# [e2e] Opportunistic Scheduling.

Detlef Bosau detlef.bosau at web.de
Tue Jul 10 10:03:22 PDT 2007

ksingh at irisa.fr wrote:
>> Hm. The question is, whether this "formula mapping" really suffices to
>> keep/apply Kelly´s rationale.
>>
>
> another things to look could be to see if "PF scheduling" fulfills the
> criteria of being proportionaly fair defined in "Charging and rate control
> ..."
>
> \Sum{ (\lambda_{i}{*} - \lambda_{i})/(\lambda_{i}) }  <= 0
>
>  \lambda_{i}: set of throughput obtained that we want to know are PF or not
>  \lambda_{i}{*} : any other feasible vector of throughput
>
> Kamal
>
>
That misses the problem. Whatever Kelly talks about in his rationale,
Kelly starts with a very precise system model. In this system model, he
defines utility functions which are then to be maximized and boundary
conditions which essentialy make the discussed optimization problem have
a unique solution.

At the moment, and in Hosein´s paper as well, we talk about utility
functions. And we don´t care about the boundary conditions.

In Kelly´s approach, "rates" mean ressource shares. And the Kelly
approach yields a set of ressource shares which solve a given
optimization problem.
The only one shared ressource in the HSDPA downlink is service time at
the base station. The "rates" used here are in fact coding schemes and
not ressource shares.

So, my criticism is, that the Kelly paper is simply based upon a totally
different model / problem and is simply not applicable here! Even if
there are formulae which look similar.

Detlef

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