# Queueing Analysis of Network Traffic Methodology and by jbw10297

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```									     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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