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
selfsimilarity and longrange dependence are visible. In
small timescales, 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
timescale analysis by considering Gaussian processes and
queueing systems with Gaussian input. In order to
understand the small timescale dynamics, first steps are
taken towards general multifractal models offering a
suitable basis for short timescale teletraffic modeling.
The family of Gaussian processes with stationary
increments serves as the traffic model for large
timescales. 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 onthefly. 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
semistationary 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 Tmartingales 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
nondegeneracy, establish a power law for the moments and
obtain a formula for the multifractal spectrum.
Original language  English 

Qualification  Doctor Degree 
Awarding Institution 

Supervisors/Advisors 

Award date  25 Apr 2003 
Place of Publication  Espoo 
Publisher  
Print ISBNs  9513860361 
Electronic ISBNs  951386037X 
Publication status  Published  2003 
MoE publication type  G5 Doctoral dissertation (article) 
Keywords
 Gaussian processes
 multifractals
 queueing systems
 performance analysis
 traffic modeling
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Mannersalo, P. (2003). Gaussian and multifractal processes in teletraffic theory: Dissertation. VTT Technical Research Centre of Finland. http://www.vtt.fi/inf/pdf/publications/2003/P491.pdf