## The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc. | |

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of
the Department of Engineering Physics and Mathematics for public examination and debate in
Auditorium E at Helsinki University of Technology (Espoo, Finland) on the 2^{nd} of December, 2005, at 12 noon.

Overview in PDF format (ISBN 951-22-7952-5) [534 KB]

Dissertation is also available in print (ISBN 951-22-7917-7)

Stochastic networks are mathematical models for traffic flows in networks with uncertainty. The goal of this thesis is to develop new methods for analyzing performance and stability of stochastic networks, helping to better understand and control uncertainty in complex distributed systems.

The thesis considers three instances of stochastic networks, each representing a specific challenge for analytical modeling. The first case studies the impact of incomplete information to a queueing network with distributed admission control. Stability conditions for various admission policies are derived, together with a numerical algorithm for performance evaluation. In the second case, stochastic comparison is used to derive performance bounds for multiclass loss networks with overflow routing. The third model is a spatial random field generated by a large number of noninteracting sources, for which scaling and renormalization are used to show how the level of randomness of the individual sources may critically affect the macroscopic statistical properties of the field.

The results of the thesis illustrate the feasibility of stochastic comparison and stochastic analysis in deriving approximations and performance bounds for complex physical networks with uncertainty. Approximations and performance bounds based on exact mathematical methods have the advantage that they explicitly state the type of circumstances required for the accuracy of the estimates. The resulting analytical formulas can sometimes reveal interesting properties that are not easily detected using numerical simulation.

This thesis consists of an overview and of the following 4 publications:

- Leskelä, L. (2006). Stabilization of an overloaded queueing network using measurement-based admission control. Journal of Applied Probability 43 (1), to appear, 14 pages. © 2006 Applied Probability Trust. By permission.
- Leskelä, L. and Resing, J. (2004). A tandem queueing network with feedback admission control. Institut Mittag-Leffler Report No. 09, 2004/2005, fall, 9 pages. © 2004 by authors.
- George, L., Jonckheere, M. and Leskelä, L. (2005). Does repacking improve performance of multiclass loss networks with overflow routing? In: X. Liang, Z. Xin, V. B. Iversen, G. S. Kuo (Eds.), Proceedings of the 19th International Teletraffic Congress. Beijing University of Posts and Telecommunications Press, pp. 1365-1373. © 2005 by authors.
- Kaj, I., Leskelä, L., Norros, I. and Schmidt, V. (2005). Scaling limits for random fields with long-range dependence. Institut Mittag-Leffler Report No. 24, 2004/2005, fall, 25 pages. © 2005 by authors.

**Keywords:**
stochastic network, queueing, admission control, overflow routing,
stochastic comparison, scaling, renormalization, spatial random field

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© 2005 Helsinki University of Technology

Last update 2011-05-26