Description
Purpose of this lab:
In this lab you will study and compare the properties of different types of network traffic. The
traffic types considered are:
Generated Poisson traffic;
Traffic from compressed video sources; and
Measured traffic from an Ethernet segment.
The traffic sources from this lab will be used in future labs to generate network traffic.
Software Tools:
This lab requires the use of MATLAB.
Please see TAs for further instructions.
What to turn in:
A report with your answers to the questions in this lab, including the plots, copies of
your MATLAB code, and the anonymous feedback form.
Lab
1
ECE 466 LAB 1 – PAGE 2
Table of Content
Table of Content _______________________________________________________________ 2
Preparing for Lab 1 ____________________________________________________________ 2
Lab 1 ____________________________________________________________________ 3
Part 1. Poisson Traffic __________________________________________________________ 4
Part 2. Compressed Video Traffic_________________________________________________ 7
Part 3. Aggregate traffic on an Ethernet network ___________________________________ 10
Part 4. (Optional) Metrics for Characterizing Network Traffic________________________ 12
Feedback Form for Lab 1___________________________________________________ 14
Preparing for Lab 1
This lab assumes that you have a basic knowledge of MATLAB. It will be helpful to review
your background of MATLAB. Some of the tasks involved in this lab are:
1. Read and process a data file with multiple columns;
2. Use of statistical functions, such as mean value, variance, covariance, etc.
ECE 466 LAB 1 – PAGE 3
Lab 1
Please read the following comments:
Quality of plots in lab report: This lab asks you to produce plots for a lab report. It is
important that the graphs are of high quality. All plots must be properly labelled. This
includes that the units on the axes of all graphs are included, and that each plot has a
header line that describes the content of the graph.
Waiting times with reading large files: The lab requires reading large files with
traffic traces. To avoid excessive waiting times, you may truncate the files if loading a
file takes longer than 15 minutes.
Feedback: To be able to improve the labs for future years, we collect data on the
current lab experience. You must submit an anonymous feedback form for each lab.
Please use the feedback form at the end of the lab, and return the form with your lab
report.
Units: The following conventions are used:
ms = milliseconds
s = microseconds
s = seconds
Mbps = Megabits per second
Arrival functions: In this lab (and in the lecture) we will sometimes describe the
arrivals of traffic by a function A.
a. We write A(t) to denote the arrivals in the time interval [0,t]. We will write A(t1,
t2) to denote the arrivals in the time interval [t1, t2].
b. Sometimes arrivals occur only at discrete times n= 0, 1, 2, 3,…. In this case,
we write A(n) to denote the arrivals until n.
MATLAB help:
a. We have made available:
i. sample MATLAB code for Parts 1, 2, and 3.
ii. Three traffic traces for Poisson traffic used in Part 1
b. Download all files in:
http://www.comm.utoronto.ca/~jorg/teaching/ece466/labs/lab1/
Part 1: Sample code: Lab1_Part_1.m
traces: poisson1.data, poisson2.data, poisson3.data
Part 2: Sample code: Lab1_Part_2.m
traces: movietrace.data
Part 3: Sample code: Lab1_Part_3.m
traces: BC-pAug89.TL.Z BC-pAug89-small.TL
ECE 466 LAB 1 – PAGE 4
Part 1. Poisson Traffic
Suppose we want to predict the delay and throughput at a buffer of a network link that
operates at link capacity C Mbps. The situation is illustrated in the figure, where packets are
represented as rectangular boxes.
C
Arrivals Departures
Buffer
To conduct an analysis of this link, we need to make assumptions on the traffic that arrives to
the link. The traffic description must specify the spacing between packets and the size of
packets that arrive to the buffer.
A very popular model to represent the number of packet arrivals in a time interval is the
Poisson Process. In a Poisson process with rate , the number of (arrival) events in a time
interval ( t, t+ ], denoted by N(t+) – N(t), is given by
A Poisson process has some interesting and useful properties:
In a Poisson process, the time between two (arrival) events follows an exponential
distribution, i.e.,
If we add the arrivals of two Poisson processes with rate and we obtain a Poisson
process with rate +
The following exercises ask you to generate Poisson traffic and study its properties.
Exercise 1.1 Scaling Poisson traffic arrivals
Here, you create sample paths of different lengths, and compare them in scaled plots.
Consider a packet arrival pattern of a flow, where all packets have a constant size of
100 Bytes and where packet arrivals follow a Poisson process. The average traffic
rate of the flow is Mbps.
The file poisson1.data contains a traffic trace of the data. The file has three columns:
Column 1: Packet number
Column 2: Timestamp (in microseconds)
Column 3: Packet size (in bytes).
ECE 466 LAB 1 – PAGE 5
Verify the measured mean bit rate of the flow with the target rate, by calculating the
mean and the variance of the times between consecutive arrival events. Compare the
values with the theoretically expected values.
Create three graphs that plot the data generated by the trace, viewed at different time
scales. Each graph has 100 data points.
Plot 1: Generate a vector with 100 elements. Each element stores the number of
bytes from the Poisson trace that arrive in a time period of 1 second.
o 1
st element: # bytes arriving in time period [0, 1 s];
o 2
nd element: # bytes arriving in time period [1, 2 s];
o …
Plot 2: Generate a vector with 100 elements. Each element stores the number of
bytes from the Poisson trace that arrive in a time period of 100 milliseconds,
beginning at a randomly selected start time.
o Pick a random starting point, e.g., time 30 s.
o 1
st element: # bytes arriving in time period [30, 30.1 s];
o 2
nd element: # bytes arriving in time period [30.1, 30.2 s];
o ….
Plot 3: Generate a vector with 100 elements. Each element stores the number of
bytes from the Poisson trace that arrive in a time period of 10 milliseconds, beginning
at a randomly selected start time.
o Pick a random starting point, e.g., time 50.2 s.
o 1
st element: # bytes arriving in time period [50.2, 50.21 s];
o 2
nd element: # bytes arriving in time period [50.21, 50.22 s];
o ….
Plot the content of the vectors in three separate graphs, with the time intervals on the
x-axis, and the number of bytes on the y-axis. The data points should be depicted as
vertical bars (e.g., using the MATLAB function `bar()’ ).
Describe your observations of the graphs.
Exercise 1.2 Traffic with exponentially sized packets
You may skip Exercise 1.2.
Consider a packet arrival pattern of a flow, where packets arrive with an equal spacing of 800
sec (microseconds), and with an exponentially distributed packet size with parameter with
average size 1/100 Bytes. The file poisson2.data contains a traffic trace of the data.
Verify the measured mean bit rate of the flow with the target rate, by calculating the
mean and the variance of the times between consecutive arrival events. Compare the
values with the theoretically expected values.
ECE 466 LAB 1 – PAGE 6
Repeat the tasks in Exercise 1.1 with the above arrival flows.
Provide a discussion where you compare the results with those from Exercise 1.1.
Exercise 1.3 Compound Poisson arrival process
Now consider a packet arrival pattern of a flow, which is a combination of the previously
discussed flows. Here, the packet arrival events follow a Poisson process with rate = 1250
packets/sec, and the packet size has an exponential distribution with average size 1/100
Bytes. The file poisson3.data contains a traffic trace of the data.
Verify the measured mean bit rate of the flow with the target rate, by calculating the
mean and the variance of the times between consecutive arrival events. Compare the
values with the theoretically expected values.
Repeat the tasks in Exercise 1.1 with the above arrival flows.
Provide a discussion where you compare the results, with those of the other
exercises.
Lab Report:
Include your answers to the tasks.
Include the plots, a description of the plots, and your observations and discussions.
ECE 466 LAB 1 – PAGE 7
Part 2. Compressed Video Traffic
In this part of the lab, you will explore the properties of a traffic flow that consists of
compressed digital video traffic.
Digital video consists of a sequence of video frames that are displayed at a rate of typically 30
frames per seconds. Assuming a frame size of 720 x 480 pixels (a standard format used for
digital video) and a depth of 24 bits per pixel, this results in a data rate 240 Mbps per video
stream. Using modern compression methods, such as MPEG and H.264, the data rate can
be drastically reduced to a few Mbps.
An MPEG encoder (and most other compression algorithms) generates three types of
frames: Intra-coded (I), Inter-coded or predictive (P), and bi-directional (B). I frames are
coded as still images not unlike JPEG; P frames encode the differences from the most recent
I or P frame; and B are interpolations of the next and previous I or P frames. An MPEG
encoder generates these frames in a repeating pattern, called the Group-of-Picture (GOP)
pattern. With 30 frames per second, the elapsed time between two frames is approximately
33 ms. A typical GOP pattern of IBBPBBPBB, where the dependencies between frames is
indicated by arrows, is shown in the following figure:
As indicated in the figure, frame types have different sizes, with I frames being the largest and
B frames the smallest. Note that a B frame is constructed from two reference frames of type I
or P (e.g., Frame 3 above depends on Frame 1 and Frame 4). Thus, to encode or decode a
B frame the transmitter or receiver must have available the next I or P frame. To account for
this need, frames are transmitted in a different sequence than they are displayed. In the
above example, the display and transmission sequence is as follows:
Display sequence: 1 2 3 4 5 6 7 8 9 10
Transmit sequence: 1 4 2 3 7 5 6 10 8 9
Due to the different sizes of of I, P, and B frames, the data rate of an MPEG encoded video
sources changes from frame to frame. For this reason, compressed video such as MPEG, is
referred to a Variable Bit Rate (VBR) video.
ECE 466 LAB 1 – PAGE 8
Exercise 2.1 Download a VBR video trace
Your first task is to download a file that contains a trace of a VBR video source. The file
contains the frame sizes obtained from a compression of a picture movie. The size of the
file is 2.6 MB.
Content: Silence of the Lambs (~ 30 min)
Source Format: DVD
Frame size and rate: CIF 352×288 @30 fps (frames per second)
Compression Algorithm: H.264/AVC (Full)
Quantizer (compression factor): 10
GoP Pattern: I B B B P B B B P B B B P B B B
Number of Frames: ~54000
Download the trace file from the following URL:
http://www.comm.utoronto.ca/~jorg/teaching/ece466/labs/lab1/movietrace.data
Explore the content of the file. The file contains one line for each frame and has
multiple columns. The first four columns are relevant for us:
o Column 1: Sequence number of the frame (in transmit sequence)
o Column 2: Display time of the frame
o Column 3: Frame type
o Column 4: Frame size in bytes
o Columns 5 – 7: not used
Exercise 2.2 Determine statistical properties of the video trace
Compute the following properties of the video trace.
o Number of frames and total number of bytes;
o Size of the smallest frame, size of the largest frame, and mean frame
size;
o Size of the smallest, largest and mean I, P, and B frame;
o Mean bit rate (Computed as the mean frame size divided by the frame
duration);
o Peak bit rate (Computed as the max. frame size divided by the frame
duration);
o Ratio of the peak rate and the average rate. This peak-to-average rate
ratio is often used as an indicator how bursty a traffic flow is. A flow with a
peak-to-average ratio of 10 or higher is highly variable.
Generate a set of graphs that show the properties of the video trace:
1. Generate a graph that shows the frame size as a function of the frame
sequence number. (Use the sequence in which the frames are listed in the
file, i.e., the transmit sequence.)
2. Generate a graph that shows the distribution of I frames, P frames, and B
frames. (x-axis is the frame size, y-axis is the relative frequency).
ECE 466 LAB 1 – PAGE 9
Exercise 2.3 Scaling Video traffic
As before with the Poisson traces, you are asked to generate and compare scaled plots of
the video trace.
Create three plots of the video traffic trace viewed at different scales. Each graph has
100 data points.
Plot 1: Generate a vector with 100 elements. Starting with Frame 1, each element
stores the amount of data from 500 frames of the video sequence.
o 1
st element: #bytes from the first 500 frames (frames 1, 2, …, 500).
o 2
nd element: #bytes from the frames 501,502, …, 1000.
o …
Plot 2: Generate a vector with 100 elements. Starting with a randomly selected
frame, each element stores the amount of data from 50 frames of the video
sequence.
o Pick a random starting point, e.g., frame 3000.
o 1
st element: #bytes from frames 3001, 3002, … 3050.
o 2
nd element: #bytes from frames 3051, 3052, … 3100.
o ….
Plot 3: Generate a vector with 100 elements. Starting with a randomly selected
frame, each element stores the amount of data from 5 frames of the video sequence.
o Pick a random starting point, e.g., frame 5010.
o 1
st element: #bytes from frames 5010, 5011, … 5015.
o 2
nd element: #bytes from frames 5016, 5017, … 5018.
o ….
Plot the content of the vectors in three separate graphs, with the frame number on the
x-axis, and the number of bytes on the y-axis. The data points should be depicted as
vertical bars (e.g., using the MATLAB function bar() ).
Describe your observations of the graphs, and compare them to the scaled versions
of the Poisson plots from Part 1.
Lab Report:
Include your answers to the exercises. Include the plots, a description of the plots,
and your observations and discussions.
ECE 466 LAB 1 – PAGE 10
Part 3. Aggregate traffic on an Ethernet network
Until the early 1990s, it was common to represent traffic in a packet network by a Poisson
process. Measurement studies performed in late 1980s showed that this is not a good
assumption. One of the most influential such studies, done by Will Leland and Dan Wilson in
1989, measured the total traffic in an Ethernet network at the Bellcore Morristown Research
and Engineering facility. The researchers collected traffic traces that each contains a million
packet arrivals seen on an Ethernet network.
These traces, the most extensive measurement study at the time, were studied extensively,
and led to the conclusion that aggregate traffic (=traffic from many traffic sources) is not
“Poisson-like”. In fact, it was convincingly argued that aggregate packet traffic is “self-similar”,
meaning, that it looks roughly the same if viewed at different scales. This discovery of the
self-similarity of Ethernet traffic had important implications on the design of networks and
packet switches.
Exercise 3.1 Download an Ethernet traffic trace
Download one of the Bellcore traffic traces. The file contains one line for each captured
Ethernet packets, with two columns. The first column is a timestamp (in seconds), the
second column is the size of the captured Ethernet packets (in Bytes).
Content: August 1989 trace from Bellcore
Start date: Aug 29, 1989, 11:25am
Data is recorded for about 3142.82 seconds (until 1,000,000 packets had been
captured).
The total trace can be downloaded as a compressed file (5 MB) is available from
http://www.comm.utoronto.ca/~jorg/teaching/ece466/labs/BC-pAug89.TL.Z
The file can be uncompressed with the Unix command uncompress, yielding a
file size of approximately 20 MB.
A smaller version of the file (the first 100,000 lines, corresponding to
approximately 250 seconds) can be downloaded in uncompressed ASCII format
from
http://www.comm.utoronto.ca/~jorg/teaching/ece466/labs/BC-pAug89-small.TL
Exercise 3.2 Determine statistical properties of the Ethernet
trace
You may work with the smaller version of the file (with 100,000 lines). You receive
extra credit (5 marks) if you work with the longer version.
Analyze the trace of the Ethernet traffic:
o Compute the number of captured packets and total number of bytes;
o Compute the mean bit rate of the entire trace;
o Compute the peak bit rate of the trace (defined as the rate that maximizes
the ratio “packet size”/”time since last packet”).
o Compute the ratio of the peak rate and the average rate. Compare this
value to the peak-to-average rate ratio from the video trace in Part 2.
ECE 466 LAB 1 – PAGE 11
Generate a set of graphs that show properties of the Ethernet traffic trace:
1. Generate a graph that depicts the packet size as a function of time.
2. Generate a graph that shows the distribution of packet sizes (x-axis shows
the packet size, y-axis shows the relative frequency).
Exercise 3.3 Scaled depiction of Ethernet traffic
This repeats the exercise from Exercise 2.2 for Ethernet traffic where you generate and
compare scaled plots.
Continue with the 100 second excerpt of Ethernet traffic from the previous exercise.
Create three plots of the Ethernet traffic trace viewed at different scales. Each graph
has 100 data points.
Plot 1: Generate a vector with 100 elements, where each element stores the amount
of data captured in a 1 s interval.
o 1
st element: #bytes from the first second of traffic, i.e., interval [0, 1 s].
o 2
nd element: #bytes from the interval [1, 2 s].
o …
Plot 2: Generate a vector with 100 elements, where each element stores the traffic
from 100 ms worth of captured traffic. Select a random starting time.
o Pick a random starting point, e.g., t = 20 s.
o 1
st element: #bytes from the interval [20, 20.1 s].
o 2
nd element: #bytes from the interval [20.1, 20.2 s].
o …
Plot 3: Generate a vector with 100 elements, where each element stores the traffic
from 10 ms worth of captured traffic. Select a random starting time.
o Pick a random starting point, e.g., t = 90 s.
o 1
st element: #bytes from the interval [90, 90.01 s].
o 2
nd element: #bytes from the interval [90.01, 90.02 s].
o …
Plot the content of the vectors in three separate graphs, with the packet number on
the x-axis, and the number of bytes on the y-axis. The data points should be depicted
as vertical bars (e.g., using the MATLAB function bar() ).
Describe your observations of the graphs, and compare them to the plots from the
Poisson traffic and the video trace.
Lab Report:
Include your answers to the exercises. Include the plots, a description of the plots,
and your observations and discussions.
ECE 466 LAB 1 – PAGE 12
Part 4. (Optional) Metrics for Characterizing Network Traffic
The comparison of the plots from Poisson, video traffic, and measured Ethernet traffic should
have illustrated the vast differences of these sources. There is a whole collection of metrics
that help with quickly characterizing the properties of a certain traffic mix on a network. You
have already seen the peak-to-average rate ratio, a widely used metrics to describe the
burstiness of VBR video traffic. In this part of the lab, you will compute other metrics for the
three traffic types.
Exercise 4.1 Autocorrelation function
The autocorrelation is a mathematical tool to analyze if a function has a repeating or
periodic pattern. The autocorrelation function is the covariance of a random process with a
time-shifted version of itself, divided by the variance. The definition is as follows:
where, E[ ], Var[ ], and Cov[ ] indicate the expected value, the variance and the
covariance. We also use .
Generate graphs that compare the autocorrelation function of the packet sizes from
the Poisson traffic in Part 1 (Exercise 1.4), the frame sizes of the video trace in Part 2,
and the sizes of Ethernet packets from Part 3, and provide a comparison of the plots.
Exercise 4.2 Burstiness function
The burstiness function plots the worst case average bit rate over a time interval of a given
length. The function gives a more detailed view of the burstiness than the peak-to-average
rate ratio. The function is defined as follows
Generate graphs that show the index of burstiness function of the arrivals from the
Poisson traffic in Part 1 (Exercise 1.2), the frame sizes of the video trace in Part 2,
and the sizes of Ethernet packets from Part 3, and provide a comparison of the plots.
Exercise 4.3 Index of dispersion
The index of dispersion can also be used as an indication of the burstiness of traffic. The
index of dispersion for an arrival function A(t) (which describes the arrivals in the time interval
[0,t]) is defined as:
ECE 466 LAB 1 – PAGE 13
Generate graphs that show the index of dispersion function of the arrivals from the
Poisson traffic in Part 1 (Exercise 1.2), the frame sizes of the video trace in Part 2,
and the sizes of Ethernet packets from Part 3.
The index of dispersion should be shown for times up to 100 seconds.
Provide a comparison of the plots.
ECE 466 LAB 1 – PAGE 14
Feedback Form for Lab 1
Complete this feedback form at the completion of the lab exercises and submit the form
when submitting your lab report.
The feedback is anonymous. Do not put your name on this form and keep it separate
from your lab report.
For each exercise, please record the following:
Difficulty
(-2,-1,0,1,2)
-2 = too easy
0 = just fine
2 = too hard
Interest Level
(-2,-1,0,1,2)
-2 = low interest
0 = just fine
2 = high interest
Time to complete
(minutes)
Part 1. Poisson Traffic
Part 2. Compressed Video Traffic
Part 3. Aggregate traffic on an Ethernet
network
Part 4. Characterizing Traffic
Please answer the following questions:
What did you like about this lab?
What did you dislike about this lab?
Make a suggestion to improve the lab.
