Th`ese de Doctorat de l'université Paris VI Pierre et Marie Curie Mlle ...

Chapter 6
Mathematical Model
This Chapter introduces a novel and flexible mathematical model, Ideal Bandwidth Al-
location (IBA), that maximizes the total network revenue and provides bounds to the
performance achievable by any online dynamic bandwidth allocation algorithm.
Such model assumes the exact knowledge of the future traffic offered to the network.
The bandwidth allocations are performed optimizing the operation of the network loaded
with the actual present and future traffic. No practical bandwidth allocation scheme can
perform better.
This mathematical model extends the optimization problem related to utility maximiza-
tion introduced in [7] and its solution can be obtained using Lagrangian methods. Further,
if the objective function can be approximated using piece-wise linear concave functions,
the problem can be solved using standard linear programming (LP) techniques.
IBA allows us to gauge the impact of the traffic predictor used to assign bandwidth to
non-greedy connections (Section 5.1), as well as of the granularity in bandwidth assignment
(i.e. the sensitivity to the parameter Tu) on the performance of our proposed dynamic
bandwidth allocation algorithms.
The structure of this Chapter is as follows. In Section 6.1, we first illustrate the network
model, then we define some notations needed for our mathematical model. In Section 6.2,
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