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In the context of team Cornet’s seminars, Olivier Bilenne (ENPC) will present his research work on Solutions of Poisson’s equation for first-policy improvement in parallel queueing systems, on November 18, 2022, at 11:35 in the meeting room. Abstract: This talk addresses the problem of (state-aware) job dispatching at minimum long-run average cost in a parallel queueing system with Poisson arrivals. Policy iteration is a technique for approaching optimality through improvement of an initial dispatching policy. Its implementation rests on the computation of value functions. In this context, we will consider the M/G/1-FCFS queue endowed with an arbitrary cost function for the waiting times of the incoming jobs. The associated relative value function is a solution of Poisson’s equation for Markov chains, which I propose to solve in the Laplace transform domain by considering an ancillary stochastic process extended to (imaginary) negative backlog states. This construction enables us to issue closed-form solutions for simple cost functions (polynomial, exponential, and their piecewise compositions), in turn permitting the derivation of interval bounds for the relative value functions to more general cost functions. Such bounds allow for an exact implementation of the first improvement step of policy iteration in a parallel queueing system.One objective Plus d'infos

In the context of team Cornet’s seminars, Omar Boufous (OrangeLabs) will present his research work on Learning a Correlated Equilibrium with Perturbed Regret Minimization, on October 22, 2021, at 11:35 in the meeting room. Abstract: We consider the problem of learning a correlated equilibrium of a finite non-cooperative game and show a new learning procedure, called Correlated Perturbed Regret Minimization (CPRM), for this purpose. CPRM uses a perturbed variant of a regret minimization to approach the set of correlated equilibrium distributions and a simple correlation device to stabilize the empirical probability distribution over action profiles. Numerical experiments provide evidence of the long run convergence of the realized sample paths to points in the set of approximate correlated equilibrium distributions. Additional simulation results suggest that CPRM is adaptive to changes in the game such as departures or arrivals of players.

In the context of team Cornet’s seminars, Rosa Figueiredo (LIA) will present her research work on Multiplicity in Signed Graph Partitioning, on June 6, 2022, at 11:35 in the meeting room. Abstract: In order to study real-world systems many works model them through signed graphs, i.e. graphs whose edges are labeled as either positive or negative. Such a graph is considered as structurally balanced when it can be partitioned into a number of modules, such that positive (negative) edges are located inside (in-between) the modules. When it is not the case, authors look for the closest partition to such balance, a problem called Correlation Clustering (CC). The standard approach used in the literature is to find a single partition and focus the rest of the analysis on it, as if it was sufficient to fully characterize the studied system. Yet, it may not reflect the structure of the network, and one may need to seek for other partitions to build a better picture. We study the space of optimal solutions of the CC. We propose an efficient enumeration method allowing to retrieve the complete space of optimal solutions of the CC. It combines an exhaustive enumeration strategy with neighborhoods of Plus d'infos

In the context of team Cornet’s seminars, Mandar Datar (LIA) will present his research work on Fisher market model-based resource allocation for 5G network slicing, on June 6, 2022, at 11:35 in the meeting room. Abstract: Network slicing is one of the potential technologies to support a higher degree of heterogeneity and flexibility required by next-generation services in 5G networks. In a 5G network, slicing is a specific form of virtualization that allows multiple logical networks (e.g., Mobile Virtual Network Operators (MVNOs)) to run on top of shared physical infrastructure. In the multi-resource allocation scheme, a set of heterogeneous resources (e.g., radio resource, CPU, memory, bandwidth) is shared among Slice tenants or MVNOs, and a portion of them is allocated to each MVNO to support dedicated service to their customers. We consider a scenario where service providers or slice tenants need heterogeneous resources at geographically distributed locations to support the service for their end-users. We propose a resource sharing scheme based on the Fisher market model and the Trading post mechanism. In the proposed scheme, each slice owns the budget representing its infrastructure share or purchasing power in the market. The slices acquire different resources by spending their budgets to Plus d'infos

In the context of team Cornet’s seminars, Naresh Modina (LIA) will present his research work on Multi Resource Allocation (MRA) for network slices with Multi-Level Fairness, on May 5, 2022, at 11:35 in the meeting room. Abstract: Network slicing is becoming the platform of choice for several applications and services. Nowadays most applications are virtualized to gain flexibility and portability. With network slicing, operators can create multiple network slices or tenants, which can be used for certain applications with specific requirements. Behind the network slicing, a slice expresses the need to access a precise service type, under a fully qualified set of computing and network requirements. Resource allocation decision encompasses a combination of different resource types (e.g., radio resource, CPU, memory, bandwidth). In this paper, we explore a differential pricing scheme that maximizes social welfare among slices as well as among end-users. To do so, we propose a pricing mechanism that makes fairness at multiple levels: fairness among slices and fairness among slice locations supported by each slice. Therefore, the proposed scheme is beneficial for both the slices and the end-users independent of their location. Additionally, we study the case where slices can manipulate their preferences to improve their utility. Plus d'infos