We consider a congestion control problem in computer networks. The problem
is posed as an optimal control problem and reduced to a problem of
finding solutions to delay differential equations. Systems involving time delays
in the dynamics are actually very difficult to model and therefore very
difficult to solve. We consider three approaches in our congestion control
problem: an elastic queue approach leading to an optimal control problem
with a state–dependent delay differential equation; three approaches in flow
models (also leading to systems containing delay differential equations), precisely
the dual control approach, the primal–dual control approach and the
control approach based on queueing delay. The elastic queue approach is not
explored due to the lack of software good enough to solve optimal control
problems involving delay differential equations.
In flow models, we consider the standard case, that is where the feedback
from sources to links is exact and the network behaves perfectly well (without
any unexpected event). We also consider some non–standard cases such as
the case where this feedback contains errors (for example overestimation,
underestimation or noise), and the case where one link breaks in the network.
We numerically solve the delay differential equations obtained and use the
results we get to determine all the considered dynamics in the network.
This is followed by an analysis of the results. We also explore the stability
of some simple cases in the dual control approach, with weaker conditions
on some network parameters, and discuss some fairness conditions in some
simple cases in all the flow model approaches. Non–standard cases are also
solved numerically and the results can be compared with those obtained in
the standard case.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/5884 |
| Date | 10 December 2008 |
| Creators | Kamga, Morgan |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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