08-790 44 55
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
• Required reading:
– Kumar, Manjunath, & Kuri, Communication Networking, Elsevier,
– G. Blom, et.al., Sannolikhetsteori och statistikteori med
tillämpningar, Studentlitteratur, 2005
• Course Webpage:
• Anders Västberg
– [email protected]
– 08-790 44 55
• Göran Andersson
– [email protected]
– 08-790 44 28
• Bengt Lärka
– [email protected]
– 08-790 44 47
Supplementary rules for
• Rule 1: All group members are responsible for
• Rule 2: Document any help received and all
• Rule 3: Do not copy the solutions of others
• Rule 4: Be prepared to present your solution
• Rule 5: Use the attendance list correctly
• Download the program from:
• General introduction to Mathematica
• 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
• Find/built/invent a model of some specific system
– 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!
• 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
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
Example: Efficient Transport of
Packet Voice Calls
Problem: Given a link speed of C, maximize
the number of simultaneous calls subject
to a constraint on voice quality.
[Kumar, et. al., 2004]
– The voice is sampled and encoded by, for example, 4
– 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.
– 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.
• 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
• Bit-dropping at the multiplexer
– If the buffer level would exceed B, then drop excess
– Buffer adaptive coding (the queue length controls the
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
Multiplexer Buffer Level
Maximum load that can be offered
low-bit -rate coding
delay bound (in packet transmission times)
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]
Input-queued (IQ) switch
c4 b3 a1
f1 e1 d1
a e d
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).
Markov chain representation
Number of states = N
N Saturation throughput
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
Converges to: 2 2 0.586