of routes associatedwith each first hop. The distribution of such fraction numbersare shown in Figure 11. Surprisingly, we see that 90% casesthere is only one dominant route (the fraction is 1) for eachprefix. But examining from all prefixes of same origin AS,we observe a much smaller fraction. It suggests that operatorscommonly use ASPP to make best routes go through differentneighbors for different prefixes.
C. Dynamic characterization
15000
20000
25000
30000
35000
40000
45000
1/066/06 1/076/07 1/086/08 1/096/09 1/106/101/11
Num
ber o
f pre
fixes
with
ASP
P (K
)
months
Fig. 12. Trends of routes with ASPP in the default-free routing table
0.5
0.6
0.7
0.8
0.9
1
1/06 1/07 1/08 1/09 1/10 1/11
Avg.
frac
tion
of ro
utes
per
nei
ghbo
rmonths
Fig. 13. Trends of route distribution amongst neighbors over time
We next demonstrate how the prepending AS path involvesover time. Figure 12 shows the number of prefixes withany prepending AS paths from January 2006 to March 2011from RouteView. It presents significant increases, suggestingthat ASPP as a traffic engineering method has been morecommonly used. We next depict the trends of the impactof ASPP. Figure 13 shows the average fraction per monthover five years. The trend is very stable, i.e., 70%-80%,suggesting that each prefix often has a primary carrier amongstall neighbors.
VI. VALIDATION
In the following, we first validate the accuracy of ourprediction on route selection. Then we evaluate the algorithms’effectiveness from three aspects, i.e., load balancing, backuproute provisioning and bypassing a particular AS. The topol-ogy is extracted from multiple BGP routing tables and thetopology reported by CAIDA [17].
A. Validation of route predictionSince we cannot directly modify the prepending behavior on
the Internet, we evaluate the simulation accuracy by comparingthe predicted routes with the adopted routes on the Internet.One of the key steps in our proposal is the prediction of routesseen and chosen by each AS in Figure 2. We validate itsaccuracy using observed best routes from RouteView. Fromone month of RouteView table and update files, we extractall the prefixes which is announced to multiple neighborsby the origin AS padding its ASN different times. We plugthe observed padding numbers for each neighbor into thealgorithm in Figure 2 to compute the best route observed oneach AS. For each prefix and padding vector, we compute thefraction of ASes where the predicted route matches with the
66
0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99
1
0 5 10 15 20 25 30 35
CD
F
Difference in prepended ASN num. for same prefix
0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99
1
0 5 10 15 20 25 30 35
CD
F
Difference in prepended ASN num. for same prefix
routing tablerouting updates
Fig. 8. Difference in number of prependedASNs for the same prefix
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
CD
F
Fraction of routes with prepending paths per prefix
Fig. 9. Fraction of routes with prependingAS paths for the same prefix
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
CD
F
Fraction of monitors select routes with ASPP
Fig. 10. Fraction of monitors adopting routeswith ASPP.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
CD
F
first hop distribution among all routes
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
CD
F
first hop distribution among all routes
prefixorigin AS
Fig. 11. First hop distribution among neighbors
the prepending AS paths are likely to be longer than otherpaths, thus less preferable. However, there are 20% of theroutes are still adopted by most of the monitors. With furtherinvestigation, we found that it’s the origin AS that prependsits ASNs multiple times consistently for announcements to allits neighbors. Therefore, even the prepending increases the ASpath length, it is an equal inflation for all monitors.
ASPP can be used to balance the traffic among all neighborsor to provision a backup route. We categorize routes from allmonitors for the same prefix at any time according to their firsthop ASes. We then calculate the fraction of routes associatedwith each first hop. The distribution of such fraction numbersare shown in Figure 11. Surprisingly, we see that 90% casesthere is only one dominant route (the fraction is 1) for eachprefix. But examining from all prefixes of same origin AS,we observe a much smaller fraction. It suggests that operatorscommonly use ASPP to make best routes go through differentneighbors for different prefixes.
C. Dynamic characterization
15000
20000
25000
30000
35000
40000
45000
1/066/06 1/076/07 1/086/08 1/096/09 1/106/101/11
Num
ber o
f pre
fixes
with
ASP
P (K
)
months
Fig. 12. Trends of routes with ASPP in the default-free routing table
0.5
0.6
0.7
0.8
0.9
1
1/06 1/07 1/08 1/09 1/10 1/11
Avg.
frac
tion
of ro
utes
per
nei
ghbo
r
months
Fig. 13. Trends of route distribution amongst neighbors over time
We next demonstrate how the prepending AS path involvesover time. Figure 12 shows the number of prefixes withany prepending AS paths from January 2006 to March 2011from RouteView. It presents significant increases, suggestingthat ASPP as a traffic engineering method has been morecommonly used. We next depict the trends of the impactof ASPP. Figure 13 shows the average fraction per monthover five years. The trend is very stable, i.e., 70%-80%,suggesting that each prefix often has a primary carrier amongstall neighbors.
VI. VALIDATION
In the following, we first validate the accuracy of ourprediction on route selection. Then we evaluate the algorithms’effectiveness from three aspects, i.e., load balancing, backuproute provisioning and bypassing a particular AS. The topol-ogy is extracted from multiple BGP routing tables and thetopology reported by CAIDA [17].
A. Validation of route predictionSince we cannot directly modify the prepending behavior on
the Internet, we evaluate the simulation accuracy by comparingthe predicted routes with the adopted routes on the Internet.One of the key steps in our proposal is the prediction of routesseen and chosen by each AS in Figure 2. We validate itsaccuracy using observed best routes from RouteView. Fromone month of RouteView table and update files, we extractall the prefixes which is announced to multiple neighborsby the origin AS padding its ASN different times. We plugthe observed padding numbers for each neighbor into thealgorithm in Figure 2 to compute the best route observed oneach AS. For each prefix and padding vector, we compute thefraction of ASes where the predicted route matches with the
66To acquire the needed data only
To have the needed alternaQve only
To establish a good criteria (minimum price, balancing, …)
Márcio De Deus
Acquiring data+ :Prepend characterizaQon
hwp://bgp.potaroo.net/as6447/bgptable.txt
AS1 AS2 AS3 AS4 AS5 AS6 AS7 AS8 No Prepend
AS1 AS2 AS3 AS22 AS23 Prepend
0
500000000
1E+09
1,5E+09
2E+09 Distância 0
Distância 1
Distância 2
Distância 3
Distância 4
Distância 5
Distância 6
Distância 7 Distância 8 Distância 9
Distância 10
Distância 11
Distância 12
Distância 13
Distância 14
Distância 15
Distância 16
AS distance
Distância Number of hops
Márcio De Deus
Improving the prepend decision-‐making Process Start
Network CharacterizaQon
Internet full rouQng
Prepend CharacterizaQon
Internet full rouQng
Success Probability to use Prepend
Over 50%
Resource ForecasQng
BGP ModificaQon 2nd Plane opQon or Man2Man negoQaQon
Traffic CharacterizaQon
A
A
UQlizaQon ForecasQng
Best Path SelecQon
Network Change TentaQve
Monitoring results
End
y
n
Stable ?
y
n Wait
Next Window
Stability Window
Márcio De Deus
BGP Decision-‐Making parameters
Atribute Priority
Local Preference Highest Priority
Shortest ASPATH
Traffic Engineering Tentative
Lowest MED
iBGP < eBGP
Lowest iGP Cost to BGP egress
Lowest Router ID Lowest Priority
III. THE BGP CHARACTERIZATION: 1ST STEP TO DECISION-MAKING PROCESS
The BGP Best Path Selection Process is defined with some external dependence, depending what kind of policy is used. According [8], [9] two different kind of policy can be found: external or internal, is shown that the Local attributes as shown in Fig. 4 have more priority than other attributes.
Atribute Priority
Local Preference Highest Priority
Shortest ASPATH
Traffic Engineering Tentative
Lowest MED
iBGP < eBGP
Lowest iGP Cost to BGP egress
Lowest Router ID Lowest Priority
Figure 4. BGP Condensed Priority Decision Making Preferences
In the same way the import routing policy (pin) or the (pout) can be defined as scalar filters applied on Graph on equation (1) as shown in [10] as a way to control the advertised routes inbound or outbound direction.
G=(V, E, B) (1)
The routing policy will define if a route will be announced or acquired in terms of table. The Gpol is the Graph after an inbound or outbound filter. The pin or pout can be written as a scalar.
Gpol=(V,E,B) * pin (G) for ingress (2)
Gpol=(V,E,B) * pout(G) for egress (3)
pin (G) assuming discrete values of “0” to block or “1” to accept a route set. pout(G) assuming discrete values of “0” to not advertise or “1” to advertise a route set.
This is a way to make a police controlled system with a possibility to insert filters. This makes an ingress traffic change by the destination a hard task, because AS_PATH attribute is the first external to be considered and is only the fourth in order of preference [11], [12]. This decision process can be divided in three different layers. The local preference is the highest priority parameter and internally controlled only. There are also the Traffic Engineering purpose parameters used as a tentative of traffic control by an external AS, these are always used when a someone wants to try to interfere in the internal decision making process. The lowest router ID is the lowest priority followed by iGP cost, iBGP learned, eBGP learned, MED, ASPATH Local Preference as the higher.
As described in [9],[12],[13] the hot potato routing can interfere in terms of routing convergence. By other side, if the
hot potato do not lead to new BGP update messages, some delay increment can occurs inside AS [4].
A. The Internet Radius Characterization. The Internet radius for decision-making process can be defined as the path count number. On the Bellmand criterion [13] a vertex ! ! ! lies on a shortest path between vertices !! ! ! !! !"!!"#!!"#$!!! !! ! ! !!! !! ! ! !! !! ! ! !Algorithm:
Get a full routing table T=dG(s,t)
For Subnet Sj
For PathSj={AS0, AS1; ASj-1; ASj}
Aggregate { PathSj}
Min {PathSj}
Count j
{Sj} ! ASk
rASk = j
end
end
Using this algorithm in weka project [weka] as the tool to find the AS Radius with a full table routing as shown in Fig.5
Fig.5. The Internet radius r. Each n ASn denotes the Internet radius using weka [14]
In Fig.6 Measured using internet full table (400k+ routes) information from [routeviews, potaroo] using weka [14] to filter. The (r + var) is shown in the ordinate axys variation
Fig.6. The Internet radius average and var.
!"
#"
$"
%"
&"
'"
("
)*+,-" ./$0(" ./1!#" ./1!#0" ./0'$" ./#$('&" ./%'&2" ./#'&(2"!"
#$%&#'()
%$*%+,#''
-%.*/0'
!12'
III. THE BGP CHARACTERIZATION: 1ST STEP TO DECISION-MAKING PROCESS
The BGP Best Path Selection Process is defined with some external dependence, depending what kind of policy is used. According [8], [9] two different kind of policy can be found: external or internal, is shown that the Local attributes as shown in Fig. 4 have more priority than other attributes.
Atribute Priority
Local Preference Highest Priority
Shortest ASPATH
Traffic Engineering Tentative
Lowest MED
iBGP < eBGP
Lowest iGP Cost to BGP egress
Lowest Router ID Lowest Priority
Figure 4. BGP Condensed Priority Decision Making Preferences
In the same way the import routing policy (pin) or the (pout) can be defined as scalar filters applied on Graph on equation (1) as shown in [10] as a way to control the advertised routes inbound or outbound direction.
G=(V, E, B) (1)
The routing policy will define if a route will be announced or acquired in terms of table. The Gpol is the Graph after an inbound or outbound filter. The pin or pout can be written as a scalar.
Gpol=(V,E,B) * pin (G) for ingress (2)
Gpol=(V,E,B) * pout(G) for egress (3)
pin (G) assuming discrete values of “0” to block or “1” to accept a route set. pout(G) assuming discrete values of “0” to not advertise or “1” to advertise a route set.
This is a way to make a police controlled system with a possibility to insert filters. This makes an ingress traffic change by the destination a hard task, because AS_PATH attribute is the first external to be considered and is only the fourth in order of preference [11], [12]. This decision process can be divided in three different layers. The local preference is the highest priority parameter and internally controlled only. There are also the Traffic Engineering purpose parameters used as a tentative of traffic control by an external AS, these are always used when a someone wants to try to interfere in the internal decision making process. The lowest router ID is the lowest priority followed by iGP cost, iBGP learned, eBGP learned, MED, ASPATH Local Preference as the higher.
As described in [9],[12],[13] the hot potato routing can interfere in terms of routing convergence. By other side, if the
hot potato do not lead to new BGP update messages, some delay increment can occurs inside AS [4].
A. The Internet Radius Characterization. The Internet radius for decision-making process can be defined as the path count number. On the Bellmand criterion [13] a vertex ! ! ! lies on a shortest path between vertices !! ! ! !! !"!!"#!!"#$!!! !! ! ! !!! !! ! ! !! !! ! ! !Algorithm:
Get a full routing table T=dG(s,t)
For Subnet Sj
For PathSj={AS0, AS1; ASj-1; ASj}
Aggregate { PathSj}
Min {PathSj}
Count j
{Sj} ! ASk
rASk = j
end
end
Using this algorithm in weka project [weka] as the tool to find the AS Radius with a full table routing as shown in Fig.5
Fig.5. The Internet radius r. Each n ASn denotes the Internet radius using weka [14]
In Fig.6 Measured using internet full table (400k+ routes) information from [routeviews, potaroo] using weka [14] to filter. The (r + var) is shown in the ordinate axys variation
Fig.6. The Internet radius average and var.
!"
#"
$"
%"
&"
'"
("
)*+,-" ./$0(" ./1!#" ./1!#0" ./0'$" ./#$('&" ./%'&2" ./#'&(2"
!"#$%&#'()
%$*%+,#''
-%.*/0'
!12'
Accept or not ?
Márcio De Deus
More parameters: The Internet Radius
III. THE BGP CHARACTERIZATION: 1ST STEP TO DECISION-MAKING PROCESS
The BGP Best Path Selection Process is defined with some external dependence, depending what kind of policy is used. According [8], [9] two different kind of policy can be found: external or internal, is shown that the Local attributes as shown in Fig. 4 have more priority than other attributes.
Atribute Priority
Local Preference Highest Priority
Shortest ASPATH
Traffic Engineering Tentative
Lowest MED
iBGP < eBGP
Lowest iGP Cost to BGP egress
Lowest Router ID Lowest Priority
Figure 4. BGP Condensed Priority Decision Making Preferences
In the same way the import routing policy (pin) or the (pout) can be defined as scalar filters applied on Graph on equation (1) as shown in [10] as a way to control the advertised routes inbound or outbound direction.
G=(V, E, B) (1)
The routing policy will define if a route will be announced or acquired in terms of table. The Gpol is the Graph after an inbound or outbound filter. The pin or pout can be written as a scalar.
Gpol=(V,E,B) * pin (G) for ingress (2)
Gpol=(V,E,B) * pout(G) for egress (3)
pin (G) assuming discrete values of “0” to block or “1” to accept a route set. pout(G) assuming discrete values of “0” to not advertise or “1” to advertise a route set.
This is a way to make a police controlled system with a possibility to insert filters. This makes an ingress traffic change by the destination a hard task, because AS_PATH attribute is the first external to be considered and is only the fourth in order of preference [11], [12]. This decision process can be divided in three different layers. The local preference is the highest priority parameter and internally controlled only. There are also the Traffic Engineering purpose parameters used as a tentative of traffic control by an external AS, these are always used when a someone wants to try to interfere in the internal decision making process. The lowest router ID is the lowest priority followed by iGP cost, iBGP learned, eBGP learned, MED, ASPATH Local Preference as the higher.
As described in [9],[12],[13] the hot potato routing can interfere in terms of routing convergence. By other side, if the
hot potato do not lead to new BGP update messages, some delay increment can occurs inside AS [4].
A. The Internet Radius Characterization. The Internet radius for decision-making process can be defined as the path count number. On the Bellmand criterion [13] a vertex ! ! ! lies on a shortest path between vertices !! ! ! !! !"!!"#!!"#$!!! !! ! ! !!! !! ! ! !! !! ! ! !Algorithm:
Get a full routing table T=dG(s,t)
For Subnet Sj
For PathSj={AS0, AS1; ASj-1; ASj}
Aggregate { PathSj}
Min {PathSj}
Count j
{Sj} ! ASk
rASk = j
end
end
Using this algorithm in weka project [weka] as the tool to find the AS Radius with a full table routing as shown in Fig.5
Fig.5. The Internet radius r. Each n ASn denotes the Internet radius using weka [14]
In Fig.6 Measured using internet full table (400k+ routes) information from [routeviews, potaroo] using weka [14] to filter. The (r + var) is shown in the ordinate axys variation
Fig.6. The Internet radius average and var.
!"
#"
$"
%"
&"
'"
("
)*+,-" ./$0(" ./1!#" ./1!#0" ./0'$" ./#$('&" ./%'&2" ./#'&(2"
!"#$%&#'()
%$*%+,#''
-%.*/0'
!12'
Márcio De Deus
10.1.0.0/16
BGP Traffic Engineering
ASp
AS2 AS3
ASs ASa
AS4
Outbound Source: ASS
DesQnaQon: ASp
Inbound Source: ASS
DesQnaQon: Asp Subnet 10.1.0.0/16
Asp Needs to control the inbound traffic to balance: l2-‐p; l3-‐p e l4-‐p
l2-‐p l3-‐p
l4-‐p
Márcio De Deus
ASp
AS2 AS3
ASs ASa
AS4
Source: ASS DesQnaQon: ASp
Inbound Source: ASS
DesQnaQon: Asp Subnet 10.1.0.0/16
Prepend with ASPath 10.1.128.0/18 AS4 shortest Path
l2-‐p l3-‐p
l4-‐p
10.1.0.0/18 10.1.64.0/18
10.1.192.0/18
10.1.128.0/18
BGP Traffic Engineering
Márcio De Deus
ASp
AS2 AS3
ASs ASa
AS4
Outbound Source: ASS
DesQnaQon: ASp
Inbound Source: ASS
DesQnaQon: Asp Subnet 10.1.0.0/16
Prepend with ASPath 10.1.128.0/18 AS4 Shortest Path
l2-‐p l3-‐p
l4-‐p
10.1.0.0/18 10.1.64.0/18
10.1.192.0/18
10.1.128.0/18
No traffic balance guarantee because the 10.1.0.0 and 10.1.64.0 subnets can have more traffic demand per user. No Inbound 100% control.
BGP Traffic Engineering
Márcio De Deus
ASp
AS2 AS3
ASs ASa
AS4
Outbound Source: ASS
DesQnaQon: ASp
Inbound Source: ASS
DesQnaQon: Asp Subnet 10.1.0.0/16
Prepend with ASPath 10.1.128.0/18 AS4 shortest Path wins
l2-‐p l3-‐p
l4-‐p
10.1.0.0/18 10.1.64.0/18
10.1.192.0/18
10.1.128.0/18
The soluQon must be more intelligent than use BGP parameters only. Other parameters extract from the network must be used.
BGP Traffic Engineering
Márcio De Deus
Improving the prepend decision-‐making Process Start
Network CharacterizaQon
Internet full rouQng
Prepend CharacterizaQon
Internet full rouQng
Success Probability to use Prepend
Over 50%
Resource ForecasQng
BGP ModificaQon 2nd Plane opQon or Man2Man negoQaQon
Traffic CharacterizaQon
A
A
UQlizaQon ForecasQng
Best Path SelecQon
Network Change TentaQve
Monitoring results
End
y
n
Stable ?
y
n Wait
Next Window
Stability Window
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Traffic Engineering: Decision-‐making
Traffic&Jam
&
Decision/Making&Process&
BGP&&
ATTRIBUTES&
BGP&&
ATTRIBUTES&
BGP&&
ATTRIB
UTES&
BGP&&
ATTRIBU
TES&
EUA&EUA&
EUA&South&America&
A?er&Decision/Making&Process&
US
US
US
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Conclusion The traffic is mostly asymmetric even when in the same link, because the huge dependence of content from South America to US. This also can be explain because the faciliQes low prices in US hosQng services when compare to South America. The traffic is mulQfractal and because that the forecasQng must to use this model to represent future needs. Anyway, the traffic opQmizaQon is a huge task even when the task is internal only, considering the whole Internet environment makes this task much difficult because by definiQon any AS is itself managed, with own policies and procedures.
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References [1] -‐ Gireesh Shrimali, Aditya Akella, Almir Mutapcic. Stanford University & University of Wisconsin-‐Madison. CooperaQve Inter-‐Domain Traffic Engineering Using Nash Bargaining and DecomposiQon. [2] -‐ R. Mahajan, D. Wetherall, and T. Anderson, “Towards coordinated interdomain traffic engineering,” in HotNets-‐III, 2004.
[3] -‐ DEUS, M.A.; CARVALHO, P. H. P.; LEITE, J.P. BGP Traffic Engineering: Understanding South America Traffic Pawerns to Improve Decision-‐Making. In: XXXI Simpósio Brasileiro de Telecomunicações, 2013, Fortaleza. SBrT 2013, 2013. [4] -‐ DEUS, M. A.* ; CARVALHO, P. H. P.; SOLIS BARRETO, P. S. . IP and 3G Bandwidth Management Strategies applied to Capacity Planning. In: OrQz, Jesus H.. (Org.). TelecommunicaQons Networks -‐ Current Status and Future Trends. 1ed.CroaQa: In Tech Open Access, 2012, v. 01, p. 1-‐16.