Hidden Markov models  Traffic modeling and subspace methods
(2002) Abstract
 The main motivation for this thesis, however not the only one, is the search for models for traffic in telecommunication networks. Traffic characterization and modeling are of great importance in the analysis and dimensioning of communication systems. During the last decades we have experienced an explosive growth of our telecommunication networks. New important properties, both on macroscopic and microscopic time scales, have been revealed. These new features have a profound impact on network performance and thus needs to be taken into consideration. In Paper A we study the microdynamics of some data sets of traffic on the link level. Our approach is Poissonification, a kind of random local smoothing of a point process. The idea is to use... (More)
 The main motivation for this thesis, however not the only one, is the search for models for traffic in telecommunication networks. Traffic characterization and modeling are of great importance in the analysis and dimensioning of communication systems. During the last decades we have experienced an explosive growth of our telecommunication networks. New important properties, both on macroscopic and microscopic time scales, have been revealed. These new features have a profound impact on network performance and thus needs to be taken into consideration. In Paper A we study the microdynamics of some data sets of traffic on the link level. Our approach is Poissonification, a kind of random local smoothing of a point process. The idea is to use Poissonification on empirical data materials in order to find the (small) time scale where the process switch from a doubly stochastic to a homogeneous behavior.
The models used and studied are hidden Markov models (HMMs). In Paper B we study specifically the Markovmodulated Poisson process (MMPP). In fitting an MMPP to some sets of observed traffic we concentrate on maximum likelihood (ML) methods, but also use moment methods. The ML methods are computationally more complex but concerning performance they prove to be superior to moment methods.
As a possible candidate for a method to combine the simplicity of the moment methods, and the accuracy of the likelihood methods, we have subspace methods. To be able to use subspace methods for HMMs the process needs to be represented in state space form. In Paper C of this thesis we show that it is possible to represent an HMM as a state space system in innovation form. This reformulation is complicated by the nonminimality within the state space representation of the HMM. The reformulation involves deriving solutions to algebraic Riccati equations which are usually treated under minimality assumptions.
In Paper D we develop a subspace identification algorithm especially designed for HMMs. Some of the crucial assumptions on the system, needed for the subspace methods to work, fail to be met by HMMs and thus commonly used methods are not directly applicable. Therefore we need to consider each of the steps in existing algorithms with regard to the specific conditions of the HMM and in this way develop a new algorithm. Consistency is proved of this algorithm. However, we manage to estimate the system parameters only seen as a projection on a certain subspace and only up to a similarity transformation. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/464752
 author
 Andersson, Sofia ^{LU}
 supervisor
 opponent

 Professor Gustafsson, Fredrik, Linköping University
 organization
 publishing date
 2002
 type
 Thesis
 publication status
 published
 subject
 keywords
 programming, actuarial mathematics, Statistik, operationsanalys, Statistics, operations research, subspace identification, state space representation, likelihood estimation, Poissonification, traffic analysis, hidden Markov model, Markovmodulated Poisson process, programmering, aktuariematematik
 pages
 144 pages
 publisher
 Centre for Mathematical Sciences, Lund University
 defense location
 Centre of Mathematical Sciences, Sölvegatan 18, Lund, sal C
 defense date
 20020607 13:15:00
 ISBN
 9162852531
 language
 English
 LU publication?
 yes
 additional info
 Articles: 1) Local dependencies and Poissonification of data traffic  A case study 2) Maximum likelihood estimation of a structured MMPP with applications to traffic modeling 3) Linear filtering and state space representations of hidden Markov models 4) Subspace methods for hidden Markov models  Algorithms and consistency
 id
 c95524902702451ba424ba8685678e39 (old id 464752)
 date added to LUP
 20160401 16:25:41
 date last changed
 20181121 20:41:20
@phdthesis{c95524902702451ba424ba8685678e39, abstract = {{The main motivation for this thesis, however not the only one, is the search for models for traffic in telecommunication networks. Traffic characterization and modeling are of great importance in the analysis and dimensioning of communication systems. During the last decades we have experienced an explosive growth of our telecommunication networks. New important properties, both on macroscopic and microscopic time scales, have been revealed. These new features have a profound impact on network performance and thus needs to be taken into consideration. In Paper A we study the microdynamics of some data sets of traffic on the link level. Our approach is Poissonification, a kind of random local smoothing of a point process. The idea is to use Poissonification on empirical data materials in order to find the (small) time scale where the process switch from a doubly stochastic to a homogeneous behavior.<br/><br> <br/><br> The models used and studied are hidden Markov models (HMMs). In Paper B we study specifically the Markovmodulated Poisson process (MMPP). In fitting an MMPP to some sets of observed traffic we concentrate on maximum likelihood (ML) methods, but also use moment methods. The ML methods are computationally more complex but concerning performance they prove to be superior to moment methods.<br/><br> <br/><br> As a possible candidate for a method to combine the simplicity of the moment methods, and the accuracy of the likelihood methods, we have subspace methods. To be able to use subspace methods for HMMs the process needs to be represented in state space form. In Paper C of this thesis we show that it is possible to represent an HMM as a state space system in innovation form. This reformulation is complicated by the nonminimality within the state space representation of the HMM. The reformulation involves deriving solutions to algebraic Riccati equations which are usually treated under minimality assumptions.<br/><br> <br/><br> In Paper D we develop a subspace identification algorithm especially designed for HMMs. Some of the crucial assumptions on the system, needed for the subspace methods to work, fail to be met by HMMs and thus commonly used methods are not directly applicable. Therefore we need to consider each of the steps in existing algorithms with regard to the specific conditions of the HMM and in this way develop a new algorithm. Consistency is proved of this algorithm. However, we manage to estimate the system parameters only seen as a projection on a certain subspace and only up to a similarity transformation.}}, author = {{Andersson, Sofia}}, isbn = {{9162852531}}, keywords = {{programming; actuarial mathematics; Statistik; operationsanalys; Statistics; operations research; subspace identification; state space representation; likelihood estimation; Poissonification; traffic analysis; hidden Markov model; Markovmodulated Poisson process; programmering; aktuariematematik}}, language = {{eng}}, publisher = {{Centre for Mathematical Sciences, Lund University}}, school = {{Lund University}}, title = {{Hidden Markov models  Traffic modeling and subspace methods}}, year = {{2002}}, }