Max-Olivier Hongler

By using a fluid modeling approach, we study the fluctuations around the average throughput delivered by simple production system. A special attention is paid to the buffered production dipole for which an explicit estimation for an stationary variance of the throughput is calculated.

A dynamic scheduling heuristic is derived to solve the multi-armed bandit problem (MABP) with set-up costs and/or time delays. While our heuristic is based on priority indices of the Gittins' type, the presence of set-up costs requires a couple of indices to be defined for each project of the MABP. Doubling the number of priority indices enables hysteretic buffers to be obtained in the scheduling diagram. In the presence of set-up costs, hysteresis zones are clearly mandatory to avoid high-frequency switchings between the various projects of the MABP. The performance of our general heuristic is tested on the class of deteriorating MABP for which the explicit optimal scheduling can be constructed.

We consider a single non-markovian failure prone machine which delivers a single product. The operating policy of the machine is chosen to be of the hedging point type. In the infinite horizon limit, we calculate the position of the hedging point that minimizes a convex cost function.

Westudy the optimal stopping problem for a class of continuoustime random evolutions described by stochastic differential equationswith alternating renewal processes as noise sources. The exactsolution of this stopping problem provides, in explicit form,an expression for the Gittins' indices needed to derive the optimalscheduling of a class of multi-armed bandit problems in continuoustime. The underlying random processes to which the bandits' armsobey are random velocity models. Such processes are commonlyused to describe, in the fluid limit, the random production flowsdelivered by failure prone machines.

The fundamental idea that synchronized patterns emerge in networks of interacting oscillators is revisited by allowing a parametric learning mechanism to operate on the local dynamics. The local dynamics consist of stable limit cycle oscillators which, due to mutual interactions, are allowed, via an adaptive process, to permanently modify their frequencies. Adaptivity is made possible by conferring to each oscillator’s frequency the status of an additional degree of freedom. The network of individual oscillators is ultimately driven to a stable synchronized oscillating state which, once reached, survive even if mutual interactions are removed. Such a permanent, plastic type deformation of an initial to a final consensual state is realized by a dissipative mechanism which vanishes once a consensus is established. By considering diffusive couplings between position- and velocity-dependent state variables, we are able to analytically explore the resulting dynamics and in particular to calculate the resulting consensual state. The ultimate consensual state is topology network-independent. However, the interplay between the graph connectivity and the local dynamics does strongly influence the learning rate.