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An InformationTheoretic Approach to Traffic Matrix Estimation
 In Proc. ACM SIGCOMM
, 2003
"... Traffic matrices are required inputs for many IP network management ..."
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Cited by 142 (16 self)
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Traffic matrices are required inputs for many IP network management
Network tomography: recent developments
 Statistical Science
, 2004
"... Today's Int ernet is a massive, dist([/#][ net work which cont inuest o explode in size as ecommerce andrelatH actH]M/# grow. Thehet([H(/#]H( and largelyunregulatS stregula of t/ Int/HH3 renderstnde such as dynamicroutc/[ opt2]3fl/ service provision, service level verificatflH( and det(2][/ of ..."
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Cited by 110 (4 self)
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Today's Int ernet is a massive, dist([/#][ net work which cont inuest o explode in size as ecommerce andrelatH actH]M/# grow. Thehet([H(/#]H( and largelyunregulatS stregula of t/ Int/HH3 renderstnde such as dynamicroutc/[ opt2]3fl/ service provision, service level verificatflH( and det(2][/ of anomalous/malicious behaviorext/[(22 challenging. The problem is compounded bytS fact tct onecannot rely ont[ cooperatH2 of individual servers and routSS t aid intS collect[3 of net workt/[S measurement vits fort/]3 t/]3] In many ways, net workmonit]/#[ and inference problems bear a st[fl[ resemblancet otnc "inverse problems" in which key aspect of asystfl are not direct/ observable. Familiar signal processing orst[]23/#[S problems such ast omographic imagereconst[/#[S] and phylogenet# tog identn/HH2[M have int erest3/ connect[HU t tonn arising in net working. This artflMM int/ ducesnet workt/H3]S]/ y, a new field which we believe will benefit greatU from tm wealt of stH2](/#S( ttH2 andalgorit#S( It focuses especially on recent development s int2 field includingtl applicat[fl of pseudolikelihoodmetfl ds andt reeestfl3](/# formulat]M23 Keyw ords:Net workt/HflS33/ y, pseudolikelihood,t opology identn/]H22(/ tn est/]H tst 1 Introducti6 Nonet work is an island, ent/S ofitS[S] everynet work is a piece of an int/]SS work, a part of t/ main . Alt[]][ administHSHSS of smallscale net works can monit( localt ra#ccondit][/ and ident ify congest/# point s and performance botU((2/ ks, very few net works are complet/# # Rui Castroan Robert Nowak are with theDepartmen t of Electricalan ComputerEnterX Rice Unc ersity,Houston TX; Mark Coates is with the Departmen t of Electricalan ComputerEnterX McGill UnG ersity,Mon treal, Quebec,Can Gan Lian an Bin Yu are with theDepartmen t of Statistics,...
A methodology for estimating interdomain web traffic demand
 In IMC ’04: Proceedings of the 4th ACM SIGCOMM conference on Internet measurement
, 2004
"... This paper introduces a methodology for estimating interdomain Web traffic flows between all clients worldwide and the servers belonging to over one thousand content providers. The idea is to use the server logs from a large Content Delivery Network (CDN) to identify client downloads of content prov ..."
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Cited by 33 (3 self)
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This paper introduces a methodology for estimating interdomain Web traffic flows between all clients worldwide and the servers belonging to over one thousand content providers. The idea is to use the server logs from a large Content Delivery Network (CDN) to identify client downloads of content provider (i.e., publisher) Web pages. For each of these Web pages, a client typically downloads some objects from the content provider, some from the CDN, and perhaps some from third parties such as banner advertisement agencies. The sizes and sources of the nonCDN downloads associated with each CDN download are estimated separately by examining Web accesses in packet traces collected at several universities. The methodology produces a (timevarying) interdomain HTTP traffic demand matrix pairing several hundred thousand blocks of client IP addresses with over ten thousand individual Web servers. When combined with geographical databases and routing tables, the matrix can be used to provide (partial) answers to questions such as “How do Web access patterns vary by country?”, “Which autonomous systems host the most Web content?”, and “How stable are Web traffic flows over time?”.
Estimating PointtoPoint and PointtoMultipoint Traffic Matrices: An InformationTheoretic Approach
 IEEE/ACM Trans. Netw
, 2005
"... Traffic matrices are required inputs for many IP network management tasks, such as capacity planning, traffic engineering and network reliability analysis. However, it is difficult to measure these matrices directly in large operational IP networks, so there has been recent interest in inferring tra ..."
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Cited by 31 (8 self)
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Traffic matrices are required inputs for many IP network management tasks, such as capacity planning, traffic engineering and network reliability analysis. However, it is difficult to measure these matrices directly in large operational IP networks, so there has been recent interest in inferring traffic matrices from link measurements and other more easily measured data. Typically, this inference problem is illposed, as it involves significantly more unknowns than data. Experience in many scientific and engineering fields has shown that it is essential to approach such illposed problems via "regularization". This paper presents a new approach to traffic matrix estimation using a regularization based on "entropy penalization". Our solution chooses the traffic matrix consistent with the measured data that is informationtheoretically closest to a model in which source/destination pairs are stochastically independent. It applies to both pointtopoint and pointtomultipoint traffic matrix estimation. We use fast algorithms based on modern convex optimization theory to solve for our traffic matrices. We evaluate our algorithm with real backbone traffic and routing data, and demonstrate that it is fast, accurate, robust, and flexible.
A factor graph approach to link loss monitoring in wireless sensor networks
 IEEE JSAC, Special Issue on SelfOrganizing Distributed Collaborative Sensor Networks
, 2005
"... Abstract—The highly stochastic nature of wireless environments makes it desirable to monitor link loss rates in wireless sensor networks. In a wireless sensor network, link loss monitoring is particularly supported by the data aggregation communication paradigm of network traffic: the data collectin ..."
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Cited by 30 (1 self)
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Abstract—The highly stochastic nature of wireless environments makes it desirable to monitor link loss rates in wireless sensor networks. In a wireless sensor network, link loss monitoring is particularly supported by the data aggregation communication paradigm of network traffic: the data collecting node can infer link loss rates on all links in the network by exploiting whether packets from various sensors are received, and there is no need to actively inject probing packets for inference purposes. In this paper, we present a low complexity algorithmic framework for link loss monitoring based on the recent modeling and computational methodology of factor graphs. The proposed algorithm iteratively updates the estimates of link losses upon receiving (or detecting the loss of) recently sent packets by the sensors. The algorithm exhibits good performance and scalability, and can be easily adapted to different statistical models of networking scenarios. In particular, due to its low complexity, the algorithm is particularly suitable as a longterm monitoring facility. Index Terms—Factor graphs, link loss monitoring, network tomography, sensor networks, sumproduct algorithm. I.
On the costquality tradeoff in topologyaware overlay path probing
, 2003
"... Path probing is essential to maintaining an efficient overlay network topology. However, the cost of a fullscale probing is as high as, which is prohibitive in largescale overlay networks. Several methods have been proposed to reduce probing overhead, although at a cost in terms of probing complet ..."
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Cited by 26 (4 self)
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Path probing is essential to maintaining an efficient overlay network topology. However, the cost of a fullscale probing is as high as, which is prohibitive in largescale overlay networks. Several methods have been proposed to reduce probing overhead, although at a cost in terms of probing completeness. In this paper, an orthogonal solution is proposed that trades probing overhead for estimation accuracy in sparse networks such as the Internet. The proposed solution uses networklevel path composition information (for example, as provided by a topology server) to infer path quality without fullscale probing. The inference metrics include latency, loss rate and available bandwidth. This approach is used to design several probing algorithms, which are evaluated through analysis and simulation. The results show that the proposed method can significantly reduce probing overhead while providing bounded quality estimations for all overlay paths. The solution is well suited to mediumscale overlay networks in the Internet. In other environments, it can be combined with extant probing algorithms to further improve performance. 1.
The many facets of Internet topology and traffic
 Networks and Heterogeneous Media
"... ABSTRACT. The Internet’s layered architecture and organizational structure give rise to a number of different topologies, with the lower layers defining more physical and the higher layers more virtual/logical types of connectivity structures. These structures are very different, and successful Inte ..."
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Cited by 21 (11 self)
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ABSTRACT. The Internet’s layered architecture and organizational structure give rise to a number of different topologies, with the lower layers defining more physical and the higher layers more virtual/logical types of connectivity structures. These structures are very different, and successful Internet topology modeling requires annotating the nodes and edges of the corresponding graphs with information that reflects their networkintrinsic meaning. These structures also give rise to different representations of the traffic that traverses the heterogeneous Internet, and a traffic matrix is a compact and succinct description of the traffic exchanges between the nodes in a given connectivity structure. In this paper, we summarize recent advances in Internet research related to (i) inferring and modeling the routerlevel topologies of individual service providers (i.e., the physical connectivity structure of an ISP, where nodes are routers/switches and links represent physical connections), (ii) estimating the intraAS traffic matrix when the AS’s routerlevel topology and routing configuration are known, (iii) inferring and modeling the Internet’s ASlevel topology, and (iv) estimating the interAS traffic matrix. We will also discuss recent work on Internet connectivity structures that arise at the higher layers in the TCP/IP protocol stack and are more virtual and dynamic; e.g., overlay networks like the WWW graph, where nodes are web pages and edges represent existing hyperlinks, or P2P networks like Gnutella, where nodes represent peers and two peers are connected if they have an active network connection. 1. Introduction. The
Network tomography: A review and recent developments
 In Fan and Koul, editors, Frontiers in Statistics
, 2006
"... The modeling and analysis of computer communications networks give rise to a variety of interesting statistical problems. This paper focuses on network tomography, a term used to characterize two classes of largescale inverse problems. The first deals with passive tomography where aggregate data ar ..."
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Cited by 19 (5 self)
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The modeling and analysis of computer communications networks give rise to a variety of interesting statistical problems. This paper focuses on network tomography, a term used to characterize two classes of largescale inverse problems. The first deals with passive tomography where aggregate data are collected at the individual router/node level and the goal is to recover pathlevel information. The main problem of interest here is the estimation of the origindestination traffic matrix. The second, referred to as active tomography, deals with reconstructing linklevel information from endtoend pathlevel measurements obtained by actively probing the network. The primary application in this case is estimation of qualityofservice parameters such as loss rates and delay distributions. The paper provides a review of the statistical issues and developments in network tomography with an emphasis on active tomography. An application to Internet telephony is used to illustrate the results.
A Fast Lightweight Approach to OriginDestination IP Traffic Estimation Using Partial Measurements
"... In this paper, we propose a novel approach to estimating traffic matrices that incorporates lightweight OriginDestination (OD) flow measurements coupled with a computationally lightweight algorithm for producing the OD estimates. There are two key ingredients in our method, called PamTram, for PArt ..."
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Cited by 15 (1 self)
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In this paper, we propose a novel approach to estimating traffic matrices that incorporates lightweight OriginDestination (OD) flow measurements coupled with a computationally lightweight algorithm for producing the OD estimates. There are two key ingredients in our method, called PamTram, for PArtial Measurement of TRAffic Matrices. The first is to actively select a small number of informative OD flows to measure in each estimation time interval. To avoid the heavy computation of an optimal selection, we use a heuristic based on intuition from game theory. Randomized selection rules are developed based on the goals of reducing errors and adapting to traffic changes. We provide an algorithm for selecting a good flow to measure that is fast because it avoids the computations, such as integrating over past intervals, that are needed for optimal selection. The second key aspect of our method is an explanation and proof that an Iterative Proportional Fitting (IPF) algorithm can be used to approximate the traffic matrix estimate when the goal is a minimum mean squared error and the optimization starts from a maximum entropy initial estimate. In addition, we provide a onestep average error bound for PamTram when the randomized selection rule is uniform and no link counts are used. This bounds the average error for the worst case selection rule. Finally, we validate our method using data from Sprint’s European Tier1 IP backbone network. Results show that our method generates average errors below the 10% carrier target error rate. Interestingly, we show that it suffices to measure a single OD flow in each estimation interval, which renders our partial measurement method very lightweight in terms of measurement overhead.