TCOM 540

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(No Transcript)
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TCOM 540

• Session 4

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Agenda

• Review Session 2 assignment and Quiz
• Economies of Scale
• Traffic and Cost Generation Techniques
• Case Study of Traffic Generation

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Economies of Scale

• Highly important in telecommunications
• Big pipes often (but not always!) cheaper than
  small ones per unit capacity
• Big pipes carry traffic more efficiently lower
  blocking/more effective capacity

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Big Pipes are (Usually) Cheaper per Unit capacity

• FTS2001 price for dedicated circuit from
• Falls Church, VA to Englewood, CO

Access Transport Access Total Cost/DS0
DS0 40 276 59 375 375
4xDS0 155 798 175 1128 282
T1 155 1787 175 2117 88
3xDS1 1813 6025 1245 9083 126
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Efficiency of Big Pipes

• Example Max minutes per circuit for p 0.03

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Traffic Models

• Topics
• Uniform
• Random
• Population power
• Modified population power
• Normalized model
• Asymmetric model

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Uniform

• Traffic from site a to site b is
• T(a,b) C
• Not realistic for most situations

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Random

• T(a,b) R
• Where R is a random number generated on a defined
  interval Tmin, Tmax
• This simple model is useful in some applications
• WWW-type traffic
• As one component of a more complex model

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Population Power

• If the sites a and b have populations Pa and Pb,
  and are distance Da,b apart, then
• T(a,b) a(papb)b/Da,bg
• where a, b, g are suitably-chosen constants

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Modified Population Power

• Large, close sites can dominate the simple
  population power model
• Fails if D 0
• Use offsets Doff and poff
• T(a,b) a(papb poff)b/(Da,b Doff )g

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Normalization

• Choose a so as to give the desired level of
  traffic on the network by matching
• Total traffic on network
• Traffic from each site (row normalization)
• Traffic to and from each site (row and column
  normalization)
• Must have S traffic in S traffic out for this
  to be possible!
• Algorithmic iterative approach can be used

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Asymmetric Traffic

• Models considered so far are symmetric
• T(a,b) T(b,a)
• Real traffic is often not symmetric
• E.g., WWW access
• Introduce concept of Levels
• Each site is assigned to a level Li, i1, , n
• Matrix of multipliers M(Li, Lj)

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Asymmetric Traffic (2)

• If M ( ) then traffic from a level 1 node
  to a level 2 node will be one-third of the
  traffic from a level 2 node to a level 1 node
• Revised model is then
• T(a,b) aM(La, Lb)(papb poff)b/(Da,bDoff
  )g

0 1 3 0
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More Complex Models

• Introduce a random element into the previous
  model
• Superimpose multiple components representing
  different types of traffic
• Redefine the distance function
• Organizational distance

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Tariff Structures

• Fundamental distinction
• Fixed cost per month
• Private lines, PVCs, some internet access
• Cost may also depend on bandwidth, distance,
  quality,
• Usage based
• Switched pipes e.g., switched voice
• Price may also depend on distance, bandwidth,
• Data per packet

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Tariff Structures (2)

• Additional fees may include
• Initiation charge
• Cancellation charge
• Features charges
• Access charges

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Tariff Structures (3)

• Tariff structures are not simple
• Depend on level of competition, administrative
  and other boundaries, other factors
• Best deals are not tariffed
• Usually competed/negotiated by large customers

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Tariff Structures (4)

• In some cases (especially international), tariffs
  may not exist, or may be for half-circuit only
• I.e., to a notional mid-ocean meeting point
• Commercial tariff services (e.g., Valucom, CCMI)
  are not cheap

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Linear Distance-Based Charges

• Underlying tariff structure for many dedicated
  circuits and PVCs is distance-based, e.g.,
• Cost a bdistance
• Rates for individual location-pairs may vary
• Carrier may have excess capacity on certain
  routes gt may be cheaper
• Carrier may have to buy capacity from others gt
  may be more expensive

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Piecewise-Linear Charges
Cost/month
Distance

• Each segment is linear

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Step Function
Cost/month
Distance
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Cost Generators

• Cahn provides 5 cost generators
• 1. Linear (TARIFF-UNIVERSAL)
• 2. Piecewise linear (2 pieces)
  (TARIFF-UNIVERSAL)
• 3. Piecewise linear (limited international)
  (TARIFF-NATIONAL)
• 4. International half-circuit (TARIFF-HCKT)
• 5. Exceptions (TARIFF-OVERRIDE)

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Case Study of Traffic Generation
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Outline

• Background and Problem Statement
• Current Academic Researchers in this Problem
• Proposed Algorithm
• Sample NetHealth Data Description
• Numerical Example with Proposed Algorithm
• O-D Matrix Tool Interface
• O-D Matrix Tool Outputs
• Next Steps
• References

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Background and Problem Statement

• Background
• Client uses Concords NetHealth to monitor
  performance
• NetHealth only generates link statistics such as
  link utilization
• When what if analyses on the network are
  required, the origin destination (O - D)
  traffic matrix that generated the measured link
  utilization reported by NetHealth is required
• The O-D traffic is the matrix of offered loads
  that originates at one node and is destined for
  another node1
• Problem
• To estimate the O-D traffic matrix given
  aggregate link utilization
• 1 Note nodes are groups of users that enter a
  router on a common interface, not single users

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Problem Background

• Vardi (1996) first used the term network
  tomography to refer to this problem due to the
  similarity between network inference and medical
  tomography1.
• There are two forms of network tomography (our
  problem is the 2nd) (Coates, 2001)
• Link level parameter estimation based on
  end-to-end, path level traffic measurements, or
• Sender-receiver path-level traffic intensity
  estimation based on link-level traffic
  measurements (antithesis of first form)
• 1 Tomography a method of producing a
  three-dimensional image of the internal
  structures of a solid object (as the human body
  or the earth) by the observation and recording of
  the differences in the effects on the passage of
  waves of energy impinging on those structures
  (Merriam-Webster Dictionary).

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Current Academic Researchers in this Problem

• Bell Labs Cao, Cleveland, Lin, Sun, Vander Wiel,
  Davis, Yu, Zhu
• UC Berkeley Coates, Hero, Nowak, Yu
• Vardi (Rutgers)

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Current Academic Approaches Used

• Frequently a linear model is assumed for the O-D
  traffic matrix estimation problem (Vardi (1996),
  Coates et al. (2001), Cao et al. (2001), Cao et
  al. (2000))
• y A x
• where
• y (y1, , ynL) is the observed column vector of
  incoming and outgoing byte counts for each of nL
  links
• x (x1, , xnP) is the unobserved vector of byte
  counts for all OD nP pairs in the network, where
  nP n(n-1) in a network of n nodes
• A nL x nP routing matrix (0/1)
• Elements aij of A are 1 if link i belongs to
  the directed path of the O-D pair j

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Current Academic Approaches Used

• Often the matrix A has a very large dimension
  (thousands of rows and columns for a moderate
  number of sites), and thus iterative algorithms
  are used
• Although the model is linear, it is not a typical
  linear regression because of the the
  nonnegativity constraints on the parameters x
• Also, because nP is typically larger than nL,
  identifiability of the parameters is a problem

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Current Academic Approaches
A matrix
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Current Academic Approaches (2)

• Vardi (1996) assumes the O-D byte counts are
  Poisson
• Maximum likelihood via the Expectation-maximizatio
  n1 (EM) algorithm is used to solve for O-D matrix
• O-D byte counts can be assumed Normal as an
  approximation to Poisson may allow simpler
  solution techniques
• A moment method for estimation is also proposed
• Cao et al. (2000) embellish the above Poisson
  model by assuming all quantities are time-varying
• Maximum likelihood estimation is done via a
  combination of the EM algorithm and a
  second-order global optimization method
• 1 EM algorithm is an algorithm for finding
  likelihood estimators from incomplete data. It is
  an iterative algoirthm in which a starting
  estimate is updated using a transformation called
  the EM operator. (Vanderbei and Iannone, 1994).

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Current Academic Approaches (2)

• Cao et al. (2001) describe a divide-and-conquer
  approach that can be used for large networks
• O-D pairs are partitioned into a number of
  disjoint sets
• Clustering methods used to group the O-D pairs
• For each O-D set, a corresponding set of links
  are selected for estimation (not disjoint)
• Heuristics used to select links, balancing
  estimation accuracy and computational cost
• Parameters are estimated for each O-D set, which
  aggregates the remaining rates for other O-D
  pairs not in the current set
• Computational complexity can be reduced from
  O(Ne5) to O(Ne2), where Ne is the number of edge
  nodes

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Current Academic Approaches (2)

• ? Exceeds requirements, highly desirable 
• è Meets requirements
• ? Does not meet requirements, less desirable
•  
• 1 This method can also be used with parallel
  computing

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Need for New Algorithm

• Academic methods are not feasible due to number
  of nodes in Clients network (approximately 1000
  nodes)
• Proposed algorithm is a heuristic faster

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Proposed Algorithm

• Compute the probability of originating at node i
  and terminating at node j
• p(i,j) is the fraction of all (unidirectional)
  network traffic coming in to node j, if i to j
  within a certain number of hops
• Estimate the total load originating at each node
  as the outgoing load from each node
• Compute TM(i,j), the estimate of packets per
  second originating at node i and terminating at
  node j, using estimate of the total load
  originating at each node times the probability
  p(i,j)
• Route traffic via Enhanced Interior Gateway
  Routing Protocol (EIGRP)

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Proposed Algorithm (2)

• Sum up the estimated load on each link from
  TM(i,j), compare to given link loads
• Compute an adjustment factor based on the ratio
  of the given link loads to the estimated link
  loads
• Adjust the estimate of total load originating at
  each node using the ratio of the given link loads
  to the estimated link loads, then re-estimate
  TM(i,j)
• Iterate above until convergence in the link loads
  is achieved
• Final adjustment if load originating at each node
  is greater than total load at node

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Sample NetHealth Data Description

• Net data from January 2001
• Data
• 1169 unique links
• 991 nodes
• Data fields for each link record
• Originating and terminating nodes for each link
• Link utilizations in each direction
• Link speed

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O-D Matrix Tool Interface

• Input Parameters
• Max Hops max number of hops between nodes for
  nonzero traffic probability
• Link Factor maximum deviation of estimated from
  measured link loads

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Numerical Example with Proposed Algorithm

• Input Parameters
• Link Factor 1.1
• Number of Hops varied from 2 to 10

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Numerical Example with Proposed Algorithm (2)

• Results (run times on 866 Mhz PC)
• Problem with Backbone Links only runs quickly (1
  min)
• Full Network problem about 4 hours
• Error in link utilizations under 1 percent for
  either problem
• Small increase in run times with number of hops
  (e.g., 20 increase as number of hops doubles
  from 4 to 8)

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O-D Matrix Tool Outputs

• Network Performance
• Average link percentage error
• Expected packet delay
• Average number of hops
• Link Performance
• Estimated and measured packets per second in each
  direction
• Expected packet delay
• Node Performance
• Originating packets per second
• Total packets per second in and out of each node
• Number connected to each node

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Sample Map Output
Client CONUS Network
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References

• A Scalable Method for Estimating Network Traffic
  Matrices from Link Counts, Bell Labs Tech
  Report, 2001, Jin Cao, D. Davis, Scott Vander
  Wiel Bin Yu, and Zhengyuan Zhu.
• Time-Varying Network Tomography Router Link
  Data, Journal of the American Statistical
  Association, 95, 1063-1075, 2000, Jin Cao, D.
  Davis, Scott Vander Wiel and Bin Yu.
• Mark Coates, Alfred Hero, Robert Nowak, and Bin
  Yu (2001). Large scale inference and tomography
  for network monitoring and diagnosis. Technical
  Report 604, Stat Dept, UC Berkeley. August, 2001.
  
• Y. Vardi, "Network Tomography Estimating
  Source-Destination Traffic Intensities From Link
  Data", Journal of the American Statistical
  Association March 1996,Vol.91 No 433, Theory and
  Methods
• R.J. Vanderbei and J. Iannone, "An EM approach to
  OD matrix estimation," Technical Report,
  Princeton University, 1994

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Assignment Session 4
For the following set of sites and traffic,
design a minimum-cost network with reasonable
performance
Sites
Traffic (kbps)
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Assignment Session 4 (2)

• You have two types of links available for this
  design
• Capacity 1.5 Mbps, cost 80 8/mile
• Capacity 64kbps, cost 10 1/mile
• You may use multiple links to satisfy demand.
• Note What is the maximum utilization you will
  allow per link?