Annoce de thèse : Robust dimensioning of wireless optical networks with multiple partial link failur

Context of the thesis:
The thesis is part of the project activities of the Laboratory of Excellence (LABEX) at the Université de Technologie de Compiègne (UTC) in France on the Control of Technological Systems of Systems (MS2T) (www.utc.fr/labexms2t).

PhD Supervisors:
 Dritan Nace, Professor
Heudiasyc laboratory, UMR CNRS-UTC 7253
+33 (0)3 44 234302, nace@.utc.fr
 Michal Pioro, Professor at Institute of Telecommunications, Warsaw University of Technology, Poland, and Department of Electrical and Information Technology, Lund University, Sweden. michal.pioro@eit.lth.se

PhD thesis description:
The thesis is in continuation of the work presented in [1, 2 ,3] and is essentially devoted to wireless fiber networks, like FSO (Free Space Optics), that are subject to failures involving partial loss of links capacity. FSO is a well established wireless transmission technology, considered as an alternative to radio links in such applications as metropolitan wireless mesh networks. A disadvantage of FSO links is their sensitivity to environmental conditions such as fog, rain, snow and pollution, causing substantial loss of the optical transmission power over the channel due mostly to absorption and scattering. All this raises the problem of how to represent the weather condition in a mathematical model in order to take into account the robustness of such networks facing these situations. Second, we will study in deep restoration methods dealing with partial link failures. The following points will be investigated during the thesis:
1. Developing a method for converting in a reliable way the weather scenarios to partial failure scenarios on networks. In other words, the method will allow representing the weather conditions in terms of decrease of transmission ratio per link and thus as multiple link failure scenarios.
2. Proposing a generic restoration method dealing with both total link failures and partial link failures.
3. The first stage will produce a realistic representation of the problem but most likely involving a large number of multiple link partial failures (as the weather scenarios is huge). Solving the link dimensioning problem for the restoration method (proposed in second stage) with the whole set of failure scenarios is computationally intractable while solving the problem for all possible scenarios will lead to a highly expensive solution since some strong failures, even though unlikely to happen, may imply a very high cost. In order to avoid this, we plan to compute the dimensioning cost of the network for a subset of scenarios covering the most substantial part of the scenarios. Hence, we are dealing with a chance constrained programming problem, known to be computationally intractable in practice. We have realized a preliminary study but the problem is huge and very complicated, and we plan to investigate in deep this issue.
4. As an important part of the PhD work, we plan to study the practical aspects of applying the proposed algorithm on FSO networks, especially from protocol point of view.
5. Finally, there is also a theoretical issue that we plan to investigate during this PhD Thesis. During precedent works on the subject, we have discovered that the LP formulation contains an exponential number of rows and columns, which is unusual in multi-commodity flows. We have solved this issue for the particular case, but it is of high interest to study it in a general LP formulation and identify conditions leading to tractable cases.

Candidate’s profile:
Aptitudes in C++ programming.
Knowledge in applied mathematics in general and in linear programming and statistics in particular. Knowledge in networks are also very useful.
Documents required to apply:
Send to nace@utc.fr
- Curriculum vitae
- Motivation letter
- At least two references and/or recommendation letters
- A statement of research experience and interests
Location:
Laboratory Heudiasyc UMR CNRS 7253
Université de Technologie de Compiègne (UTC)
Centre de recherche de Royallieu
BP 20529 Rue Personne de Roberval
60205 Compiègne cedex –France

Selected references:
1. M. Pióro, D. Nace and Y. Fouquet, An optimization model for multicommodity flow networks with partial multiple link failures, RNDM-13, 10-13 September 2013, Almaty, Kazakhstan.
2. Yoann Fouquet, Dritan Nace, Michal Pioro, Michael Poss, et Mateusz Zotkiewicz, “Generalized Elastic Flow Rerouting Scheme” Networks, Networks 66(4): 267-281 (2015).
3. M. Pioro, Y. Fouquet, D. Nace, M. Poss, Optimizing Flow Thinning Protection in Multicommodity Networks with Variable Link Capacity, Operations Research, 64(2):273--289, 2016.