Abstract
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) 
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Keywords
 Gaussian processes
 multifractals
 queueing systems
 performance analysis
 traffic modeling
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Gaussian and multifractal processes in teletraffic theory : Dissertation. / Mannersalo, Petteri.
Espoo : VTT Technical Research Centre of Finland, 2003. 47 p.Research output: Thesis › Dissertation › Collection of Articles
TY  THES
T1  Gaussian and multifractal processes in teletraffic theory
T2  Dissertation
AU  Mannersalo, Petteri
PY  2003
Y1  2003
N2  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.
AB  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.
KW  Gaussian processes
KW  multifractals
KW  queueing systems
KW  performance analysis
KW  traffic modeling
M3  Dissertation
SN  9513860361
T3  VTT Publications
PB  VTT Technical Research Centre of Finland
CY  Espoo
ER 