1. 1 IK1500 Communication Systems IK1500 Anders Västberg vastberg@kth.se 08-790 44 55

2. HT08/P1IK15002 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/program- kurser/kurshemsidor/ict/cos/IK1500/HT08-1http://www.kth.se/student/program- kurser/kurshemsidor/ict/cos/IK1500/HT08-1

3. HT08/P1IK15003 Teachers Anders Västberg –vastberg@kth.sevastberg@kth.se –08-790 44 55 Göran Andersson –goeran@kth.segoeran@kth.se –08-790 44 28 Bengt Lärka –bengan@kth.sebengan@kth.se –08-790 44 47

4. HT08/P1IK15004 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

5. HT08/P1IK15005 Mathematica Download the program from: –http://progdist.ug.kth.se/public/http://progdist.ug.kth.se/public/ General introduction to Mathematica –http://www.cos.ict.kth.se/~goeran/archives/Ma thematica/Notebooks/General/

6. HT08/P1IK15006 Course Overview

7. HT08/P1IK15007

8. HT08/P1IK15008

9. HT08/P1IK15009 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

10. HT08/P1IK150010 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!

11. HT08/P1IK150011 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

12. HT08/P1IK150012 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

13. HT08/P1IK150013 Example: Efficient Transport of Packet Voice Calls Voice coder and packetizer Voice coder and packetizer Voice coder and packetizer Depacketizer voice decoder Depacketizer voice decoder Depacketizer voice decoder Communication link Router Problem: Given a link speed of C, maximize the number of simultaneous calls subject to a constraint on voice quality. [Kumar, et. al., 2004] C bits/s

14. HT08/P1IK150014 Voice Quality Distortion –The voice is sampled and encoded by, for example, 4 bits. –At least a fraction  of the coded bits must be received for an acceptable voice quality. Example: If  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.

15. HT08/P1IK150015 Queuing Model 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

16. HT08/P1IK150016 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

17. HT08/P1IK150017 Multiplexer Buffer Level

18. HT08/P1IK150018 Results Maximum load that can be offered

19. HT08/P1IK150019 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 [kumar, et. al., 2004]

20. HT08/P1IK150020 Input-queued (IQ) switch

21. HT08/P1IK150021 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).

22. HT08/P1IK150022 Markov chain representation N=2 Number of states

23. HT08/P1IK150023 Saturation throughput NSaturation throughput 1 1.0000 2 0.7500 3 0.6825 4 0.6553 5 0.6399 6 0.6302 7 0.6234 8 0.6184 Converges to: 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