Transcript Document

Communication Systems
IK1500
Anders Västberg
[email protected]
08-790 44 55
IK1500
1
IK1500 Communication Systems
• TEN1: 7,5 hec.
• Problem assignments
– Each assignment covers one problem of the exam. If you
complete the problem assignment successfully, then you will get
the full points for the corresponding problem on the exam
(only for the ordinary exam – not for any makeup exam
(“omtenta”)).
• Required reading:
– Kumar, Manjunath, & Kuri, Communication Networking, Elsevier,
2004.
– G. Blom, et.al., Sannolikhetsteori och statistikteori med
tillämpningar, Studentlitteratur, 2005
• Course Webpage:
– http://www.kth.se/student/programkurser/kurshemsidor/ict/cos/IK1500/HT08-1
HT08/P1
IK1500
2
Teachers
• Anders Västberg
– [email protected]
– 08-790 44 55
• Göran Andersson
– [email protected]
– 08-790 44 28
• Bengt Lärka
– [email protected]
– 08-790 44 47
HT08/P1
IK1500
3
Supplementary rules for
examination
• Rule 1: All group members are responsible for
group assignments
• Rule 2: Document any help received and all
sources used
• Rule 3: Do not copy the solutions of others
• Rule 4: Be prepared to present your solution
• Rule 5: Use the attendance list correctly
HT08/P1
IK1500
4
Mathematica
• Download the program from:
– http://progdist.ug.kth.se/public/
• General introduction to Mathematica
– http://www.cos.ict.kth.se/~goeran/archives/Ma
thematica/Notebooks/General/
HT08/P1
IK1500
5
Course Overview
HT08/P1
IK1500
6
HT08/P1
IK1500
7
HT08/P1
IK1500
8
Course Aim
• Gain insight into how communication
systems work (building a mental model)
• Develop your intuition about when to
model and what to model
• Use mathematical modelling to analyse
models of communication networks
• Learning how to use power tools
HT08/P1
IK1500
9
Modelling
• Find/built/invent a model of some specific system
• Why?
– We want to answer questions about the system’s
characteristics and behaviour.
• Alternative: Do measurements!
– However, this may be:
• too expensive: in money, time, people, …
• too dangerous: physically, economically, …
– or the system may not exist yet (a very common cause)
• Often because you are trying to consider which system to build!
HT08/P1
IK1500
10
Modelling
• Models have limited areas of validity
• The assumptions about input parameters
and the system must be valid for the
model to give reliable results.
• Models can be verified by comparing the
model to the real system
• Models help you not only with design, but
give insight about what to measure
HT08/P1
IK1500
11
Use of models
• Essential as input to simulations
• Use models to detect and analyse errors
– Is the system acting as expected?
– Where do I expect the limits to be?
• Model-based control systems
HT08/P1
IK1500
12
Example: Efficient Transport of
Packet Voice Calls
Voice coder
and packetizer
Depacketizer
voice decoder
Voice coder
and packetizer
Depacketizer
voice decoder
Communication link
Router
C bits/s
Voice coder
and packetizer
Router
Depacketizer
voice decoder
Problem: Given a link speed of C, maximize
the number of simultaneous calls subject
to a constraint on voice quality.
HT08/P1
IK1500
13
[Kumar, et. al., 2004]
Voice Quality
• Distortion
– The voice is sampled and encoded by, for example, 4
bits.
– At least a fraction a of the coded bits must be
received for an acceptable voice quality.
Example: If a=0.95, then at least 3.8 bits per sample
must be delivered.
• Delay
– Packets arrive at the link at random, only one packet
can be transmitted at a time, this will cause queuing
of packets, which will lead to variable delays.
HT08/P1
IK1500
14
Queuing Model
B
C
• B bits: The level of the multiplexer buffer that should
seldom be exceeded.
• C bits/s: Speed of the link
 Leads to the delay bound B/C (s) to be rarely exceeded
HT08/P1
IK1500
15
Design alternatives
• Bit-dropping at the multiplexer
– If the buffer level would exceed B, then drop excess
bits
– Buffer adaptive coding (the queue length controls the
source encoder)
 Closed loop control
• Lower bit-rate coding at the source coder
– Lower the source encoder bit rate
– The probability of exceeding buffer level B is less than
a small number (e.g. 0.001).
 Open loop control
HT08/P1
IK1500
16
Multiplexer Buffer Level
bits dropped
B
0
time
HT08/P1
IK1500
17
Maximum load that can be offered
Results
1.2
1
0.8
0.6
0.4
bit-dropping
low-bit -rate coding
0.2
0
0
HT08/P1
5
20
15
10
delay bound (in packet transmission times)
IK1500
25
30
18
Achievable Throughput in an
Input-Queuing Packet Switch
• N input ports and N output ports
• More than one cell with the same output
destination can arrive at the inputs
• This will cause destination conflicts.
• Two solutions:
– Input-queued (IQ) switch
– Output –queued (OQ) switch
HT08/P1
IK1500
19
[kumar, et. al., 2004]
Input-queued (IQ) switch
time
c4 b3 a1
f1 e1 d1
h2 g2
j3 i2
HT08/P1
1
1
2
2
f
a e d
i
h g
4 X4
3
Switch
4
3
4
IK1500
b
j
c
20
Output – queued (OQ) switch
• All of the input cells (fixed size small
packets) in one time slot must be able to
be switched to the same output port.
• Can provide 100% throughput
• If N is large, then this is difficult to
implement technically (speed of memory).
HT08/P1
IK1500
21
Markov chain representation
N=2
0.25
0.5
1, 1
0.25
0.25
0.25
Number of states = N
0.25
0.25
N
0.25
0.25
0.25
0.25
0.25
1, 2
2, 1
2, 2
0.5
0.25
HT08/P1
IK1500
22
Saturation throughput
N Saturation throughput
1 1.0000
Capacity of a switch is the maximum
2 0.7500
rate at which packets can arrive and be
served with a bounded delay.
3 0.6825
4 0.6553
The insight gained:
5 0.6399
capacity ≈ saturation throughput
6 0.6302
7 0.6234
8 0.6184
Converges to: 2  2  0.586
HT08/P1
IK1500
23