GlobM Network Positioning: A New Approach to Network Distance Prediction T. S. Eugene Ng and Hui Zhang, Department of Computer Science, Carnegie Mellon University* I o.| o.g 0.7 I oJ 0.| .... M.u.md Obmm:g emmmNrk= D ~ m : a (~y~irF2-Dlm~i:nsl Euclidean~--~ ~ o.4 o.a 0.1 NF V H ~' = , . , , ~ - - o.ll I !/t 0 I O.l | 1 P,dali~ Emx e~.=~ GNP, | tardmadm - . . . . . . . . . Figure i: Computing GNP coordinates. We propose a new approach to the network distance (roundtrip transmission and propagation delay) prediction problem called Global Network Positioning (GNP). We demonstrate that it is feasibleto inexpensively model the Internet as a geometric space (e.g. a 3-dimensionaJ Euclidean space), and characterize the position of any host in the Internet by a point in this space such that the network distance between two hosts can be predicted accurately by the geometric distance implied by their coordinates in this space. Figure 1 shows h o w G N P efficientlymaps Interuet hosts to points in a geometric space. The key technique is to first compute the coordinates of a small distributed set of cooperating hosts called Landmarks based on measured interLandmark distances such that the overall error between the measured distances and the geometric distances is minimized. The Landmarks' coordinates are disseminated to ordinary hosts and serve as a frame of reference. With this frame of reference, each ordinary host measures its distances to the Landmarks (the Landmarks are passive) and computes a set of coordinates for itself that minimizes the overall error between the measured and the geometric hostto-Landmark distances. The computations of Landmark and ordinary host coordinates can be cast as generic multidimensional global minimization problems that can be approximately solved by m a n y available methods. Although off-linepro-computations are required to derive the coordinates of Landmarks and hosts, modeling the Internet as a geometric space and commmJ_icating distance information using coordinates have several advantages over the traditional approach of modeling the Internet as a simplified topology and communicating distance information using individual path distances. First of all, a distance prediction in the geometric space model is simply an evaluation of the distance b.mction which is generally both straight-forward to implement and extremely fast to compute comparing to a shortest path search in the topology model. Secondly, in a multi-party application, the distances of all paths between K hosts can be efficientlycommunicated by ff sets of coordinates of size D each (i.e. O(K- D) of data), where D is the dimensionality of the geometric space, as opposed to K(K- 1)/2 individual distances (i,e., O ( K =) of data). Thirdly, host coordinates are relatively fixed local properties that can be exchanged easily among hosts when they discover each other, allowing network distance predictions to be locally computed by end hosts in a timely fashion. Fourthly, "Email addresses: {eugeneng, hzhang}Qcs.emu.edu IDMqm, Z "rm~m ......... iOkt,~, e Tri~'m . . . . . . l.,.--r.r, e ' r f m ~ - 1,,~ ..... - Figure 2: Relative error of GNP and IDMaps. I.~ndmarks are very simple and non-intrusive, hence they are easy to deploy and ordinary hosts behind fu'ewalls can a.IJoparticipate. Finally, we can exploit the structured nature of the coordinates to efficientlyperform interesting operations such as nearest neighbors searches. To evaluate G N P , we apply it to off-line collected Internet distance measurements. In the last week of M a y 2001, we measured the distances between 19 distributed probes and the distances between each probe and 869 Interuet hosts distributed over the globe. W e then conduct G N P experiments over this data by clustering the 19 probes and selecting a subset of them as Landmarks, and using the remaining probes and the 869 Internet hosts as ordinary hosts. To measure h o w well the predicted distance between two ordinary hosts matches the corresponding measured distance, we uBe a metric called relative error that is defined as ~aredlcted d l a t a n c s - - m e s s u r s d dlatance mm(mBam~red dlatancas,predicted d i s t a n c e ) " We experimented with the 5-dimeusional Euclidean space model and varied the number of Land.marks from 6 to 15. Each experiment was repeated multiple times with sfightiy different Landmarks and the overall result is reported. For comparison, we also evaluated the performance of the current state-of-the-art distance prediction approach IDMaps [1] when applied to our data, using the corresponding Landmark nodes as the I D M a p s Tracers. Figure 2 shows the cumulative probability distribution functions of the relative error for G N P (top 4 lines) and IDMaps. As can be seen, G N P predicts distances more accurately than IDMaps, and benefits consistently from the addition of Landmarks. Using G N P with 15 Landmarks, 9 0 % of all distance predictions are within a relative error of 0.53. G N P makes it possible to provide scalable, fast, and effective network performance optimization in distributed network services and applications because it requires no ond e m a n d network measurements. W e are working towards improving the G N P techniques and understanding how underlying Internet properties affect GNP's performance.

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