Friday, November 09, 2012

Principles of Communications 2012 up to L15 - week 6

This week, Optimisation, and a start on Scheduling.

One question came up in optimisation - In the formulation of delay as
F/(C-F),  which I characterised as the load over the "headroom",
this is a dimensionless result - yes - its basically the average number of customers in an M/M/1 Queue (see Richard Gibbens slides from Computer Systems Modelling). However, in a work conserving router with a fixed speed output link, this translates into delay by multiplying by the
mean packet size/the output link line rate (which would have dimension time:)

Several people asked for more info about control theory - the chapter in Keshav's book (as per course web sight) is really quite clear (goes a bit past what I would ask, but knowledge is good, right?)...so recommend an hour reading that chapter - it also has exercises that are useful.
Keshav, S. (2011). Mathematical Foundations of Computer Networking. Addison-Wesley,
covers all but the graph theory bits of the maths I cover (and also covers some queueing and other performance things you might find useful as an alternative text, if you are attending Dr Gibbens' course too).

As per previous blog,
Keshav, S. (1997). An engineering approach to computer networking. Addison-Wesley
is also a useful text for the more protocol-oriented parts of this course.


Finally, if you are interested in the optimisation framework, then I recommend some of Frank Kelly's papers from the statslab - for example, this one briefly menions why we might take the sum of willing to pay times log of rates
w ln(x) 
as the  network view of the utility function..
.Fairness and stability of end-to-end congestion control

The two plots of functions of u_l (link utilisation of link l) are for
two different cost functions where the first one is exp(u_l)
and the second is n*(u_l^n) where n is a parameter (not the number of users - its just to generalise the function to a class of functions whose steepness/convexity can be varied by increasing n!

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