CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

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Internet Traffic Demand and Traffic Matrix Estimation

• Challenges in directly measuring traffic demand or traffic matrix

• granularity and time scale of traffic demand matrix ?

• Focus mainly on two studies representing two approaches

– Partial (or “sampled”) measurement at ingress/egress points/links (optional material: will go over only briefly) – Inference of traffic matrix based on link loads (aggregate SNMP link load measurement)• gravity model• tomogravity model (optional material)

Readings: Please do the required readings

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Traffic Demands• How to measure and model the traffic demands?

– Know where the traffic is coming from and going to• Why do we care about traffic demands?

– Traffic engineering utilizes traffic demand matrices in balancing traffic loads and managing network congestion

– Support what-if questions about topology and routing changes– Handle the large fraction of traffic crossing multiple domains

• Understanding traffic demand matrices are critical inputs to network design, capacity planning and business planning!

• How to populate the demand model?– Typical measurements show only the impact of traffic demands

• Active probing of delay, loss, and throughput between hosts• Passive monitoring of link utilization and packet loss

– Need network-wide direct measurements of traffic demands• How to characterize the traffic dynamics?

– User behavior, time-of-day effects, and new applications– Topology and routing changes within or outside your network

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Traffic DemandsBig Internet

Web Site User Site

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Traffic DemandsInterdomain Traffic

•What path will be taken between AS’s to get to the User site?•Next: What path will be taken within an AS to get to the User site?

AS 4, AS 3, U

Web Site User Site

AS 1

AS 2

AS 3

AS 4

U

AS 3, U

AS 3, U

AS 3, U

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Traffic Demands

Web SiteUser Site

Zoom in on one AS

200

11010

110

300

25

75

50

300

IN

OUT3

OUT2

OUT1

110

Change in internal routing configuration changes flow exit point!

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Defining Traffic Demand Matrices• Granularity and time scale:

– Source/destination network prefix pairs, source/destination AS pairs

– ingress/egress routers, or ingress/egress PoP pairs?– Finer granularity: traffic demands likely unstable or fluctuate too widely!

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Traffic Matrix (TM)• Point-to-Point Model: T: = [Ti,j ], where Ti,j from an ingress point i to an egress

point j over a given time interval – ingress/egress points: routers or PoPs – an ingress-egress pair is often referred to as an O-D pair

• Point-to-Multipoint Model:– Sometimes it may be difficult to determine egress points due

to uncertainty in routing or route changes

Definition: V(in, {out}, t)• Entry link (in)• Set of possible exit links ({out})• Time period (t)• Volume of traffic (V(in,{out},t))

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Ideal Measurement Methodology• Measure traffic where it enters the network

– Input link, destination address, # bytes, and time

• Determine where traffic can leave the network– Set of egress links associated with each network address (forwarding tables)

• Compute traffic demands– Associate each measurement with a set of egress links

• Even at PoP-level, direct measurement can be too expensive! – We either need to tap all ingress/egress links, or collect netflow records at all

ingress/egress routers • May lead to reduced performance at routers• large amount of data: limited router disk space, export Netflow records consumes

bandwidth!• Either packet-level or flow-level data, need to map to ingress/egress points, and a lot of

processing to generate TM!

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Adapted Measurement MethodologyInter-domain Focus

[F+01] Paper (Optional Material): Driving traffic demands from netflow

measurements based on selected links• A large fraction of the traffic is interdomain• Interdomain traffic is easiest to capture

– Large number of diverse access links to customers– Small number of high speed links to peers

• Practical solution– Flow level measurements at peering links (both directions!)– Reachability information from all routers

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Measuring Only at Peering Links

• Why measure only at peering links?– Measurement support directly in the interface cards– Small number of routers (lower management

overhead)– Less frequent changes/additions to the network– Smaller amount of measurement data

• Why is this enough?– Large majority of traffic is interdomain– Measurement enabled in both directions (in and out)– Inference of ingress links for traffic from customers

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Inbound & Outbound Flows on Peering Links

Peers Customers

Inbound

Outbound

Note: Ideal methodology applies for inbound flows.

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Full Classification of Traffic Types at Peering Links

Peers Customers

Internal

Inbound

Outbound

Transit

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Identifying Where the Traffic Can Leave

• Traffic flows– Each flow has a dest IP address (e.g., 12.34.156.5)– Each address belongs to a prefix (e.g.,

12.34.156.0/24)

• Forwarding tables– Each router has a table to forward a packet to “next

hop”– Forwarding table maps a prefix to a ”next hop” link

• Process– Dump the forwarding table from each edge router– Identify entries where the ”next hop” is an egress link– Identify set of all egress links associated with a prefix

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Flows Leaving at Peer Links

• Single-hop transit– Flow enters and leaves the network at the same router– Keep the single flow record measured at ingress point

• Multi-hop transit– Flow measured twice as it enters and leaves the network– Avoid double counting by omitting second flow record– Discard flow record if source does not match a customer

• Outbound – Flow measured only as it leaves the network– Keep flow record if source address matches a customer– Identify ingress link(s) that could have sent the traffic

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Most Challenging Part: Inferring Ingress Links for Outbound

FlowsOutbound traffic flowmeasured at peering link

Customersdestination

output

Use outing simulation to trace back to the ingress links!

? input

? input

Example

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Computing the Demands

• Data– Large, diverse, lossy– Collected at slightly different, overlapping time

intervals, across the network.– Subject to network and operational dynamics.

Anomalies explained and fixed via understanding of these dynamics

• Algorithms, details and anecdotes in paper!

ForwardingTables

ConfigurationFiles

NetFlow SNMP

NETWORK

researcher in data mining gear

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Experience with Populating the Model

• Largely successful– 98% of all traffic (bytes) associated with a set of egress links– 95-99% of traffic consistent with an OSPF simulator

• Disambiguating outbound traffic– 67% of traffic associated with a single ingress link– 33% of traffic split across multiple ingress (typically, same city!)

• Inbound and transit traffic (uses input measurement)– Results are good

• Outbound traffic (uses input disambiguation)– Results are pretty good, for traffic engineering applications, but

there are limitations– To improve results, may want to measure at selected or sampled

customer links; e.g., links to email, hosting or data centers.

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Proportion of Traffic in Top Demands (Log Scale)

Zipf-like distribution. Relatively small number of heavy demands dominate.

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Time-of-Day Effects (San Francisco)

Heavy demands at same site may show different time of day behaviormidnight EST midnight CST

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Discussion• Distribution of traffic volume across demands

– Small number of heavy demands (Zipf’ s Law!)– Optimize routing based on the heavy demands– Measure a small fraction of the traffic (sample)– Watch out for changes in load and egress links

• Time-of-day fluctuations in traffic volumes– U.S. business, U.S. residential, & International traffic– Depends on the time-of-day for human end-point(s)– Reoptimize the routes a few times a day (three?)

• Stability?– No and Yes

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

TM Estimation Using Link Loads

[M+02] Paper: TM estimation using SNMP link loads

• Available information:– Link counts from SNMP data.– Routing information. (Weights of links)– Additional topological information. ( Peerings, access

links)– Assumption on the distribution of demands.

• TM Estimation => using indirect measurements (here link loads), solving an inference problem! – Y: link load measurements, A “routing

matrix”– Given Y, solving for X, where Y=AX

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Terminology• c=n*(n-1) origin-destination (OD) pairs.• X: Traffic matrix. (Xj data transmitted by

OD pair j)• Y=(y1,y2,…,yr ) : vector of link counts.• A: r-by-c routing matrix (aij=1, if link i

belongs to the path associated to OD pair j)

Y=AXr<<c => Infinitely many solutions!

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Three Existing Techniques• Key issue: linear equations under-strained!

– More (N^2) unknowns (X_{ij}’s) than # of knowns Y_{l}’ s

• Linear Programming (LP) approach.– O. Goldschmidt - ISMA Workshop 2000

• Bayesian estimation.– C. Tebaldi, M. West - J. of American Statistical

Association, June 1998.

• Expectation Maximization (EM) approach.– J. Cao, D. Davis, S. Vander Weil, B. Yu - J. of American

Statistical Association, 2000

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Linear Programming• Objective:

• Constraints:

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Statistical Approaches

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Bayesian Approach

• Assumes P(Xj) follows a Poisson distribution with mean λj. (independently dist.)

• needs to be estimated. (a prior is needed)

• Conditioning on link counts: P(X,Λ|Y)Uses Markov Chain Monte Carlo (MCMC)

simulation method to get posterior distributions.

• Ultimate goal: compute P(X|Y)

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Expectation Maximization (EM)

• Assumes Xj are ind. dist. Gaussian.

• Y=AX implies:

• Requires a prior for initialization.• Incorporates multiple sets of link

measurements.• Uses EM algorithm to compute MLE.

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Comparison of Methodologies

• Considers PoP-PoP traffic demands.• Two different topologies (4-node, 14-node).• Synthetic TMs. (constant, Poisson, Gaussian,

Uniform, Bimodal)• Comparison criteria:

– Estimation errors yielded.– Sensitivity to prior.– Sensitivity to distribution assumptions.

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

4-node Topology

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

4-node Topology Results

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

14-node Topology

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

14-node Topology Results

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Marginal Gains of Known Rows

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

New Directions

• Lessons learned:– Model assumptions do not reflect the true

nature of traffic (multimodal behavior)– Dependence on priors– Link count is not sufficient (Generally more

data is available to network operators.)• Proposed Solutions:

– Use choice models to incorporate additional information.

– Generate a good prior solution.

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

New Statement of the Problem

• Xij= Oi.αij– Oi : outflow from node (PoP) i.– αij : fraction Oi going to PoP j.

Equivalent problem: estimating αij .

• Solution via Discrete Choice Models (DCM).– User choices.– ISP choices.

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Choice Models

• Decision makers: PoPs• Set of alternatives: egress PoPs.• Attributes of decision makers and

alternatives: attractiveness (capacity, number of attached customers, peering links).

• Utility maximization with random utility models.

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Random Utility Model• Ui

j= Vij + εi

j : Utility of PoP i choosing to send packet to PoP j.

• Choice problem:• Deterministic component:

• Random component: mlogit model

used.

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Gravity Modeling

• General formula:

• Simple gravity model: Try to estimate the amount of traffic between edge links.

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Results• Two different models (Model 1:attractiveness, Model 2: attractiveness + repulsion )

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Further Improvement: Tomogravity Model

(Optional Material)

• Two step modeling.– Gravity Model: Initial solution obtained using edge

link load data and ISP routing policy.

– Tomographic Estimation: Initial solution is refined by applying quadratic programming to minimize distance to initial solution subject to tomographic constraints (link counts).

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Highlights

• Router to router traffic matrix is computed instead of PoP to PoP.

• Performance evaluation with real traffic matrices.

• Tomogravity method (Gravity + Tomography)

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Recall: Gravity Model

• General formula:

• Simple gravity model: Try to estimate the amount of traffic between edge links.

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Generalized Gravity Model

• Four traffic categories– Transit– Outbound– Inbound– Internal

• Peers: P1, P2, …

• Access links: a1, a2, ...

• Peering links: p1,p2,…

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Generalized Gravity Model

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Tomography• Solution should be consistent with the link

counts.

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Reducing the Computational Complexity

• Hundreds of backbone routers, ten thousands of unknowns.

• Observations:• Some elements of the BR to BR matrix

are empty. (Multiple BRs in each PoP, shortest paths)

• Topological equivalence. (Reduce the number of IGP simulations)

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Quadratic Programming

• Problem Definition:

• Use SVD (singular value decomposition) to solve the inverse problem.

• Use Iterative Proportional Fitting (IPF) to ensure non-negativity.

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Evaluation of Gravity Models

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Performance of Proposed Algorithm

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Comparison

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CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Robustness• Measurement errorsx=At+εε=x*N(0,σ)

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