Queueing Analysis of Network Traffic Methodology and by jbw10297

VIEWS: 8 PAGES: 15

									     Queueing Analysis of Network Traffic:
     Methodology and Visualization Tools




D. A. Rolls, G. Michailidis, F. Hernandez-Campos

              rollsd@uncw.edu
               UNC Wilmington



                                            p.1/15
Abilene Comparison: Cleveland and Replayed Data




  The original data is less ‘spiky’ than the replayed
              data, but is it significant?
                                                p.2/15
Abilene Comparison: Marginal Distributions




   The marginal distributions of the original and the
          replayed data are comparable.



                                                p.3/15
Abilene Comparison: Logscale Diagrams




   The log-scale diagrams of the original and the
   replayed data reveal similar scaling behaviors,
        especially for the middle time scales.

                                               p.4/15
Abilene Comparison: Queue Length CCDFs

                 Queue Length CCDF−65% Utilization                       Queue Length CCDF−85% Utilization
         10^0




                                                                 10^0
         10^−2




                                                                 10^−2
P(Q>x)




                                                        P(Q>x)
         10^−4




                                                                 10^−4
                                           replay                                                  replay
                                           original                                                original
         10^−6




                                                                 10^−6
                  0    10^6   2*10^6           4*10^6                     0    10^6   2*10^6           4*10^6

                                       x                                                       x

The tails of the queue length CDFs are very different.

                                                                                                         p.5/15
Simulation
• arrival sequence: {Xn ; n = 1, 2, · · · , N }
• queue length process (Lindley recurrence formula):
        Q0 = 0, Qn = max{Qn−1 + Xn − C, 0}

• the server rate, C, is a user-defined parameter
determines the utilization rate, ρ, through the formula
                         E[X(n)]
                      ρ=
                           C
• for a finite buffer with size B
    Q0 = 0, Qn = min{max{Qn−1 + Xn − C, 0}, B}


                                                p.6/15
Visualizations
 1. Queue Length Time Plot (i.e. Qn vs. n)
 2. Queue Length CCDF Plots
 3. QQ Plots
 4. Loss Rate plots (finite buffers)
 5. Integrated plots, multiscale maps




                                             p.7/15
Loss Rate Plots




 Aggregated loss rate processes for the original (left
  panel) and replayed (right panel) traces at 95%
     utilization and with a buffer of size 20000.


                                                p.8/15
Integrated plot: Mean queue length vs. utilization




                                                p.9/15
Mean loss rate vs. utilization rate vs. buffer size (IPLS)




                                                 p.10/15
Multiscale Map




                 p.11/15
More recent testbed comparison

                 Queue Length CCDF−70% Utilization                            Queue Length CCDF−75% Utilization
         10^0




                                                                      10^0
                          replay                                                       replay
                          original                                                     original
         10^−2




                                                                      10^−2
P(Q>x)




                                                             P(Q>x)
         10^−4




                                                                      10^−4
         10^−6




                                                                      10^−6
                  0     20000        40000   60000   80000                     0    100000    200000   300000   400000

                                      x                                                           x

         Original and replayed data is quite similar for
    utilizations 70% and below, but different at 75% and
                            above.                   p.12/15
Problems and Issues
1. Statistical measures don’t easily translate
2. Non-Gaussian Data
3. Mean trends and shifts
4. Utilization doesn’t scale like the data
5. Packet counts vs. byte counts




                                                 p.13/15
UNC Inbound Traffic (Bytes)




                             p.14/15
UNC Inbound Traffic (Packets)




                               p.15/15

								
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