Capturing Internet tra� dynami s throughgraph distan esSteve Uhlig1, Bingjie Fu2, and Almerima Jamakovi 31 TU Berlin/Deuts he Telekom labs, Berlin, Germany,steve�net.t-labs.tu-berlin.de2 Delft University of Te hnology, Delft, Netherlands,B.Fu�tudelft.nl

3 TNO ICT, Delft, Netherlands,almerima.jamakovi �tno.nlAbstra t. Studies of the Internet have typi ally fo used either on therouting system, i.e. the paths hosen to rea h a given destination, oron the evolution of tra� on a physi al link. In this paper, we ombinerouting and tra� , and study for the �rst time the evolution of the tra� on the Internet topology. We rely on the tra� and routing data of alarge transit provider, spanning almost a month.We ompute distan es between the tra� graph over small and largetimes ales. We �nd that the global tra� distribution on the AS graphlargely di�ers from tra� observed at small times ales. However, vari-ations between onse utive time periods are relatively limited, i.e. thetopology spanned by the tra� from one time period to the next is small.This di�eren e between lo al and global tra� distribution is found inthe times ales at whi h tra� dynami s o urs on AS-level links. Smalltimes ales, i.e. less than a few hours, do not a ount for a signi� antfra tion of the tra� dynami s. Most of the tra� variability is on en-trated at times ales of days. Models of Internet tra� on its topologyshould thus fo us on apturing the long-term hanges in the global tra� pattern.Key words: Internet tra� , AS topology, graph distan e, multi-resolutionanalysis1 Introdu tionMost of the studies on tra� dynami s fo us on a single link [6, 7, 11, 17, 9, 24℄. Inreality, Internet tra� is the out ome of end-hosts ex hanging data, not througha single link, but over paths 1. The Internet is omposed of more than 30, 000autonomous systems (AS). An AS is a network under a single administrative au-thority. Ea h AS hooses independently its paths to rea h destinations, amongthe paths that its neighboring ASs advertise. Typi al examples of ASs are In-1 Paths in the Internet are typi ally asymmetri [16, 4℄, so that pa kets ex hangedbetween two hosts follow di�erent paths in the two dire tions.

2 Steve Uhlig et al.ternet Servi e Provider networks, or university ampuses. In this paper, we usethe abstra tion of the Internet topology at the AS-level.When an AS re eives tra� that has to be sent towards a destination, it relieson the interdomain routing proto ol, BGP [14℄, to �nd the next AS on the pathto rea h the destination. Ea h AS knows the full AS path that will be followedby its pa kets to rea h a destination. Ea h path is made of AS-level links oredges. As topologi al failures happen within ASs or on the links between twoASs, and as ASs hange their path preferen es over time, AS paths may hange.Tra king the a tual dynami s in tra� on the AS topology requires to modelthe routing state of the onsidered AS over time [13℄, as explained in Se tion 2.In this paper, we study the dynami s in the set of AS-level edges used forforwarding tra� , as well as the dynami s of the amount of tra� arried by ea hAS-level edge over time, for a large transit AS. This knowledge of the �ow of thetra� in the Internet is important not only for operational purposes like tra� engineering [12, 21, 23℄, but also to understand the Internet as a omplex system[10℄. For the �rst time, we study in this paper the global dynami s of the tra� onthe Internet topology, as seen from a large transit AS. More spe i� ally, we try tounderstand the dynami s of the AS-level topology spanned by the tra� . We �ndthat this topology at small times ales di�ers onsiderably from the global tra� distribution over a long time period. This indi ates that modeling Internet tra� requires models that apture the small times ales behavior of the topologi altra� distribution. This small times ales topologi al tra� distribution is highlydependent on the tra� dynami s observed by individual AS-level edges.We present the data used in this paper and how the tra� is mapped to theAS-level onne tivity in Se tion 2. In Se tion 3, we de�ne the distan e betweentwo AS-level graphs, and the distan e between two tra� distributions on the orresponding AS-level graphs. We �rst study the distan e between individualtime intervals and the global tra� topology in Se tion 4. Then, we analyze hanges of tra� distribution between onse utive time intervals in Se tion 5.We rely on multi-resolution analysis to study the varian e of tra� on ea h AS-level edge a ross di�erent times ales in Se tion 6. Finally, Se tion 7 on ludesthis paper.2 Data and methodologyWe obtained tra� and routing information from the GÉANT network. GÉANTis the pan-European resear h network. It arries resear h tra� from the Euro-pean National Resear h and Edu ation Networks (NRENs) onne ting universi-ties and resear h institutions. GÉANT has a point of presen e in ea h European ountry.To properly re onstru t paths followed by the tra� , a model of the routingof GÉANT must be built [13℄. To ompute paths between routers inside itsnetwork, GÉANT uses the ISIS routing proto ol. We obtained a tra e of its ISISmessages. With these messages, we keep an up-to-date view of the internal stateof GÉANT and ompute the paths from any router to any other router inside

Capturing Internet tra� dynami s through graph distan es 3the GÉANT network during the whole time of the study. On e we know theinternal path followed by the tra� inside the GÉANT network, we an �nd outthe exit router of GÉANT that forwarded tra� outside the network.Then, we rely on information from the BGP routing proto ol to determinethe global AS-level paths taken by tra� observed by GÉANT to rea h its desti-nations. BGP [14℄ is the urrent routing proto ol used between ASs. With BGP,ea h AS learns the paths to rea h ea h destination in the Internet. In GÉANT,the BGP routes are olle ted using a dedi ated workstation running GNU Zebra[25℄, a software implementation of di�erent routing proto ols in luding BGP.The workstation has an iBGP session with all the border routers of the network.Using this te hnique, it is possible to olle t all the BGP routes sele ted by theborder routers of GÉANT and thus �nd out the global AS-level path followed bytra� entering GÉANT towards any destination in the Internet. With this, weknow the set of ASs rossed by tra� entering GÉANT towards any destination,at any time instant of the study [13℄.We also obtained Net�ow [8℄ tra es olle ted from all external links of theGÉANT network, i.e. all the tra� entering the network was re orded. Net�owprovides the aggregated information of the layer-4 �ows, by re ording the startingtime, the ending time and the total volume in bytes for ea h unidire tional TCPand UDP �ow. Net�ow was on�gured with a 1/1000 pa ket sampling rate. Withthis sampling, only one out of 1000 is onsidered by Net�ow. In a large networksu h as GÉANT, the amount of tra� prohibits to use low sampling rates as it isunsafe for the proper operation of the routers. Given that the aim of this paperis not to study the small times ales, the de ision was made to use a granularityof 15 minutes for the �nest times ale.On e we have a model of the routing of GÉANT, we ompute for ea h Net�owentry the orresponding AS path the tra� takes to rea h its destination, andattribute the tra� seen to ea h AS-level link along the path. We all an edge2 e of the AS graph G, a pair ASX − ASY appearing as two onse utive anddistin t ASs in the AS path omputed by our model of GÉANT. We attribute toea h edge e the amount of tra� it arries during ea h time interval. For moredetails about this data, we refer to [22℄.We study a ontiguous 26 days period between May 5 2005 and May 31 2005, orresponding to 2592 15-minutes time intervals.3 Distan es3.1 Distan e between two topologiesIn this paper, we de�ne the distan e between two graphs G0 and G1 as follows:2 We use the terms edge and link inter hangeably in this paper, but they always referto an AS-level edge. An AS-level edge does not orrespond to a physi al link of therouter-level graph, but may orrespond to several physi al links on the topology.

4 Steve Uhlig et al.DG(G0, G1) = 1 −

I(G0, G1)

U(G0, G1)(1)where I(G0, G1) represents the number of AS-level edges in the interse tionof G0 and G1 and where U(G0, G1) represents the number of AS-level edgesin the union of G0 and G1. A graph distan e of 0 means that the two graphsare identi al. A distan e of 1 means that the two graphs do not have a singleAS-level edge in ommon.3.2 Distan e between two tra� topologiesAs we are not only interested in the AS-level topology, but the tra� that rossesea h AS-level edge, we de�ne a distan e between two graphs weighted by thetra� seen on AS-level edges:

DGtraf (G0, G1) = 1 −

Itraf (G0, G1)

Utraf(G0, G1)(2)where

Itraf (G0, G1) =∑

e∈I(G0,G1)

min(TRe(G0), TRe(G1)) (3)andUtraf(G0, G1) =

∑

e∈U(G0,G1)

max(TRe(G0), TRe(G1)). (4)TRe(G) denotes the amount of tra� that edge e has on graphG. Itraf (G0, G1)is equivalent to the interse tion of the two graphs I(G0, G1), but where we on-sider that the interse tion is de�ned by the sum of the minimum amount oftra� ommon to all edges in the graph interse tion I(G0, G1). Utraf(G0, G1) isde�ned similarly, as the sum of the maximum amount of tra� of all edges inthe graph union U(G0, G1).4 Distan e between individual time intervals and globaltra� topologyGlobal tra� patterns in the Internet have typi ally been studied without he k-ing whether the tra� properties do depend on the onsidered times ale [5, 3, 15℄.Those studies have on luded that a few popular sour e-destinations (end-hostsor networks) do a ount for the majority of the tra� . [19℄ has shown that thispi ture of tra� over-simpli�es reality. In pra ti e, only a subset of the sour e-destination pairs is stable on times ales smaller than hours. We thus expe t thatthe AS-level topology spanned by the tra� on small times ales will di�er fromthe topology spanned over large times ales.

Capturing Internet tra� dynami s through graph distan es 54.1 Graph similarityTo ompare the topology spanned by tra� over short and large times ales, webuild the graphs spanned by tra� for ea h 15 minutes time interval over the 26studied days, denoted by Gi, i = 1, ..., 2592. We also build the graph from thetra� over the 26 days of the study, denoted by Gglobal. We then ompute forea h Gi the graph distan e (see equation 1) between Gi and Gglobal.Figure 1 shows the umulative distribution of the distan e between the Giand Gglobal for the 2592 time intervals. For all time intervals, the distan e islarger than 0.57. Less than 43% of the AS-level edges known by Gglobal appearduring any 15 minutes time interval. The distan e an be as large as 0.72, hen esampling only 28% of the existing AS-level edges of Gglobal.

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Graph distanceFig. 1. Distribution of graph distan e between the Gi's and Gglobal.The graphs of tra� during 15 minutes time intervals are thus very di�erentfrom the global tra� over large times ales. The Gi's and Gglobal annot be onsidered as topologi ally similar.4.2 Tra� similarityGglobal ontains all AS-level edges for whi h tra� has been observed over the26 studied days. Now, we want to ompute the distan e between the Gi's andGglobal, but in terms of the amount of tra� . Our tra� distan e de�ned inequation 2 ompared the tra� on ea h edge of the two ompared graphs. Asedges of Gglobal umulate tra� over a far longer time period than the Gi's, wedivide the amount of tra� seen on ea h edge of Gglobal by 2592, i.e. we average

6 Steve Uhlig et al.tra� over time for ea h edge. We denote Gglobal where the tra� of ea h edgehas been averaged by Gtrafglobal. The graphs for ea h 15 minutes time interval wheretra� is attributed on ea h edge are denoted by G

trafi , i = 1, ..., 2592. Then, we ompute the tra� distan e as in equation 2 between ea h G

trafi and G

trafglobal.Figure 2 shows the umulative distribution of the distan e between the G

trafiand G

trafglobal for the 2592 time intervals. For most (99%) of the time intervals, thedistan e is larger than 0.82. This indi ates that the global tra� distributionis very di�erent from the short-term tra� distribution. As already hinted in[19℄, the topologi al tra� distribution observed over large times ales is notrepresentative of the tra� distribution over shorter time intervals.

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Traffic distanceFig. 2. Distribution of graph distan e between the Gtrafi 's and G

traf

global.5 Distan e between onse utive time intervalsIn Se tion 4, we showed that the tra� over 15 minutes time intervals and overthe whole studied period di�ers very mu h, as seen through the graph distan e.The impli ations of Se tion 4 reinfor e the �ndings of [19℄. These impli ationsdo not mean that modeling Internet tra� on the AS-topology is out of rea h.Rather, the long-term tra� distribution does not represent well the short-termone, so that short-term tra� hanges should be taken into a ount in a tra� model. To better understand the short-term dynami s of the tra� on the AS-level graph, in this se tion we study hanges between onse utive time intervals.

Capturing Internet tra� dynami s through graph distan es 75.1 Graph distan e between time intervalsIn Se tion 4.1, it was shown that tra� on the AS-level graph varies mu h,at least when distan e was with respe t to Gglobal. Instead of omputing thedistan e between the Gi and Gglobal, we ompute the distan e between Gi andGi+1, for i = 1, ..., 2591. The umulative distribution of those distan es is shownon Figure 3.

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Graph distanceFig. 3. Distribution of graph distan e between Gi and Gi+1.Contrary to the �gures in Se tion 4.1, the graph distan e between onse -utive time intervals is small, betwen 0.1 and 0.2. Conse utive AS-level graphsspanned by tra� over 15 minutes time intervals are thus lose to ea h other.This means that the graph of tra� evolves relatively smoothly over time oversu h times ales.5.2 Tra� distan e between time intervalsIf we ompare the onse utive Gtrafi instead of the Gi, we obtain the distributionshown on Figure 4. On this �gure, we obtain even smaller distan es for the tra� between onse utive time intervals, typi ally between 0.06 and 0.1. Only veryfew onse utive time intervals have large distan es, up to 0.5.The distan es between onse utive time intervals give a far more optimisti pi ture of tra� variability on the AS topology than found in Se tion 4.1. Mod-eling tra� dynami s should thus require relatively small hanges over time.However, as shown in [19℄, the tra� on di�erent parts of the AS topology hasdi�erent dynami s. In Se tion 6, we will analyze this dynami s of the tra� onAS-level edges.

8 Steve Uhlig et al.

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0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55Per

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Traffic distanceFig. 4. Distribution of graph distan e between Gtrafi and G

trafi+1

.6 Tra� dynami s on AS-level edgesIn this se tion, we seek to �nd out explanations for the rather large distan esbetween the Gi's and Gglobal, and the small distan es between onse utive Gi's.The dynami s of the tra� on di�erent AS-level edges should explain thosedistan es between the graphs spanned by the tra� . In Se tion 6.1 we studythe relationship between the lifetime of AS-level edges and the amount of tra� they arry. In Se tion 6.2 we perform a multi-resolution analysis of the tra� dynami s on AS-level edges.6.1 Amount of tra� vs. lifetimeFirst, we look at the relationship between the amount of tra� seen by an AS-level edge and for how many 15 minutes time intervals this edge has tra� at all.Previous work has shown that tra� observed by an AS has a tree-like stru turerooted at the observing AS and whose leafs are the destination ASs [18, 19℄, andon average edges farther away from the root see less tra� . We thus expe t thatdi�erent edges observed di�erent tra� dynami s.We all the total number of 15 minutes time intervals that an AS-level edge isobserved to arry tra� its lifetime. The x-axis of Figure 5 gives the lifetime. They-axis gives the per entage of tra� , in logarithmi s ale. The dots in Figure 5give the per entage of tra� that edges having a given lifetime represent. We seethat most of the dots orrespond to large lifetimes. The solid urve in Figure 5gives the umulative tra� as a fun tion of edge lifetime. On this urve, we seethat edges that have a small lifetime do not represent a signi� ant fra tion of the

Capturing Internet tra� dynami s through graph distan es 9tra� . About 80% of the tra� is arried by those AS-level edges that appearalmost all the time.

0.1

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0 500 1000 1500 2000 2500

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tal t

raffi

c (lo

gsca

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Lifetime

traffic per edgecumulative traffic

Fig. 5. AS-level edges' life time and the amount of tra� they arry.6.2 Edge varian e de ompositionFrom Se tion 6.1, we know that only edges having a large enough lifetime shouldbe onsidered, as other edges do not represent a signi� ant fra tion of the totaltra� . Now, we would like to better understand the tra� dynami s on thoseedges that apture most of the tra� on the AS topology. Be ause of knownnon-stationarity of Internet tra� [1, 20℄, we do not rely on spe tral analysisbut wavelets [2℄. Wavelets belongs to multi-resolution analysis and allow to de- ompose the varian e of the tra� on ea h edge into the respe tive ontributionof ea h times ale.Figure 6 provides the breakdown of the tra� varian e within ea h edgea ross the di�erent times ales, as omputed through the wavelet oe� ients.Times ales go from 30 min (s ale 1) to about 5 days (s ale 9), and are indi- ated with di�erent olors. Independently for ea h edge, we sta k the relative ontribution of ea h times ale to the total varian e of the tra� of this edge, bystarting from the smallest times ale and su essively adding the ontribution oflarger times ales.The x-axis of Figure 6 gives the edges, ordered by de reasing amount oftra� . We observe that edges having most tra� (left of Figure 6) have onaverage more of their varian e within the larger times ales (8 hours or more).For edges that do not have mu h tra� , the lowest three times ales (between 30

10 Steve Uhlig et al.

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0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

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scale 9 (128 hours)scale 8 (64 hours)scale 7 (32 hours)scale 6 (16 hours)scale 5 (8 hours)

scale 4 (4 hours)scale 3 (2 hours)scale 2 (1 hour)scale 1 (30 min)Fig. 6. De omposition of tra� varian e among times ales.minutes and 2 hours) a ount for almost 30% of their varian e. Edges that seea lot of tra� are thus less bursty on small times ales than edges that see lesstra� . The burstiness of the tra� varies mu h a ross edges.This behavior is onsistent with previous studies in the networking literaturethat have debated on the tra� variability on di�erent types of links. Studiesof large ba kbone links have on luded that tra� burstiness tends to a non-stationarity Poisson pro ess as link apa ity in reases [1℄. Studies of smaller linksand networks on the other hand have found that self-similar pro esses betterdes ribe tra� [6, 7, 11, 17, 9, 24℄. Figure 6 shows that the pro ess that bestdes ribes tra� burstiness on a given edge has mu h to do with the amount oftra� observed on this link.From Figure 6, we do not have a feeling of what times ales are really im-portant if we want to explain the dynami s of most of the tra� . For this, weturn to Figure 7, where we weight the varian e at ea h times ale by the amountof tra� seen for the onsidered edge. As in Figure 6, edges are ordered by de- reasing amount of tra� on the x-axis. We observe on Figure 7 that the lower 4times ales do not ontribute to a signi� ant fra tion of the total tra� -weightedvarian e. S ale 9 (�128 hours�) a ounts for about 50% of the tra� -weightedvarian e. S ales 6 to 9 a ount for more than 90% of the tra� -weighted vari-an e. This means that even though burstiness appears at small times ale belowhours, most of the tra� dynami s happens for large times ales.

Capturing Internet tra� dynami s through graph distan es 11

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Fig. 7. Tra� -weighted distribution of the varian e.We are now in a position to explain the behavior of the graph and tra� dis-tan es observed in Se tions 4 and 5. As most of the tra� dynami s is ontainedwithin large times ales, the distan e between the tra� graph during a smalltime period (e.g. Gi) and the global graph (e.g. Gglobal) will be large. Unless twographs are lose in time, e.g. onse utive Gi's, the distan e between two tra� graphs will be signi� ant due to edge dynami s. Models of Internet tra� onthe AS topology need to onsider relevant times ales, e.g. hours or more, unlessthey will have to deal with omplex tra� burstiness that is not important toreprodu e for tra� dynami s on the Internet topology.7 Con lusionIn this paper, we ombined routing and tra� , and studied the evolution overtime of the tra� on the Internet topology. We relied on the tra� observedby a large transit provider for almost a month, to measure the hanges of thetopology spanned by the tra� .We omputed distan es between the tra� graph over small and largetimes ales. We found that the tra� observed at large times ales di�ers fromtra� observed at small times ales. However, variations between onse utivetime periods are relatively limited, i.e. the topology spanned by the tra� fromone time period to the next is small. Small times ales, i.e. less than a few hours,do not a ount for a signi� ant fra tion of the tra� dynami s. Most of the traf-� dynami s on the Internet topology happens for times ales of several hours.The slowly hanging tra� pattern is responsible for large distan es observedbetween the tra� graphs on small times ales and the global tra� graph.

12 Steve Uhlig et al.There are several impli ations of this paper on omplex networks. First, mod-els of the Internet tra� on the topology should on entrate on large times ales,and try to reprodu e the long-term variations of the tra� pattern on the topol-ogy. Se ond, other omplex networks undergo omplex dynami s like the Inter-net, e.g. road tra� networks or biologi al networks. Studying the topologi aldynami s of those systems will help understand the global behavior of those sys-tems, and in turn help to understand the fun tions implemented within them.A knowledgementsWe thank DANTE for making the GEANT tra� and routing data available.This work was funded by the Federal Ministry of Edu ation and Resear h of theFederal Republi of Germany (support ode 01 BK 0805, G-Lab). The authorsalone are responsible for the ontent of the paper.Referen es1. Cao J., Cleveland W., Lin D., and Sun D.: On the nonstationarity of Internet tra� .In: International Conferen e on Measurement and Modeling of Computer Systems(SIGMETRICS), pp. 102�112, ACM press, New York (2001)2. Daube hies I.: Ten Le tures onWavelets. Volume 61 in CMBS-NSF Series in AppliedMathemati s. SIAM press, Philadelphia (1992)3. Fang W. and Peterson L.: Inter-AS tra� patterns and their impli ations. In: GlobalTele ommuni ations Conferen e (GLOBECOM), pp. 1859�1868, IEEE press, New-York (1999)4. He G. Y., Faloutsos M., and Krishnamurthy S.: Quantifying routing asymmetry inthe Internet at the AS level. In: Global Tele ommuni ations Conferen e (GLOBE-COM), pp. 1474�479, IEEE press, New-York (2004)5. Kleinro k, L., and Naylor, W.E.: On measured behavior of the ARPA network.Pro . of the 1974 National Computer Conferen e, Vol. 43, pp. 767�780, AFIPSPress, Arlington, Va. (1974)6. Leland W. and Wilson D.: High time-resolution measurement and analysis of LANtra� : Impli ations for LAN inter onne tion. In: Conferen e on Computer Commu-ni ations (INFOCOM), pp. 1360�1366, IEEE press, New-York (1991)7. Leland W., Taqqu M., Willinger W., and Wilson D.: On the self-similar nature ofEthernet tra� . IEEE/ACM Transa tions on Networking 2(1), pp. 1�15 (1994)8. Cis o NetFlow servi es and appli ations. http://www. is o. om/warp/publi /732/netflow9. Park K. andWillinger W.: Self-Similar Network Tra� and Performan e Evaluation.Wiley-Inters ien e (2000)10. Park K. and Willinger W.: The Internet as a Large-S ale Complex System. OxfordUniversity Press (2005)11. Paxson V. and Floyd S.: Wide-Area Tra� : The Failure of Poisson Modeling.IEEE/ACM Transa tions on Networking 3(3), 226?-244 (1995)12. Quoitin B., Uhlig S., Pelsser C., Swinnen L., and Bonaventure O.: Interdomaintra� engineering with BGP. IEEE Communi ations Magazine 41(5), pp. 122�128(2003)

Capturing Internet tra� dynami s through graph distan es 1313. Quoitin B. and Uhlig S.: Modeling the Routing of an Autonomous System withC-BGP. IEEE Network Magazine 19(6), 12-19 (2005)14. Rekhter Y., Li T., and Hares S.: A Border Gateway Proto ol 4 (BGP-4). InternetRFC 4271 (2006)15. Rexford J., Wang J., Xiao Z., and Zhang Y.: BGP Routing Stability of PopularDestinations. In: Internet Measurement Workshop, pp. 197�202, ACM press, New-York (2002)16. Tangmunarunkit H., Govindan R., Shenker S., and Estrin D.: The Impa t of Rout-ing Poli y on Internet Paths. In: Conferen e on Computer Communi ations (INFO-COM), pp. 736?-742, IEEE press, New-York (2001)17. Thompson K., Miller G.J., and Wilder R.: Wide-area internet tra� patterns and hara teristi s. IEEE Network Magazine 11(6), 10?23 (1997)18. Uhlig S. and Bonaventure O.: Impli ations of interdomain tra� hara teristi s ontra� engineering. European Transa tions on Tele ommuni ations 13(1), pp. 23�32,Wiley, New-York (2002)19. Uhlig S., Magnin V., Bonaventure O., Rapier C., and Deri L.: Impli ations of thetopologi al properties of Internet tra� on tra� engineering. In: Symposium onApplied Computing, pp. 339�346, ACM press, New-York (2004)20. Uhlig S.: Non-stationarity and high-order s aling in TCP �ow arrivals: a method-ologi al analysis. Comput. Commun. Rev. 34(2), 9-24 (2004)21. Uhlig S. and Quoitin B.: Tweak-it: BGP-based interdomain tra� engineering fortransit ASes. In: Next Generation Internet Networks, pp. 75�82, IEEE press, New-York (2005)22. Uhlig S., Quoitin B., Lepropre J., and Balon S.: Providing publi intradomaintra� matri es to the resear h ommunity. Comput. Commun. Rev. 36(1), 83-86(2006)23. Uhlig S.: From the tra� properties to tra� engineering in the Internet. VDMVerlag Dr. Müller (2008)24. Willinger W., Paxson V., Riedi R., and Taqqu M.: Long-Range Dependen e andData Network Tra� . In: Doukhan P., Oppenheim G. and Taqqu M. (eds.) Longrange Dependen e : Theory and Appli ations, pp. 373�408, Birkhäuser (2003)25. GNU Zebra Routing Suite. http://www.zebra.org