arXiv subjects

Jean-Michel Fourneau

Publications and source records attributed to Jean-Michel Fourneau.

4 recordsLinked to original sources

arXiv2026

Strong aggregation of the Markov chains associated with matching models based on the automorphism group of their compatibility graphs

We extend the analysis of strong aggregation to general compatibility graphs, focusing on item counts rather than positions, and exploring generalized greedy matching disciplines. We prove that under a condition of automorphism-based transition consistency, the associated Markov chain is strongly aggregable for an arbitrary graph with a non-trivial automorphism group. Furthermore, we extend our analysis to non-greedy matching disciplines, distinguishing scenarios where compatible items can or cannot coexist within the same state. This result is illustrated with a simple compatibility graph with a rich automorphism structure: the odd rings. For all scenarios, we investigate the strong aggregation properties of the resulting Markov chains. This work enhances the theoretical understanding of lumpability in stochastic matching models and provides a foundation for analyzing complex graph structures.

cs.PF↗

arXiv2025

Efficient Solving of Large Single Input Superstate Decomposable Markovian Decision Process

Solving Markov Decision Processes (MDPs) remains a central challenge in sequential decision-making, especially when dealing with large state spaces and long-term optimization criteria. A key step in Bellman dynamic programming algorithms is the policy evaluation, which becomes computationally demanding in infinite-horizon settings such as average-reward or discounted-reward formulations. In the context of Markov chains, aggregation and disaggregation techniques have for a long time been used to reduce complexity by exploiting structural decompositions. In this work, we extend these principles to a structured class of MDPs. We define the Single-Input Superstate Decomposable Markov Decision Process (SISDMDP), which combines Chiu's single-input decomposition with Robertazzi's single-cycle recurrence property. When a policy induces this structure, the resulting transition graph can be decomposed into interacting components with centralized recurrence. We develop an exact and efficient policy evaluation method based on this structure. This yields a scalable solution applicable to both average and discounted reward MDPs.

math.OC↗

arXiv2024

A slot-based energy storage decision-making approach for optimal Off-Grid telecommunication operator

This paper proposes a slot-based energy storage approach for decision-making in the context of an Off-Grid telecommunication operator. We consider network systems powered by solar panels, where harvest energy is stored in a battery that can also be sold when fully charged. To reflect real-world conditions, we account for non-stationary energy arrivals and service demands that depend on the time of day, as well as the failure states of PV panel. The network operator we model faces two conflicting objectives: maintaining the operation of its infrastructure and selling (or supplying to other networks) surplus energy from fully charged batteries. To address these challenges, we developed a slot-based Markov Decision Process (MDP) model that incorporates positive rewards for energy sales, as well as penalties for energy loss and battery depletion. This slot-based MDP follows a specific structure we have previously proven to be efficient in terms of computational performance and accuracy. From this model, we derive the optimal policy that balances these conflicting objectives and maximizes the average reward function. Additionally, we present results comparing different cities and months, which the operator can consider when deploying its infrastructure to maximize rewards based on location-specific energy availability and seasonal variations.

math.OC↗

arXiv2020

Flexibility can hurt dynamic matching system performance

We study the performance of general dynamic matching models. This model is defined by a connected graph, where nodes represent the class of items and the edges the compatibilities between items. Items of different classes arrive one by one to the system according to a given probability distribution. Upon arrival, an item is matched with a compatible item according to the First Come First Served discipline and leave the system immediately, whereas it is enqueued with other items of the same class, if any. We show that such a model may exhibit a non intuitive behavior: increasing the services ability by adding new edges in the matching graph may lead to a larger average population. This is similar to a Braess paradox. We first consider a quasicomplete graph with four nodes and we provide values of the probability distribution of the arrivals such that when we add an edge the mean number of items is larger. Then, we consider an arbitrary matching graph and we show sufficient conditions for the existence or non-existence of this paradox. We conclude that the analog to the Braess paradox in matching models is given when specific independent sets are in saturation, i.e., the system is close to the stability condition.

cs.GT↗