Abstract
In this thesis, we consider two classes of stochastic
models which both capture some of the essential
properties of teletraffic. Teletraffic has two time
regimes where profoundly different behavior and
characteristics are seen. When traffic traces are
observed at coarse resolutions, properties like
self-similarity and long-range dependence are visible. In
small time-scales, traffic exhibits complex scaling laws
with much more spiky bursts than in coarser resolutions.
The main part of the thesis is devoted to a large
time-scale analysis by considering Gaussian processes and
queueing systems with Gaussian input. In order to
understand the small time-scale dynamics, first steps are
taken towards general multifractal models offering a
suitable basis for short time-scale teletraffic modeling.
The family of Gaussian processes with stationary
increments serves as the traffic model for large
time-scales. First, we introduce a fast and accurate
simulation algorithm, which can be used to generate long
approximate Gaussian traces. Moreover, the algorithm is
also modified to run on-the-fly. Then approximate queue
length distributions for ordinary, priority and
generalized processor sharing queues are derived using a
most probable path approach. Simulation studies show that
the performance formulae appear to be quite accurate over
the full range of buffer levels. Finally, we construct a
semi-stationary predictor, which uses a constant variance
function and mean rate estimation based on a moving
average method. Moreover, we show that measuring the past
of a process by geometrically increasing intervals is a
good engineering solution and a much better way than
equally spaced measurements.
We introduce a family of multifractal processes which
belongs to the framework of T-martingales and
multiplicative chaos introduced by Kahane. The family has
many desirable properties like stationarity of
increments, concave multifractal spectra and simple
construction. We derive, for example, conditions for
non-degeneracy, establish a power law for the moments and
obtain a formula for the multifractal spectrum.
Original language | English |
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Qualification | Doctor Degree |
Awarding Institution |
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Supervisors/Advisors |
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Award date | 25 Apr 2003 |
Place of Publication | Espoo |
Publisher | |
Print ISBNs | 951-38-6036-1 |
Electronic ISBNs | 951-38-6037-X |
Publication status | Published - 2003 |
MoE publication type | G5 Doctoral dissertation (article) |
Keywords
- Gaussian processes
- multifractals
- queueing systems
- performance analysis
- traffic modeling