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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

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

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

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Traffic Demands

Big Internet

User Site

Web Site

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

AS 3, U

AS 3, U

AS 4, AS 3, U

AS 3, U

- 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?

Interdomain Traffic

AS 3

User Site

Web Site

U

AS 1

AS 4

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Change in internal routing configuration changes flow exit point!

Traffic DemandsZoom in on one AS

OUT1

25

110

110

User Site

Web Site

300

OUT2

200

75

300

10

110

50

IN

OUT3

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

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!

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

6

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))

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

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 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!

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

8

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

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

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

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Inbound

Inbound & Outbound Flows on Peering LinksPeers

Customers

Note: Ideal methodology applies for inbound flows.

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Internal

Transit

Inbound

Full Classification of Traffic Types at Peering LinksPeers

Customers

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

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 all egress links associated with a prefix

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

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

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

? input

Use outing simulation to trace back to the ingress links!

Most Challenging Part: Inferring Ingress Links for Outbound FlowsExample

Outbound traffic flow

measured at peering link

output

Customers

destination

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Tables

Configuration

Files

NetFlow

SNMP

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!

researcher in data mining gear

NETWORK

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

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.

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Proportion of Traffic in Top Demands (Log Scale)

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

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

midnight EST

Time-of-Day Effects (San Francisco)Heavy demands at same site may show different time of day behavior

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

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

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Terminology

- c=n*(n-1) origin-destination (OD) pairs.
- X: Traffic matrix. (Xjdata 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=AX

r<<c => Infinitely many solutions!

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

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Linear Programming

- Objective:
- Constraints:

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Statistical Approaches

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)

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.

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.

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

4-node Topology

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

4-node Topology Results

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

14-node Topology

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

14-node Topology Results

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Marginal Gains of Known Rows

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.

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.

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.

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Random Utility Model

- Uij= Vij + εij : Utility of PoP i choosing to send packet to PoP j.
- Choice problem:
- Deterministic component:
- Random component: mlogit model used.

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.

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).

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)

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.

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Generalized Gravity Model

- Four traffic categories
- Transit
- Outbound
- Inbound
- Internal
- Peers: P1, P2, …
- Access links: a1, a2, ...
- Peering links: p1,p2,…

Generalized Gravity Model

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Tomography

- Solution should be consistent with the link counts.

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)

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.

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Evaluation of Gravity Models

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Performance of Proposed Algorithm

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Comparison

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

Robustness

- Measurement errors

x=At+ε

ε=x*N(0,σ)

CSci5221: Internet Traffic Demand and Traffic Matrix Estimation

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