Communication Systems IK1500

Anders Västberg [email protected]

08-790 44 55 IK1500 1

IK1500 Communication Systems

• TEN1: 7,5 hec. • Seminars – Active participation in the seminars gives the grade E. For higher grades or if you missed the seminars then you can write the exam.

• 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/program kurser/kurshemsidor/ict/cos/IK1500/HT09-1 HT08/P1 IK1500 2

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 3

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 4

Course Overview

HT08/P1 IK1500 5

HT08/P1 IK1500 6

HT08/P1 IK1500 7

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 8

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!

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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 10

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 11

Example: Efficient Transport of Packet Voice Calls

Voice coder and packetizer Voice coder and packetizer Depacketizer voice decoder Depacketizer voice decoder Router Communication link C bits/s Router Voice coder and packetizer 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 12 [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.

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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 14

Design alternatives

• Bit-dropping at the multiplexer – If the buffer level would exceed B, then drop excess bits – Same as 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

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B HT08/P1 0

Multiplexer Buffer Level

bits dropped IK1500 time 16

Results

1.2

1 0.8

0.6

0.4

0.2

0 0 HT08/P1 bit-dropping low-bit-rate coding 5 10 15 20 delay bound (in packet transmission times) IK1500 25 30 17

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 18 [kumar, et. al., 2004]

HT08/P1

Input-queued (IQ) switch

c4 b3 a1 1 f1 e1 d1 2 h2 g2 3 j3 i2 4 4 X 4 Switch 1 2 3 4 c time f a e d i h g b j IK1500 19

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).

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0.5

Markov chain representation N=2

0.25

1, 1 1, 2 0.25

0.25

0.25

0.25

0.25

Number of states =

N N

0.25

0.25

0.25

0.25

0.25

2, 1 2, 2 0.5

0.25

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Saturation throughput

N Saturation throughput

1 2 3 4 5 6 1.0000

0.7500

0.6825

0.6553

0.6399

0.6302

Capacity of a switch is the maximum rate at which packets can arrive and be served with a bounded delay.

The insight gained: capacity ≈ saturation throughput 7 8 0.6234

0.6184

Converges to: 2  2  0 .

586 HT08/P1 IK1500 22

Virtual Output Queuing

• A virtual output queue at input

i

for output and is denoted by

VOQ ij

• Maximum-weight matching algorithm

j

VOQ 11 VOQ 12 VOQ 21 VOQ 22 2 x 2 switch 1 Q 11 Q 12 2 Q 21 Q 22 1 2 HT08/P1 IK1500 23