Traffic Generator

1
Traffic Generator

• Real network design is 90 of file preparation
  and data collection.
• Data can be collected by, for example, monitoring
  a network (see also SNMP and MRTG in Labs)
• Some data need to be generated
• Future growth prediction
• Large traffic demands (requirements, end-to-end
  traffic) data.
• Only limited info available.
• Traffic generator can fill in the gap.

2
Traffic Generation

• Traffic matrix T TrafI,j
• Traf(i,j) Traffic from node i to node j
• Assume Uniform Traffic.
• Traf(i,j)C. Traffic from node i to node j is C.
• Assume Random Traffic
• Traf(i,j) is some distribution between a minimum
  and a maximum value.What distribution does the
  following code generate?

Uniform distributed between min_req and max_req
3
More Realistic TrafficFormula

• Proportional to some power (Pop_Power) of the
  populations
• Inversely proportional to some power (Dist_Power)
  of the distance
• a a scaling factor (for total traffic match,
  more later)

• Example Email traffic in the three location
  network
• Pop_Power1
• Dist_Power0

4
Add Offset and Scale Factor

• Population offset (say 0.05)? avoid zeros
• Distance offset

5
Example 4.1 in section 4.6.1 p. 108 in Cahn
textbook

• Suppose that a company has 50 sites linked by 85
  E1-lines (2048 Kbps). The average number of hops
  in a route is 2.75, and the links have an average
  utilization of 55. What value of a should be
  chosen to generate the traffic?
• Since we are not given the traffic matrix T yet,
  we can express a as in
• 
  
• With additional information on populations and
  coordinates of sites, a traffic generator can
  generate T. Hence
  can then be determined.

6
Example (cont.)

• But how do we determine the value of
  traffic_total?
• Recall that
• where link flow (u, v) is the total amount of
  link flows on the link uv. Hence

7
Row Normalization

• What if we desire to normalize T so that it
  reflects an observed traffic_outv for a site u?
• Instead of scaling the entire matrix T, we scale
  the row of T indexed by u. Denote the row-scale
  factor ?u for the site u with observed
  traffic_outv. Then

• Note that the summation in the denominator ? all
  sitesvTraf(u, v) gives the row-sum of the row
  indexed by u, which measures the total out-bound
  traffic from the site u.
• Other rows in T can be normalized (with respect
  to their corresponding traffic_out) similarly.

8
Column Normalization

• Similar to row normalization, we denote the
  column-scale factor ?v for a site v with observed
  traffic_inv. Then
• Note that the summation in the denominator ? all
  sitesuT(u, v) gives the column-sum of the column
  indexed by v, which measures the total in-bound
  traffic into the site v.
• Other columns in T can be normalized (with
  respect to their corresponding traffic_in)
  similarly.

9
Row and column normalization

• Here, we know the total traffics into and out of
  each site in the network and we want to normalize
  traffics generated by a traffic generator to
  agree with total traffics.
• A necessary condition for doing row and column
  normalization

10
Row and column normalization algorithm

• (Section 4.6.3 in Cahn textbook)
• Given TRAFFIN and TRAFFOUT for all nodes and an
  initial traffic matrix
• ScaleTRAFFIN/(total of the traffic matrix),
  between 0.999 and 1.001
• Row_scale, col_scale
• Procedure
• Scale according to the total traffic (total
  TRAFFIN)
• Calculate row_scaleisum of rowi/TRAFFINi and
  col_scalejsum of columnj/TRAFFOUTj
• Scale rows and columns multiply each element in
  the matrix by lreqi,jrow_scaleicolumn_scale
  j
• Iterate on total traffic and row/column traffic
  (repeat the previous two steps)

11
Example 5 node network

• TRAFFINTRAFFOUT10000 bps for all 5 nodes
• Total traffic50000
• Initial traffic matrix generated T0i,j
  tot046.34, scale50000/tot01078.96

Tot row012.55
5.61
6.61
12
1st round Row and Column Scale Factors and
Modified Traffic

• Traffi,jscaleT0i,j scaleSum(T0i,j)50000
  ? scale50000/Sum(T0I,j) ?Traffi,j50000T0i
  ,j/46.34
• Row_scale010000/SumjTraff0,j1/5
  46.34/12.550.738, row_scale11/546.34/5.611.6
  52

13
2nd Round Traffic Matrix

• Traffi,j50000/tot0T0i,jrow_scaleicol_sca
  lej
• E.g., Traff0,150000/46.341.660.7381.6522184
  .

Tot049572
14
2nd Round Row and Column Scale Factors

• Scale 1.009 (50000/tot150000/49572)
• Row_scale, col_scale

15
5 Iteration later

• Round to the next integers
• Tot50000, scale1
• Row sums 10001, 10000, 9998, 10002, 9999
• Close enough

16
Traffic Generators and Sensitivity Analysis

• Different initial traffic matrices e.g., use
  different assumptions, use different powers, etc.
• The initial matrix can be modified, for example,
  to model a change of traffic
• Often useful to generate traffic suites than a
  single set of traffic.
• It can be used to study how network responds to
  change.