Post-doctoral position « Optimal function chain placement on the fog under uncertainty »

Date limite de candidature : 21/06/2021
Date de début : 01/09/2021
Date de fin : 31/08/2022

Pôle : Télécoms et réseaux
Type de poste : Post-Doc ou ATER
Contact : EL AYOUBI Salah (

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Post-doctoral position


Optimal function chain placement on the fog under uncertainty


1.1. Context

With the rapid deployment of smart city and Industrial Internet of Things (IIoT) applications, and  the widespread adoption of machine learning in these domains, a classical centralized approach that consists in processing the data in the cloud encounters many privacy, communication, and efficiency challenges. A recent trend [McMahan2017] is the fusion of machine learning, IIoT applications, and fog computing with the exploitation of the processing capacity of smart terminals and other low-capacity processing nodes deployed on the edge. In this project, we consider supporting IIoT applications and federated learning in the distributed architecture of fog computing. To support IIoT applications and federated learning, the placement of the different functions and the scheduling of the corresponding communication flows have to be carefully designed.


1.2. Objective

The fog is composed of a multitude of low capacity nodes. The application services will be presented as a chain of functions, each of them being able to be deployed on an independent physical node, while communicating with the adjacent functions on the chain. The chain has to be deployed on the edge network according to physical infrastructures’ available resources in terms of CPU (on servers) and bandwidth (on links).

In order to place function chains, stochastic optimization techniques will be used as it is necessary to take optimal decisions in the presence of risk and uncertainty together with dependence between the  random events. The source of uncertainty is twofold. One component is exogenous, and results from substantially incomplete knowledge of important dependent problem data, like the stochastic variation of the needs of the considered application in terms of processing and bandwidth and node/link failures and other disruptions occurring with low probability. If only this kind of uncertainty is present, then the adequate methodology for modelling and solution of such decision problems is stochastic programming using copulae [chl2015]. The second component of uncertainty is endogenous and comes from the actions of independent actors who constitute the system under study. This component adds another level of complexity to an already difficult problem that makes it very difficult to solve numerically. We are going to address this uncertainty from the viewpoint of multistage optimization and probabilistic constraints.

Moreover, machine learning (ML) approaches will be adopted as they have two major benefits. First, they can be applied when  complete information about parameters and system operations required by the optimization problems is not available. Second, ML approaches are more scalable as the algorithms can evolve, learn, and adapt the decisions from past experience. The ML approaches can alleviate the issues of curse of dimensionality and curse of modeling that typically occur in stochastic optimization. In this project, we are particularly interested in developing a deep reinforcement learning (DRL) framework as an analytical tool to solve multistage stochastic problems, using similar concepts than those presented in [Anh2019].


1.3 Candidate experience

The candidate should hold a PhD degree in optimization or applied mathematics. A previous experience in the telecommunication applications domain will be appreciated.


1.4. Supervisors



[Anh2019] T. T. Anh, N. C. Luong, D. Niyato, Y.-C. Liang, and D. I. Kim, « Deep reinforcement learning for time scheduling in RF-powered backscatter cognitive radio networks, »  IEEE WCNC, Marrakech, April 2019.

[Chl2015] J. Cheng, M. Houda, A. Lisser. “Chance constrained 0-1 quadratic programs using copulas.” In Optim. Lett. 9(7): 1283-1295 (2015).

[McMahan2017] B. McMahan, E. Moore, D. Ramage, S. Hampson, B. Aguera. « Communication-efficient learning of deep networks from decentralized data. » In Artificial Intelligence and Statistics, pp. 1273-1282. PMLR, 2017.