On a New Internet Traffic Matrix (Completion) Problem

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On a New Internet Traffic Matrix (Completion)
Problem
Walter Willinger ATT LabsResearch Walter Willinger ATT LabsResearch Walter Willinger ATT LabsResearch


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Local Traffic Matrices

• At an individual router
• Gives traffic volumes (number of bytes per time
  unit 5 min, 1 hour, 1 day) between every input
  port and output port on a router
• Typical routers have a small number of ports,
  from 16 to at most 256
• Available measurements
• Netflow-enabled routers provide direct
  measurements
• Routing data
• No need for inference!

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Abilene Router (Washington, D.C.)
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Local TM (Washington, D.C., 9/1/06)
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Top 6 Local TM Elements (Wash. PoP)
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Intra-Domain Traffic Matrices

• For an individual network
• Gives traffic volumes (number of bytes per time
  unit 5 min, 1 hour, 1 day) between every ingress
  router/PoP and egress router/PoP in a network
• Some of the larger networks can have 1000s of
  routers or 100s of PoPs
• Available measurements
• SNMP data provide indirect measurements (per
  link)
• Routing data

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Intra-Domain TM Inference Problem

• Network-wide availability of SNMP data (link
  loads)
• Relying only on SNMP data, solve
• AXY
• A routing matrix Y link measurements
• In real networks, this is a massively
  underconstrained problem
• Active area of research in 2000-2010
• Zhang, Roughan, Duffield, and Greenberg (2003)
• Zhang, Roughan, Lund, and Donoho (2003, 2005)

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Intra-Domain TM Inference Problem

• Applications
• Network engineering (capacity planning)
• Traffic engineering (what-if scenarios)
• Anomaly detection
• Enormously useful for daily network operations
• Textbook example of theory impacting practice
• Things changed around 2010
• Netflow-enabled routers are now deployed
  network-wide and provide direct measurements
• Can measure the intra-domain TM directly!
• Inference approach is no longer needed!

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Example Abilene Network

• High speed Education Network
• 28 links
• 10 Gbps Capacity on each link
• 11 Points of Presence (POPs) with NetFlow
  measurement capabilities

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Abilene Traffic Matrix (9/1/06)
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Top 12 Abilene TM Elements (1 week)
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Intra-Domain TM Open Problems

• Synthesis of realistic TMs
• Cant be agnostic about the underlying network!
• What information about the underlying network is
  needed?
• Network-related root causes for observed
  properties of measured TMs
• Low-rank, deviations from low-rank
• Sparsity
• Which measurements are more critical than others
  for my network?

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What can Intra-Domain TMs tell us?

• How much of the traffic that enters my network in
  NYC is destined for ATL (per hour, per day)?
• How much of the daily traffic on my network is
  coming from (which) CDNs?
• How much of the hourly traffic that enters my
  network in NYC and is destined to ATL is coming
  from Netflix?
• How much traffic does my network carry (per hour,
  per day)?

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A Different Set of Questions

• How much traffic do Sprint and Verizon exchange
  with one another (per hour, day)?
• How much traffic does Verizon get from Netflix
  (per day, month)?
• What are the networks that exchange the most
  traffic with Google?
• How much does Facebooks traffic increase on a
  monthly basis?
• How much traffic does the Internet carry per day?

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New Problem Inter-Domain TM

• The Internet is a network of networks
• Individual networks are also called Autonomous
  Systems (ASes)
• Todays Internet consists of about 30K-40K
  actively routed ASes
• We are getting a clearer picture of the AS-level
  topology (i.e., which networks exchange routing
  information with one another and hence presumably
  also IP traffic)
• Inter-domain (or AS-level) traffic matrix
• Gives traffic volumes between ASes
• Completely unknown

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Inter-Domain TM Highly Structured

• Some numbers
• In 2010 the Internet carried some 20 EB/month
• In late 2009, ATT carried some 20PB/day in 2009
• There are some 20 ATT-like large transit
  providers in todays Internet
• Some caveats
• Large transit providers use multiple networks to
  run their business (e.g., Verizon has some 230
  ASes)
• Need to know how to map ASes to companies

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On Inter-Domain TM Completion

• Todays formulation
• About 1 of the inter-domain TM elements are
  responsible for a majority of all the traffic
• Inter-domain TM has low rank (does it?)
• (Non)standard TM completion problem
• Towards tomorrows formulation
• How to insist on strong validation criteria?
• What sort of new measurements are feasible and
  can be used to check the validity of a solution
  to todays formulation of the inter-domain TM
  completion problem?

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Internet eXchange Points (IXPs)
Content Provider 1
Content Provider 2
AS2
AS1
AS3
layer-2 switch
AS5
AS4
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Inter-Domain TM and IXPs

• Some numbers
• There are some 300 IXPs worldwide that see some
  10-20 of all Internet traffic
• They involve some 4K ASes
• Most IXPs publish their hourly/daily total
  traffic volume
• We are getting more and more accurate peering
  matrices for these 300 IXPs
• New Twist
• How to infer the local TM at each IXP?
• How to measure the local TM at each IXP?

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Back to Inter-Domain TM Completion

• Tomorrows formulation
• Start with todays formulation
• Accounts for large transit providers
• Incorporate IXP-specific information
• Accounts for large content providers
• New (non)standard TM completion problem
• and repeat
• What other sources of new measurements?
• Promising candidates CDNs (Akamai co.)
• What types of measurements are more critical than
  others?

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Summary

• Intra-domain TM research
• Beautiful example of innovative research with
  enormous practical benefits for network operators
• The intra-domain TM of an AS is a basic
  ingredient for a first-principles approach to
  understanding the ASs router-level topology
  (forget Network Science )
• Reminder that change changes things
• Inter-domain TM research
• Enormous practical value
• Adds new twist to generic matrix completion
  problem
• The inter-domain TM as critical ingredient for a
  first-principles approach to understanding the
  Internets AS-level topology (TBD)