Mohamed Rahali

Cao-Thanh Phan

Gerardo Rubino

KRS: Kubernetes Resource Scheduler for resilient NFV networks

To address the diversity of use cases envisioned by the 5G technology, it is critical that the design of the future network allows maximum flexibility and cost effectiveness. This requires that network functions should be designed in a modular fashion to enable fast deployment and scalability. This expected efficiency can be achieved with the cloud native paradigm where network functions can be deployed as containers.

Virtualization tools such as Kubernetes [1] offer multiple functionalities for the automatic management of the deployed containers hosting the network functions. These tools such as resource scheduling and replicas must be applied efficiently to improve the network functions availability and resilience. This paper focuses on resource allocation in a Kubernetes infrastructure hosting different network services. The objective of the proposed solution is to avoid resource shortage in the cluster nodes while protecting the most critical functions. A statistical approach is followed for the modeling of the problem as well as for its resolution, given the random nature of the treated information.

I. INTRODUCTION

Future 5G and 6G netorks and beyond will be based on specific 5G evolutions to address new applications such as virtual reality, augmented reality, holography, intelligent connectivity, deep sensing, etc [START_REF] David | 6g vision and requirements: Is there any need for beyond 5g?[END_REF]. These evolutions include the support of multiple new access networks, for instance in airplane communications, satellite communications and underwater acoustic communications. These applications are very demanding in terms of end-to-end performance to meet the requirements of industries. Thus, the beyond 5G architecture should evolve to enable fast and efficient management of the network infrastructure [START_REF] Boudi | Ai-based resource management in beyond 5g cloud native environment[END_REF].

One of the key enablers for this evolution is the support of the heterogeneous cloud environment and the ability to orchestrate resources among multiple technical domains like RAN, edge cloud, central/core cloud, private and public cloud. All the capability coming from the hardware acceleration should be exposed to the services to enable more flexible function placement in order to address high performance.

Another key enabler will be the generalization of the servicebased architecture (SBA) [START_REF] Mayer | Restful apis for the 5g service based architecture[END_REF], which has been introduced in 5G networks mainly for the core network. This evolution will move to the edge and the RAN to enable the convergence of RAN and core networks. This allows a more flexible deployment of the network function and enhances their life cycle management.

The adoption of a cloud native [START_REF] Sharma | A cloud-native approach to 5g network slicing[END_REF] approach for the implementation and deployment of virtual network functions helps to achieve the required flexibility and autonomy. The use of containers enables to reduce the overhead and enhances the availability of the network services [START_REF] Taleb | On service resilience in cloud-native 5g mobile systems[END_REF]. Future networks must be able to support multiple applications with different quality of service requirements. Eventually, the VNFs that compose these services will share the same infrastructure and will enter in competition for resources if the demand is too high. This situation may be more frequent in environments with limited resources such as the Edge or the RAN [START_REF] Vo | Slicing the edge: Resource allocation for ran network slicing[END_REF]. However, finding the right configuration in terms of resource allocation for the deployed functions while taking into account the temporal variability of the demands remains a major challenge to reduce resource shortage risk and protect the most important VNFs.

Resource management in cloud environments has been well studied in the literature [START_REF] Weingärtner | Cloud resource management: A survey on forecasting and profiling models[END_REF]. However, most of the work already proposed study the virtual machines (VMs) as the basic and smallest entity to deploy and manage [START_REF] Canali | Scalable and automatic virtual machines placement based on behavioral similarities[END_REF]. To the best of our knowledge, only a few papers study the particularity of containers and native cloud environments, especially the associated emerging technologies like Docker [START_REF] Anderson | Docker [software engineering[END_REF] and Kubernetes [START_REF] Brewer | Kubernetes and the path to cloud native[END_REF]. It is important to note that there are many similarities between the classic cloud environment and the cloud native one, especially in the resource management and allocation problems. However, the new technologies offer more features to improve the robustness of the deployed services. The Kubernetes technology represents an essential tool for the management and orchestration of cloud infrastructures. This technology has shown great industrial maturity and is becoming the key player in native cloud environments. It offers several features for automatic management, scalability and availability of services.

The scope of this paper is to explore some of the Kubernetes features for resource scheduling to enhance the availability and the resilience of NFV networks. We focus on specific ones dealing with resource scheduling to enhance the failure risk for the deployed network services. Then, we propose a statistical method to compute the corresponding parameters for each CNF taking into consideration the future demands and the importance of the hosted network function.

The remainder of the paper is organized as follows. Section II overviews the state-of-the-art and the main technologies for cloud resource allocation and management. Section III describes the context of our contribution and the problem model formulation. Section IV presents our solution that we call the KRS module. Section V provides a description of the performance evaluation method and the obtained results. Finally, Section VI concludes the paper and outlines some perspectives for future developments.

II. BACKGROUND AND RELATED WORK

In [START_REF] Medel | Modelling performance & resource management in kubernetes[END_REF], the authors study the Kubernetes performances and propose a Petri Net model for pods and containers management. This model can help in the design of the applications and how the pods and containers should be deployed and structured. Authors in [START_REF] Santos | Towards networkaware resource provisioning in kubernetes for fog computing applications[END_REF] propose a network-aware approach for Fog Computing service scheduling. The main objective of the proposed algorithm is reducing the network latency by optimizing the containers' placement. Meanwhile, the proposed solution do not consider the memory and CPU usage and their corresponding features offered by Kubernetes. In [START_REF] Zhang | Research on kubernetes' resource scheduling scheme[END_REF], the authors study the Kubernetes scheduling module and propose an improved one by combining two optimization methods: the Ant colony algorithm and the swarm optimization algorithm. The main difference of the proposed solution compared to the exiting scheduler is that they consider the infrastructure resource cost and not only the load-balancing aspects. In [START_REF] Kaur | KEIDS: kubernetes-based energy and interference driven scheduler for industrial iot in edge-cloud ecosystem[END_REF], the authors propose the KEIDS Kubernetes controller for Edge environments and IoT applications. The particularity of their solution is that it takes into account the energy consumption optimization while considering other aspects such as the interference between the containers. The problem is formulated and solved as a multi-objective ILP. Paper [START_REF] Adhikari | Multi-objective accelerated particle swarm optimization with a container-based scheduling for internet-ofthings in cloud environment[END_REF] also focuses on resource planning in cloud native environments with the objective of minimizing energy consumption. The task is formulated as a multi objective optimization problem with two main goals: energy consumption and computing time. Paper [START_REF] Kim | On the resource management of kubernetes[END_REF] studies the CPU usage interference between co-located containers. The results show that the performance degradation can reach 50% with intensive demands. The authors highlight the need for an efficient method of resource scheduling inside the cluster, to avoid the interference without specifying a specific solution. The scope of our paper is precisely to investigate the features offered by Kubernetes for this purpose.

III. GENERAL CONTEXT AND PROBLEM FORMULATION

A. Kubernetes architecture

Cloud native and container technologies have significantly evolved, offering great opportunities for network operators to enhance their infrastructure management. The adoption of the cloud native approach in the implementation of VNFs enables building highly resilient and autonomous networks. Indeed, moving to cloud native network functions (CNFs) for NFV networks might make it easier to overcome multiple limitations of VNFs by transforming most network functions into scalable containers.

In this context, the Kubernetes ecosystem becomes an essential tool for the deployment and management of NFV infrastructures. The interest of this technology is mainly explained by its ability to manage dynamic, complex, and distributed infrastructures with great flexibility and agility. The first one is the cluster which gathers multiple physical or virtual machines representing the available resources in terms of memory and CPU. Each cluster has a master node responsible for the management and scheduling of these resources. The cluster is composed of multiple nodes, that can be either physical or virtual. These nodes host the pods, the most basic entity that can be created and controlled by Kubernetes. Each pod runs a single service instance (a VNF instance in our case), and it can be composed of one or several containers.

Node

B. Resource allocation and scheduling in Kubernetes

Kubernetes offers multiple tools for resource management shared by the deployed VNF instances. The network infrastructure can host heterogeneous services, allowing to take full advantage of the available resources and reduce consumption costs. On the other hand, sharing the infrastructure between heterogeneous services can reveal resource allocation problems, especially in case of a resource shortage. The allocation of cloud resources must be highly efficient. They must be neither under-utilized, as this means a loss of revenue, nor over-utilized, as this can lead to service failures or SLA degradation causing penalties.

Kubernetes offers some features for pods/containers resources scheduling which are mainly requests and limits. For each container, we can configure the requested memory or CPU which correspond to the guaranteed resources that will be reserved for it. Thus, the sum of the requested resources for the containers inside a node must be less than the total node capacity. Limits specify the maximum limit of resources that can be used by a container.

These parameters are very important for the CNF lifecycle management as they are taken into consideration in the priority and location of pods deployment by the scheduler and also in the allocation of resources inside a node, especially when it is overloaded. Let's take an example of a node that hosts pods and their memory consumption reaches its limit. The Kubernetes orchestrator has to select a pod to stop it. The pods that do not have a fixed request value will be the first to be stopped. Then, the orchestrator selects those that consume the most compared to the value of the requests.

Best Effort QoS Non-Guaranteed QoS Guaranteed QoS R L R R L L Fig. 2: Different CNF deployment configurations.
For instance, in Fig. 2 we represent three pods deployed on a single node. The first one is deployed with "best-effort" QoS, the requests and limits are not specified. The second is deployed with a "non-guaranteed" QoS, where the requests value is less than the limits. The third one has a "guaranteed" QoS since the requests value is equal to the limits. In this situation, if there is a lack of resources, the pods will be stopped in the given order, the first one, then the second one, and finally the third one, in order to liberate the required resources.

The objective of this work is to give a method to schedule the resources for the pods hosting the VNF instances, to limit the failures and the caused damage in the case of lack of resources. Our strategy aims to avoid the resource shortage in the first place. However, if it is unavoidable, the goal is to protect the most critical functions.

C. Problem formulation and notation

i : the i th node V i list of pods inside N i V i,j pod j on node N i M i memory capacity of N i C i CPU capacity of N i M r i,j request memory for pod V i,j M l i,j limit memory for pod V i,j M d i,j future demand memory for pod V i,j C r i,j request CPU for pod V i,j C l i,j limit CPU for pod V i,j C d i,j future demand CPU for pod V i,j b i,j
variable representing the stopped pods, 1 if it is stopped and 0 otherwise P i,j penalty for stopping pod V i,j

Tab. I summarizes the notation adopted in this paper. We consider a Kubernetes cluster hosting multiple VNF instances. N denotes the set of nodes composing it and N i refers to the ith node. Each node has a fixed memory and CPU capacities denoted by M i and C i respectively. The set of pods deployed on node N i is denoted by V i . For each pod j on a node N i , the values of request and limits are denoted by M r i,j and M l i,j respectively for the memory, C r i,j and C l i,j for the CPU. The resources that will be consumed by each pod vary over time and depend on the VNF that hosts them. Therefore, the future resource demand for each pod is considered as a random variable denoted by M d i,j and C d i,j for the memory and CPU respectively. The VNF instances have to support the traffic load, otherwise they will be stopped and this can introduce penalties according to their importance. We denote by P i,j the penalty introduced when stopping CNF V i,j . The objective of this work is to propose an algorithm that identifies the appropriate parameters of the requests and limits for each CNF, in order to reduce the expected penalty in a given period, where the profile of the future resource demand is known. This information is presented in the form of the probabilistic distribution of random variables M d and C d which can be obtained from the monitoring system.

When the demanded resources exceed the capacity of the node, the orchestrator selects the pod to stop according to the principle explained in Section III-B. Variable b i,j represents the state of the CNF. The selected ones should respect the condition described by (1):

M d i,j -M r i,j ≤ M d i,j -M r i,j , (1)
for i = 1, 2, . . . , N and for all j, j such that b i,j = 1 and b i,j = 0. The objective is to find the appropriate parameters M r , M l , C r and C l that minimize the expected penalties:

minimize E V i=1 Vi j=1 b i,j P i,j
subject to:

Vi j=1 max(M r i,j , M d i,j )b i,j ≤ M i , i = 1, . . . , N, Vi j=1 max(C r i,j , C d i,j )b i,j ≤ C i , i = 1, . . . , N.

IV. KRS MODULE PRESENTATION

This section presents the KRS algorithm for VNF resource scheduling. The randomness of the input data for the expected needed resource justifies the adoption of statistical approaches to model and solve this problem. The unknown variables are the requests and limits parameters for CPU and memory denoted by C r , C l , M r and M l . The limits values, C l and M l , can be easily determined for each CNF from its resource demand probabilistic distribution by choosing the maximum value. Meanwhile, finding the most suitable requests values is more challenging as they are the most important ones for resource allocation.

Our resolution method is a stochastic population-based algorithm. It is based on the random generation of multiple configurations of parameters (C r , M r ) and the selection of elements that do not exceed a penalty threshold. Then, these selected elements are crossed to generate a new improved population which allows reducing the expected penalties over the iterations. To simplify the notation, we denote by X the vector of the requests values for both memory and CPU instead of the pair (C r , M r ). In the optimization process, X is considered as a discrete random variable. We consider an upper bound B of the unknown parameters which correspond to the maximum capacities of the nodes and we assume that the set of possible values of the parameters is {0, ∆, 2∆, . . . , J∆ = B} for a chosen unit ∆. The smaller the value of ∆ the finer the granularity, and therefore the better the results. However, this will increase the computation time.

The probabilistic distribution of X is denoted by α, seen as an 2V × J matrix. This distribution will be used to explore the solution space of the searched parameters. Indeed, α is initialized by a uniform distribution to explore equitably all the solution space. The general idea of the algorithm is to find the best distribution α that minimizes the expected penalty. For that, we will fix a maximum value of penalty denoted by P max that we will try to minimize along the iterative process. The first step of the algorithm is to initialize P max by a large value and α by an uniform distribution. Then, we will try to find a new distribution whose generated population denoted X α has an expected penalty lower than P max . For this, we will generate a large number of vectors X α according to distribution α. Then, knowing the distribution of the future demand of resources C and M, we compute the penalty expectation for each configuration x in X α . Afterwards, the elements that have a value lower than P max are selected to compute a new improved distribution.

To ensure the diversity of the new population, the percentage of selected elements must be greater than a minimum threshold noted D. Otherwise, the algorithm can converge quickly to a local optimum. The probability of observing value j on link , α( , j), is computed by dividing the number of samples where link takes value j∆ by the total number of selected samples |X selected | as described in [START_REF] David | 6g vision and requirements: Is there any need for beyond 5g?[END_REF].

α( , j) = |x ∈ X selected , x[ ] = j∆| |X selected | . ( 2
)
This process is repeated until the convergence of α or until reaching a maximum value of iterations.

The second step is to adjust P max depending on the outcome of the first step. If α converges, P max is reduced and the process restarts to try a more accurate target. If not, the procedure is repeated with a larger P max . To reduce P max , it is multiplied by an adaptation factor β, with values between 0 and 1. This factor is set at the initialization step before the execution of the procedure. The previous value of P max is stored in a new variable P max at each adaptation. If α does not converge at the first step, P max is reinitialized with P max . Afterwards, β is increased using (3):

β = 1 + β 2 . (3)
The two steps are reiterated until P max converges (i.e. until β becomes very close to 1). This process is globally described in Algorithm 1.

Note that our optimization approach is inspired by another algorithm called the Evolutionary Sampling Algorithm (ESA) [START_REF] Rahali | Unicast inference of additive metrics in general network topologies[END_REF] proposed for the inference of monitoring metrics. However, the principle remains adaptable to other optimization problems such as the one treated in this paper. Generate n random samples of solutions according to distribution α.

7:

Select the ones that respect E penalty (X) < P max ; put them in set X selected . Compute the new α (α iter ) from the selected samples: In this section we evaluate the performances of our KRS module compared to the Kubernetes best effort mode where the resource scheduling parameters are not configured on the CNF. For this evaluation, we use simulation as follows. At the beginning, for a given cluster with a known number of nodes, we generate randomly the memory and CPU capacity values for these nodes. Then, on each node, we vary the number of CNF deployed between 10 and 20. For each CNF, the future demand of resource is considered as a random variable (C d , M d ) following a Poisson distribution. The parameters of this distribution are randomly generated. The penalty for stopping the CNF is randomly generated and takes normalized values between 0 and 1. Then, the KRS algorithm is performed to find the correct CNF configuration. The outcome of this algorithm will be the α distribution which often converges to an exact value. Finally, the penality expectation for the obtained configuration is calculated and compared to the one given by the Kubernetes best effort mode. 3 illustrates the performance of the two approaches, namely the KRS module and the best effort mode. The number of nodes in the cluster varies between 2 and 10. For each configuration we make 50 different tests with different input data and then make the average of the results (the penalty and the computing time) . The tests show that our solution always performs better than best effort mode. For example, for tests done with 6 nodes in the cluster, the penalty expectation for the best effort mode is more than 6 while it is less than 3 with the KRS module. This result is expected since the best effort mode does not differentiate between the deployed functions and they are treated equally in the resource allocation. Concerning the computing complexity, Fig. 4 shows the required time to compute these parameters. We can see that it evolves linearly with the number of nodes. This is because the algorithm processes each node independently of the others, and it can lead to miss the optimal decisions globally, but it ensures the horizontal scalability of the solution. Meanwhile, regarding the vertical scalability of the algorithm, i.e. when we have a large number of CNFs on the same node, the computation time increases significantly. This remains a point to improve in our approach.

Another important parameter in this optimization process is the number of generated samples X rand to explore the solution space. This variable belongs to the algorithm parameters that should be fine-tuned to get good results and avoid the convergence to local optima. Fig. 5 and Fig. 6 depicts the evolution of the accuracy and the computing time according to the generated samples X rand . The results show that increasing the number of generated samples enhances the accuracy until reaching the best performance when the solution space is well explored. From this point on, increasing this value will only increase the computing time. Thus, a tradeoff must always be found to achieve the best performance with the least processing effort.

VI. CONCLUSIONS

In this paper, we study the resource scheduling problem, mainly concerning memory and CPU, in a cloud native environment. We particularly focus on the Kubernetes technology and its main features for resource scheduling. The proposed algorithm, called KRS, enables efficient provisioning for memory and CPU to avoid resource shortage, especially for the most critical CNFs. The KRS module considers the consumption profile of each CNF and allocates the appropriate resource with a trade-off between efficiency and risk. The optimization process is based on a statistical method that applies the principles of genetic algorithms. The results comparing our approach with the Kubernetes best effort mode show an interesting gain.

The utility of our algorithm appears in the post deployment phase of the CNFs to improve their coexistence in the same node and reduce the interference effects. However, Kuberentes offers various other parameters for the customization of the deployment phase. To optimize the overall resilience of network services, it is necessary to think about it in all stages of the service lifecycle from the design, the deployment, the operation phase, and finally, the shutdown. All these steps require specific supplementary in-depth studies.

Fig. 1 :

 1 Fig. 1: Kubernetes cluster components

Algorithm 1

 1 Kubernetes Resource Scheduler (KRS) INPUT: C d , M d , M, C OUTPUT: α 1: Initialize α (α 0 ), P max and β 2: iter = 0 iteration index 3: -Step 1: 4: while iter ≤ itermax do

8 :

 8 If |X selected |/|X rand | < D, repeat Step 1.

10 :

 10 α iter ( , j) = |x∈X selected , x[ ]=j| |X selected | 11: if α iter ≈ α iter-1 then

Fig. 3 :Fig. 4 :

 34 Fig. 3: Comparing the accumulated penalty for KRS and the best effort Kubernetes mode for different node number in the cluster

Fig. 5 :Fig. 6 :

 56 Fig. 5: Evaluating the KRS algorithm accuracy for different values of |X rand |

TABLE I :

 I List of main used variables

	variable	description
	N	set of nodes composing the cluster; N

ACKNOWLEDGEMENTS

This work has been partially supported by the European Union's H2020 MonB5G (grant no. 871780) project.


Le grand chaudron du PLFSS

Frédéric Pierru (CNRS-CERAPS)

Paru dans Les Tribunes de la santé, n° 70, 2021, p. 1 -16 Les PLFSS, très décriés lors de leur naissance dans le sillage du Plan Juppé, se sont progressivement inscrits dans la vie publique française. Ils ont contribué au fil du temps à structurer un débat public quasi-permanent sur l'état des finances de la Sécurité sociale. Monopoles d'une communauté de politique publique en période routinière, ils deviennent de plus en plus l'enjeu de débats politiques élargis lors des périodes pré-électorales. Les spécialistes sont alors dépossédés au profit des généralistes. Cependant, à la faveur de l'inscription de l'enjeu des dettes souveraines sur l'agenda politique au mitan des années 2000, les acteurs budgétaires n'ont cessé de gagner de l'influence aux dépens des acteurs « sociaux ». La crise des dettes souveraines a donc accéléré, à compter du début des années 2010, le processus d'européanisation des finances sociales. Elle a relancé le débat sur la fusion des PLFSS et des PLF. Si cette fusion est encore repoussée, c'est moins pour des questions techniques que pour des finalités politiques : isoler les comptes de la « Sécu » permet de mener une « pédagogie des réformes » visant à stabiliser la part des dépenses sociales dans la richesse nationale.

Lorsque le « Plan Juppé » initie les Projets de loi de financement de la Sécurité sociale (PLFSS) en 1996, la levée de bouclier syndical est immédiate. Certes, cette innovation institutionnelle majeure qui refonde la « gouvernance » de la Sécurité sociale au profit du Parlement n'est pas la seule raison qui va déboucher sur le plus important mouvement social depuis l'après-guerre. La réforme des régimes spéciaux de retraite est un véritable casus belli. Néanmoins, on se souvient de Marc Blondel, alors secrétaire général de Force Ouvrière, confédération gérant avec le patronat la Sécurité sociale, dénoncer ni plus ni moins qu'un « hold-up ».

Vingt-trois années après le premier exercice du genre, les PLFSS sont désormais bien installés dans la vie publique et politique française. Il n'y a plus guère de voix pour réclamer leur suppression et un retour au « paritarisme ». Mieux : les PLFSS ont permis de structurer un débat public annuel sur la situation financière de la « Sécu », et pas seulement au moment de son examen parlementaire à la fin novembre. Nombre de rapports publics, de la Commission des comptes de la Sécurité sociale à la Cour des comptes (CCSS) en passant par le Haut Conseil de l'Assurance Maladie (HCAAM), rythment leur élaboration. Ces rapports sont souvent relayés dans la presse et donnent lieu à des prises de position de la part des principales forces politiques.

Point d'orgue de la dynamique de construction des finances de la Sécurité sociale en problème public, la création des PLFSS est allée de pair avec la structuration de ce que les sociologues de Chicago ont appelé une « communauté d'opérateurs » transversale aux différents univers sociaux 1 : cabinets des ministres des affaires sociales et des comptes publics, Direction de la Sécurité Sociale (DSS), Direction du Budget (DB), caisses, partenaires sociaux, CCSS, Cour des comptes, HCAAM, Comité d'alerte, Commissions des affaires sociales des assemblées, parlementaires et leurs administrateurs, journalistes spécialisés, et, bien entendu, les nombreux groupes d'intérêt du secteur. L'élaboration et la discussion d'un PLFSS entremêlent tous ces acteurs à des titres, des moments et des degrés divers. L'on aurait tort de se contenter du bel ordonnancement de la Constitution : la technostructure prépare, le politique arbitre, le Parlement discute et vote, l'administration exécute. Ici, comme ailleurs, la vision linéaire et balistique de l'action publique ne résiste pas à l'enquête sociologique. Un PLFSS est le résultat d'un travail éminemment collectif qui se joue des frontières institutionnelles, fait de consultations, d'auditions, de pressions de l'amont (la préparation) vers l'aval (le vote puis l'évaluation). A cet égard, le PLFSS joue le rôle d'instrument de coordination sociale et « cognitive » de cette multitude d'acteurs héritière de la complexité institutionnelle de notre système de protection sociale et, pour ce qui nous concerne, de notre système de santé.

Pour autant, nous verrons dans un second temps, que le centre de gravité de cette « communauté d'opérateurs » a bougé depuis le milieu des années 20002 . Avec l'entrée de la question de la dette publique dans le débat politique, puis celle de la « crise des dettes souveraine », les acteurs budgétaires, nationaux et européens (Commission européenne, Ministère des comptes publics, direction du Budget), ont progressivement renforcé leur position. Au point que certains plaident désormais pour la fusion du PLFSS et du PLF dans le cadre d'une vision « intégrée » des finances publiques, obligeant les acteurs plus « sociaux » (DSS en tête) à défendre le PLFSS et ses innovations induites (consolidation et certification des comptes des caisses, conventions d'objectifs et de gestion, etc.).

I.

Quand les finances sociales deviennent un problème public La pertinence de la métaphore de la « communauté » n'apparait jamais aussi clairement que lorsque se profilent les élections présidentielles et législatives. Les spécialistes des finances sociales perdent alors la main au profit des acteurs généralistes, dont, au premier chef, les candidats pressentis et leurs porte-parole mais pas uniquement : dans le champ journalistique par exemple, les rubricards spécialisés sont dépossédés du sujet par leur rédaction en chef qui les presse de faire ressortir la dimension politique -sinon politicienne -du sujet… A « l'interdépendance restreinte et routinière » succède une « interdépendance tactique élargie » 12 qui présente au moins quatre caractéristiques : l'accélération du temps (l'urgence permanente de toute campagne électorale) ; le « désenclavement des sites de confrontation » ou, dit autrement, l'interdépendance accrue des différents univers sociaux ; la prégnance de la prudence comme règle pragmatique afin d'éviter toute faute irréversible (comme F. Fillon en 2016) ; enfin, et surtout, des phénomènes de stylisation, de généralisation et de dramatisation des enjeux inscrits sur l'agenda électoral. Dans cette configuration, il n'est pas étonnant que le taux de progression de l'ONDAM des années à venir soit revu à la hausse, même si c'est pour ensuite décevoir une fois arrivés au pouvoir, comme lors du quinquennat de François Hollande, ou que soit annoncé « la fin du tout T2A ». Les spécialistes des finances sociales, quels qu'ils soient, sont alors prompts à dénoncer la « démagogie », le tropisme « politicien » (voire « populiste » 13 ), « l'irréalisme » des propositions des candidats, au point que, faisant fi des affiliations partisanes, ils peuvent rédiger des tribunes ensemble, liés par une solidarité que l'on dirait volontiers de corps.

II.

De la sémantique politique à « l'ordre de la dette » : l'irruption des acteurs européens

On l'a dit, les PLFSS ont consacré la structuration d'une communauté d'acteurs mobilisés autour de la dimension financière de la « Sécu » de même qu'ils ont contribué à la formalisation d'un champ inédit, sui generis, des finances publiques, les finances dites « sociales » : cellesci, particulièrement en matière d'assurance maladie, se distingueraient des autres composantes des finances publiques par la nature de la dépense autant que la nature des recettes. Dans l'assurance-maladie, en effet, la dépense ne peut être bouclée macro-économiquement puisqu'elle est le résultat de milliers de décisions -celles des patients et des professionnels de santé -décentralisées. Il serait impensable d'arrêter de soigner parce que l'ONDAM serait dépassé. De plus, les recettes de la sécurité sociales sont affectées, alors que celles de l'État ne le sont que très rarement. Sans pouvoir détailler plus avant, cette communauté d'acteurs a beau jeu de mettre en évidence la modestie des déficits de la Sécurité sociale au regard de l'ampleur de ceux de l'État afin de mieux vanter les mérites des instruments qu'ils ont inventés pour « piloter » les dépenses sociales.

Jusque 2010, l'ONDAM voté dans le PLFSS était essentiellement un instrument de « sémantique politique », destiné à afficher le volontarisme des pouvoirs publics en matière de maîtrise des dépenses de santé et, de façon plus ou moins contradictoire, à réduire des déficits publics à l'intention des instances européennes. En 2010, un ancien directeur de la Sécurité sociale attirait notre attention sur la dimension éminemment politique de l'ONDAM voté :

  Cependant, il ignore l'ampleur du travail que certains « Esprits d'État » 4 ont déployé, dès la fin des années 1960, pour intéresser et enrôler dans la problématique financière des acteurs d'autres champs sociaux(syndical, politique, journalistique, etc.). Rien ne serait plus faux de n'y voir qu'une affaire de la « propagande », comme certains contempteurs du « Trou de la sécu » ont tendance à le faire. Certes, l'État et sa noblesse disposent du monopole de la violence physique et symbolique, écrivait Pierre Bourdieu. Mais, en réalité, l'on a affaire à une « orchestration sans chef d'orchestre » reposant sur des phénomènes complexes d'affinités d'habitus (de dispositions) et de « transactions collusives » (i.e. de reconnaissance croisée) entre champs sociaux. Par exemple, la montée en puissance de la problématique financière dans l'État a débouché sur le remaniement de l'espace des journalistes spécialisés (les « rubricards ») sur le sujet. Les journalistes les plus « sociaux », souvent issus du militantisme syndical et politique, ont été peu à peu remplacés par une nouvelle génération davantage portée sur la vision économique du monde de la sécurité sociale et, plus généralement, sensible aux discours « experts » 5 . Il en est de même pour le journalisme en santé 6 . La création des PLFSS est donc venue consacrer cette communauté d'opérateurs mobilisés autour des finances de la Sécurité sociale et dont la direction du même nom -la direction de la Sécurité sociale -est le centre de gravité : les membres éminents de « l'élite du Welfare » 7 , inspirateurs du Plan Juppé, y sont passés à un moment ou un autre de leur carrière. C'est donc fort logiquement que la DSS -la direction historique de Pierre Laroque -a été chargée de préparer les PLFSS. Cette préparation démarre en avril et va durer à peu près quatre mois. Elle va être scandée par plusieurs rapports ou avis : avis du comité d'alerte au printemps, premiers rapports de la CCSS et de la Cour des Comptes à la mi-juin, second rapport de ces deux instances en septembre (et, en sus, en juillet, le rapport « produits et charges » de la CNAM).Le contenu des avis et rapports dessine à hauteur de 80% le contenu du PLFSS à venir. Après avoir rédigé une esquisse générale au printemps, la DSS envoie à la mi-juin aux cabinets des ministres de tutelle un dossier volumineux comprenant un ensemble de mesures. C'est le point de départ de consultations, aux niveaux politique et technocratique, avec les caisses (qui font des contre-propositions éventuellement) et les très nombreux groupes d'intérêt du secteur : syndicats, fédérations, industrie. Selon les années, la tonique du PLFSS, structuré autour de quatre ou cinq mesures phare, va se déplacer : retraites, allocations familiales ou santé. Les derniers arbitrages ont lieu en juillet et les rapporteurs et les présidents des commissions des affaires sociales y sont associés dès la mi-septembre dans la perspective de l'examen parlementaire fin novembre. Il faut rappeler que les parlementaires les plus spécialisés ont déjà été associés via diverses instances comme la CCSS ou le HCAAM 8 . En effet, l'une des conséquences les plus notables de l'innovation des PLFSS a été d'inciter des députés et des sénateurs à se spécialiser, au sein des commissions des affaires sociales, dans le sujet des « finances sociales ». De fait, un petit groupe de députés et sénateurs, flanqués de leurs administrateurs, exerce un quasi-monopole sur cette matière.Dans tous les cas, c'est un patient « travail de Pénélope » qui préside aux PLFSS dont ressort un équilibre à la fois financier et politique qu'il sera difficile de remettre en cause par la suite, provoquant parfois l'irritation des parlementaires : le politiste Alexandre Siné a appelé la « grande pétrification » 9 se traduit par la perte de marges de manoeuvre des pouvoirs publics, la grande majorité des dépenses provenant de reconduction de politiques antérieures et le service de la dette prenant une place de plus en plus significative dans les finances publiques. C'est l'image du cargo chère aux chercheurs en sciences sociales qui ont analysé les phénomènes de « dépendance au chemin parcouru » (path dependence) : sa force d'inertie empêche toute réorientation substantielle de sa trajectoire. Les contraintes politiques, enfin, ne sont pas moins vectrices d'inertie : on l'a écrit dans cette revue, l'arène des politiques publiques de protection maladie et de santé est structurée par des rapports de force et de sens très résilients. Les médecins dits « libéraux » 10 , l'élite hospitalière ou l'industrie des complémentaires santé exercent un véritable pouvoir de véto sur les initiatives des pouvoirs publics.Au final, le grand mérite des PLFSS est d'avoir contribué à mettre en débat public la question des finances sociales en structurant ce que les politistes appellent une « communauté de politique publique » qui transcende les frontières des univers sociaux : ces acteurs (hautsfonctionnaires, parlementaires, syndicats, organisations professionnelles, journalistes, etc.), bien qu'insérés dans des jeux relativement autonomes, communiquent sans cesse entre eux et, partant, se socialisent réciproquement dans un jeu d'interconnaissance et d'interreconnaissance sans fin 11 . Les consultations officielles et officieuses sont permanentes, tout comme les auditions. De même, chaque type d'acteurs anticipe les attentes d'un ou plusieurs autres. Ainsi, par exemple, la Cour des comptes présente et met de plus en plus en scène ses rapports pour leur assurer une médiatisation et, partant, acquérir plus de poids dans le résultat final. Ils deviennent ainsi des « marronniers » pour le travail des journalistes, tout comme le sont les rapports de la CCSS. La Cour des comptes a parfois suggéré aux parlementaires des amendements… Tous ces acteurs finissent par partager les mêmes catégories, un même langage, une même vision -financière -du problème que pose(rait) la « Sécu » et, finalement, la même conception de la nature des solutions, techniques et « expertes », à y apporter. C'est en ce sens que l'on peut parler de « communauté » dont les membres sont constamment associés, au grand dam de

	jusqu'en 1997,
	les parlementaires n'avaient que peu d'occasions de se prononcer sur le sujet, l'essentiel des
	prérogatives relevant des « partenaires sociaux » et de l'Exécutif, dans une confusion propice
	aux accusations croisées (par exemple, le débat rémanent autour des « charges indues »). De
	même, les lois portant « diverses mesures d'ordre social » (DMOS), véritables lois fourre-tout,
	ne pouvaient structurer une délibération parlementaire informée. La création, en 1979, de la
	Commission des comptes de la sécurité sociale a été un premier moment de rééquilibrage entre
	« démocratie sociale » et démocratie politique puisque 8 parlementaires (4 députés et 4
	sénateurs) y siègent. Jean Marmot, secrétaire général de la CCSS, parlera même « d'os à
	ronger » donné aux parlementaires en attendant une réforme plus ambitieuse qui permettrait de
	clarifier les prérogatives respectives des partenaires sociaux, de l'Exécutif et du Parlement.
	A partir de la fin des années 1970 donc, émergent dans les différents champs -politique,
	technocratique, journalistique -des positions professionnelles qui ont pour point commun de
	porter le problème public du « trou de la Sécu » 3 . Elles assurent l'ubiquité et, partant, la
	naturalisation du problème : pour le citoyen « ordinaire », si des journalistes, des hommes
	politiques, des hauts fonctionnaires, des représentants du patronat et des syndicats évoquent à
	l'unisson l'urgence de combler le trou de la Sécu, c'est bien que ce dernier est un problème
	aussi objectif qu'incontestable. Le fonctionnement en écho produit la force de l'évidence.

L'innovation institutionnelle majeure qu'ont constitué les PLFSS est l'aboutissement d'une réflexion au long cours aux sommets de l'État et de la volonté du Parlement d'être plus impliqué dans la gestion de masses financières supérieures au budget de l'État. En effet, En résumé, la montée en puissance d'un problème public, ici celui des « déficits » ou du « trou » de la Sécu, est indissociable de celle de la communauté transversale d'opérateurs qui le porte et en (re-)produit l'actualité. Le « trou de la Sécu » est, par conséquent, indistinctement comptable, idéel et social.

Il faut cependant préciser que dire cela ne revient en aucune façon à ratifier une lecture hyperconstructiviste qui retirerait à la question des finances de la Sécurité sociale tout bien-fondé. Il ne fait aucun doute que les dimensions économiques et financières de la Sécurité sociale doivent être considérées avec rigueur et intérêt. Néanmoins, identifier, comme c'est généralement le cas dans le débat public, la Sécurité sociale à son « déficit » est une regrettable mutilation du sujet. La Sécurité sociale est d'abord l'instrument de la solidarité sociale au sens le plus rigoureux et sociologique du terme, celui des penseurs et savants -dont le fondateur de la sociologie en France, Émile Durkheim -appartenant au mouvement solidariste de la fin du XIXème et du début du XXème siècle. Ainsi, l'assurance-maladie organise une double solidarité : entre malades et bien-portants, entre riches et pauvres. Elle a contribué de façon décisive à l'amélioration de l'état de santé de la population française à compter de la fin des années 1930. Ces remarques ne sont pas seulement philosophiques car, comme nous allons le voir, l'opposition entre une vision strictement budgétaire et financière d'un côté et une vision qui, bien qu'intégrant l'enjeu financier, intègre la portée solidaire et sanitaire de la « Sécu » continue à structurer les luttes aux sommets de l'État.

« Ce sont des équilibres sociaux, qui sont négociés en amont. Quand ça arrive au Parlement, si on touche un truc, ça déséquilibre tout. Donc c'est très frustrant pour les parlementaires. Le Parlement est largement prisonnier de l'accord social. Quand on fait une grande conférence sur la famille, pour déterminer quelle prestation on avance ou pas, il y a très peu de grain à moudre à l'Assemblée Nationale. Si on a distribué 300 millions dans la conférence, il en reste 50 pour les parlementaires pour faire un petit chouilla en plus, mais c'est peu de choses car ça s'est négocié avant. La santé c'est encore pire. Non seulement on a négocié des tas de trucs en amont avec les médecins, les hospitaliers, avec la FHF, c'est le boulot du gouvernement mais en plus on sait que ça ne sera pas appliqué derrière, ou de façon imprévue parce que ça va dépendre des innombrables partenaires qui vont faire ce qu'ils veulent. Les équilibres négociés sont assez rigides et durs à remettre en cause sauf à tout bouleverser. Les limites sont donc assez fortes. C'est forcément très frustrant, même pour ceux qui mènent les débats pour les ministres. » [un ancien directeur de cabinet] C'est qu'en effet, l'élaboration d'un PLFSS est un exercice soumis à de fortes contraintes. Des contraintes institutionnelles d'abord : article 40 de la Constitution, censure par le Conseil Constitutionnel des « cavaliers sociaux », c'est-à-dire des mesures n'ayant aucun impact financier, etc. Mais il s'agit aussi, et peut-être surtout, de contraintes financières : ce que l'ordonnancement rationnel des séquences de l'action publique (identification du problème, élaboration des solution, décision, vote, mise en oeuvre, évaluation…), à l'élaboration des PLFSS à venir. Cette communauté peut être comparée à une sorte de chaudron en ébullition permanente d'où sortira le prochain PLFSS.

  Or au mitan des années 2000, la donne commence à changer, comme la mention du « comité d'alerte », mis en place par la réforme de l'assurance maladie en 2004, le suggère. Le « rapport Briet » de 2010, une fois refermée la parenthèse keynésienne post-krach 2008, atteste de la volonté des pouvoirs publics de « tenir » l'ONDAM. D'indicatif et de politique, l'ONDAM devient impératif. La dette entre alors dans le débat public et, avec elle, le thème du sacrifice des « générations futures » par un État social jugé obèse. Les retraites et la santé, les deux principaux postes de la protection sociale, ont été pointées du doigt : « les données brutes de la dette, analyse Benjamin Lemoine, sont dorénavant sous les feux de la rampe, portées par la publication des mesures européennes. Les passifs de l'État vont jouer un rôle croissant dans l'organisation de la vie politique et ce à mesure que le périmètre sur lequel porte leur exploration s'étend. Les « engagements implicites » -qu'on appelle aussi la dette « hors bilan » ou la « dette future » de l'État -émergent des controverses sur la réforme des normes comptables. » 14 La crise des dettes souveraines précipite un double mouvement de budgétisation et d'européanisation des PLFSS. Budgétisation : il n'est plus question de dépasser l'ONDAM voté en raison de l'engagement auprès de nos partenaires européens. Et, de fait, jusque 2020, il ne le sera plus grâce d'abord à la baisse, entre 2007 -2012, du taux de couverture des dépenses de santé par la Sécurité sociale puis par une action résolue sur les prix du médicament et les tarifs de la T2A. Européanisation : la surveillance multilatérale des finances publiques des États membres de la zone euro se renforce considérablement, avec le « two-pack » et le « six-pack » en 2011-2012 puis, surtout l'adoption du TSCG et de la « règle d'or ». Sous la férule allemande, il n'est plus question de laisser-aller en matière de finances publiques… donc sociales. Alors que l'Union Européenne n'a pas de compétence en matière sanitaire et sociale, l'européanisation de ces politiques fait un bond à la faveur de la rigueur budgétaire 15 . L'européanisation fait référence « aux processus de construction, de diffusion et d'institutionnalisation de règles formelles et informelles, de procédures, de paradigmes de politiques publiques, de styles, de « façons de faire » de croyances partagées et de normes qui sont dans un premier temps définis au niveau européen, puis incorporés dans la logique des discours, des identités, des structures politiques et des politiques publiques au niveau national/infranational » 16 . Les politiques de finances publiques, donc sociales, ont donc connu un saut d'intégration dans ce contexte, la commission européenne ayant centralisé le pouvoir afin de « prévenir les déficits excessifs ».A la faveur des politiques « d'assainissement des finances publiques » post-krach 2008, les acteurs budgétaires, tant au niveau national qu'au niveau européen, renforcent leurs positions dans la communauté de politique publique structurée autour des finances sociales 17 . Les « sociaux », qui défendent l'autonomie du PLFSS, sont sur la défensive. La surveillance multilatérale des finances des États membres renforce le prisme comparatif qui construit comme des « anomalies » les idiosyncrasies nationales. Le PLFSS et les finances sociales résultent d'un compromis national lié à la trajectoire historique de la Sécurité sociale nationale. Mais considérés depuis l'étranger, il s'agit seulement d'un « morcellement » et d'une « fragmentation » préjudiciables à une vision intégrée des finances publiques. C'est le sens du rapport commandé à l'OCDE par le Ministère des finances, rendu public en 2018, de celui d'Olivier Véran, publié cette même année ou, très récemment, en 2020, du rapport de la Cour des comptes.En 2010, nous interrogions le sous-directeur aux comptes sociaux de la prestigieuse direction du Budget, à propos de la fusion PLF/PLFSS : « Est-ce qu'on traite correctement les relations entre l'État et Sécu, est-ce que les objectifs sont bien articulés les uns avec les autres ? Ou est-ce qu'on raconte n'importe quoi ? La réponse est non et ça a été une exigence forte du Parlement ; donc on a deux textes qui sont parfaitement coordonnés. […] Elles sont séparées parce qu'on a des politiques de finances publiques qui sont séparées. Il y a une vraie différence. On considère que du côté de l'État, les déficits doivent être certes maîtrisés mais on n'a pas un impératif de retour à l'équilibre aussi impérieux que du côté de la Sécurité Sociale. Donc si on devait fusionner les deux, je ne pense pas qu'on y gagnerait en termes de finances publiques. Et le caractère

	« C'est un signal envoyé aux acteurs sachant que si on affiche 3%, le lendemain, le médecin qui exerce
	à Bar-le-Duc ne va pas changer de comportement. Cet affichage-là, ça lui passe complètement au-
	dessus de la tête. Mais on pensait que ce signal produirait des effets. Maintenant avec le comité d'alerte,
	la contrainte se matérialise… Ce volontarisme avait un autre destinataire, c'était Bruxelles. Si
	Matignon arbitrait dans le sens du Budget, ça n'était pas qu'il croyait que… Je ne suis même pas sûr
	que le Budget croie que le fait de fixer l'ONDAM à 3% va permettre de le réaliser, mais c'est un
	affichage vers Bruxelles. Sur le budget de l'État, on ne peut pas trop faire de l'affichage parce que ce
	qu'il y a des conséquences immédiates et c'est beaucoup plus suivi. Il n'y a qu'un domaine où on pouvait
	se dire : je mets deux et demi et si c'est cinq pour cent de toute façon ça ne craindra rien. »

Nous actualisons ici l'article, (beaucoup) plus développé mais ancien : Frédéric Pierru, « Budgétiser l'assurancemaladie », dans Philippe Bezès, Alexandre Siné (dir.), Gouverner (par) les finances publiques, Paris, Les Presses de Sciences Po, 2011.

3 Julien Duval, Le mythe du « trou de la Sécurité sociale », Raisons d'Agir, 2020'Agir, (2007)).

Pierre Bourdieu, La Noblesse d'État, Paris, Minuit, 1989.

Sandrine Lévêque, Les journalistes sociaux. Histoire et sociologie d'une spécialité journalistiques, Rennes, PUR, 2000.

Dominique Marchetti, Quand la santé devient médiatique, Grenoble, PUG, 2010.

William Genieys, L'élite des politiques de l'État, Paris, Presses de SciencesPo, 2008.

Le HCAAM revêt une fonction plus prospective et stratégique/politique -établir un « diagnostic partagé » entre tous les protagonistes du système de santé -que celle de la CCSS.

Alexandre Siné, L'ordre budgétaire,Paris, Economica, 2006.

Frédéric Pierru, « Les conséquences électorales des conflits de la santé : mythe ou réalité ? », Les Tribunes de la santé, n° 46, 2015.

Ainsi, un rapporteur du PLFSS reconnu pour son expertise a de bons espoirs de devenir un jour ministre.

Frédéric Sawicki, « Les questions de protection sociale dans la campagne présidentielle de 1988. Contribution à l'étude de la formation de l'agenda électoral », Revue française de science politique, 41(2), 1991.

Le mot de « populisme » étant l'injure suprême, puisqu'il suggère l'adjectif de « populaire » (charge négative que, curieusement, ne comporte pas le mot d'« élitisme »…).

La crise sanitaire de Covid-19 a précipité l'européanisation de la politique des prix du médicament jusqu'alors du seul ressort des États membres.

Claudio M. Radaelli, « Européanisation », dans Laurie Boussaguet et al. (dir.), Dictionnaire des politiques publiques, Paris, Les Presses de Sciences Po, 2019, p. 239 -240.

Benjamin Lemoine, « Quantifier et mettre en crise les dettes souveraines », Politique européenne, n°44, 2012 ; Philippe Bezès, Patrick Le Lidec, « La politique d'ajustement budgétaire en France (2007 -2012). Institutions et évitement du blâme », Revue internationale des sciences administratives, 81(3), 2015.

Dominique Libault, « Une gouvernance adaptée aux nouveaux enjeux ? », Regards, n° 52, 2017.


Aurélien Sibellas
email: aurelien.sibellas@insa-lyon.fr

Morgan Rusinowicz
email: morgan.rusinowicz@insa-lyon.fr

Jérôme Adrien
email: jerome.adrien@insa-lyon.fr

Damien Durville
email: damien.durville@centralesupelec.fr

Eric Maire
email: eric.maire@insa-lyon.fr

The Importance of a Variable Fibre Packing Density in Modelling the Tensile Behaviour of Single Filament Yarns

Keywords: A. Yarn, B. Directional orientation, B. Mechanical Properties, C. Analytical modelling, X-ray microcomputed tomography

A model able to reproduce the tensile response of single continuous-filament yarns based on parameters derived from geometrical descriptors is presented in this paper. Samples of yarns made of polyester and aramid fibres were scanned at rest using X-ray microtomography, allowing a detailed identification of their fibre orientation distributions for different twists. The variation of the fibre packing density along with yarn extension was characterized by means of additional scans carried out during tensile tests. An analytical model of the tensile response of these yarns, based on the orientation distribution function and the evolution of the packing density identified from microtomography is proposed and validated against experimental results, with good agreements.

Introduction

Continuous polymer fibres can be twisted together to make filament yarns providing a good flexural and torsional flexibility for a high strength in the longitudinal direction. Such yarns are widely used every day in the industry and in domestic life, in the form of ropes, cables, fabrics and reinforcement in composite materials. The initial nonlinear mechanical behaviour of these fibre assemblies is highly dependent on their arrangement. Mechanics of twisted continuous-filament yarns made of textile fibres have been studied extensively in the last century [START_REF] Hearle | Structural Mechanics of Fibers, Yarns and Fabrics[END_REF][START_REF] Treloar | A theory of the stress-strain properties of continuous-filament yarns[END_REF][START_REF] Huang | Theory of Extension of Elastic Continuous Filament Yarns[END_REF][START_REF] Hearle | Mechanics of dense fiber assemblies[END_REF][START_REF] Komori | Mechanics of Large Deformation of Twisted-Filament Yarns[END_REF] but most of the classic models remain not easily applicable in an industrial context. Nevertheless, some authors have succeeded in constructing an energy-based theory [START_REF] Treloar | A theory of the stress-strain properties of continuous-filament yarns[END_REF] simplifying calculations of the yarn mechanical properties.

The corresponding model was finally expressed in the framework of the Principle of Virtual Work by Leech [START_REF] Leech | The modelling and analysis of the mechanics of ropes[END_REF].

Improvements of these theories over the years allowed complex geometries of fibre paths to be taken into account in the form of orientation density functions [START_REF] Hearle | On The Extended Theory of Mechanics of Twisted Yarns[END_REF][START_REF] Komori | Mechanics of Large Deformation of Twisted-Filament Yarns[END_REF][START_REF] Jeon | A New Orientation Density Function of Ideally Migrating Fibers to Predict Yarn Mechanical Behavior[END_REF][START_REF] Jeon | Orientation Density Function of Ply yarn[END_REF]. Hence, ideal and irregular structures can be represented by their distribution of fibre orientations which are used as input data for a mechanical model. In a previous paper [START_REF] Sibellas | Experimental study of the fiber orientations in single and multi-ply continuous filament yarns[END_REF], fibre trajectories in twisted yarns were investigated with a new method using X-ray microtomography. Fibre paths were determined using image processing techniques which led to a complete numerical reconstruction of the yarn studied.

The orientation distributions were calculated for single-ply and multi-ply yarns with different torsions and compared to models of orientation density function from the literature.

The aim of this paper is to show the impact of considering the experimental orientation density functions (ODF) on the tensile behaviour of single and multi-ply yarns as input data for an analytical model. The considered model is based on a hypothesis relating the deformation of oriented fibre segments to the yarn extension. Different relationships were proposed in the literature either giving a specific deformation to the segment as a function of its orientation angle [START_REF] Hearle | Mechanics of dense fiber assemblies[END_REF][START_REF] Komori | Mechanics of Large Deformation of Twisted-Filament Yarns[END_REF] or using an average deformation for all the segments [START_REF] Kilby | The mechanical properties of twisted continuous-filament yarns[END_REF][START_REF] Pan | Development of a Constitutive Theory for Short Fiber Yarns: Mechanics of Staple Yarn Without Slippage Effect[END_REF] to reflect a better cooperation between them. The first approach involves a contraction ratio λ which is often set to 0.5 for an approximately constant volume deformation of the whole yarn. However, studies showed that the radius of yarns under extension decrease more than what could be expected from the predictions of a constant volume model because of the reduction of voids between the fibres. With the help of X-ray microtomography and an in-situ tensile machine designed for yarns, we experimentally measured the change of radius of the yarns during deformation as well as their average packing density over the cross-section. The predictions of the model, taking into account these experimentally validated contraction laws, are finally compared with macroscopic experimental tensile curves of these yarns.

The first section of this paper is devoted to the description of the single yarns studied and the experimental tests that were carried out to obtain their fibre orientations at rest and their packing density during extension. The theoretical background of yarn mechanics is then introduced including the use of fibre orientation distributions and deriving the non-linear yarn lateral contraction which takes into account the evolution of the fibre packing density. These two features (the orientation distribution and the packing density) are experimentally measured and fitted by means of appropriate functions in the third section. Finally, the yarn mechanical properties predicted are presented in the last section where the influence of the different parameters is discussed.

Materials and Method

Materials

Two types of fibres were used to produce continuous-filament yarns. The first bundle of a linear density of 144 tex (g/km), contains 384 polyester fibres. The second one contains 1000 aramid fibres and has a linear density of 167 tex (g/km). The bundles are twisted using a ring spinning machine to reach 3 different levels of twist : 100, 200 and 300 turns per metre (tpm). The aimed twist N 0 , the diameter d = 2r and the theoretical angle α at yarn surface (tan(α) = 2πrN 0 ) are gathered in Table 1. The actual twist measured after twisting the yarn is shown in brackets.

Accurate mean values of the initial yarn diameters were measured with a Z-Mike laser.

Experimental setup

A previous study from the same authors [START_REF] Sibellas | Experimental study of the fiber orientations in single and multi-ply continuous filament yarns[END_REF] about the fibre orientations in single and multi-ply yarns introduced the experimental setup that is used in the present article. X-ray microcomputed tomography is a non-destructive technique to obtain three-dimensional images of a sample at the microscopic scale [START_REF] Maire | On the application of X-ray microtomography in the field of materials science[END_REF]. Many radiographs are combined from different angular steps of the sample in front of the detector to build its 3D volume. An in-situ tensile machine was developed for the yarn prehension at rest and during its extension. The setup is controlled from outside the tomograph and all the data needed are stored in real time. These features allow yarns to be scanned in their initial configuration to obtain their orientation density functions (introduced in part 5) and at different steps during deformation in order to measure accurately the evolution of their radius. The voxel size is 2.6 µm for aramid fibres and 3.5 µm for polyester fibres with a scanning time of about 8 min. Even if the displacement speed is quite low (0.03 mm/min) for a gauge length of 4.5 cm, it is necessary to wait a short time before launching a scan because of the relaxation time of the sample, made of a polymer.

Measurement of the Yarn Packing Density

We assume a uniform packing density of the fibres over the yarn cross-section. This allows the packing density µ to be calculated as the ratio between the surface of the fibres S f and the total area S y of the yarn cross-section (containing the fibre cross-sections and the voids) :

µ = S f S y (1)
The 4 steps leading to the value of the packing density are described in Fig. 1. First, a median filter is applied to the image obtained with X-ray microtomography and then, the images are binarized. A threshold must be chosen carefully in order to get the fibre cross-sections without cropping them or taking some voids into account. The value of the area of cross-sections S f can show large variations (about 10%) depending on whether the threshold is underor overestimated especially at large deformation when the fibres are very close to each other. Considering this point, we choose to estimate the theoretical value of the surface S T h f of the fibre cross-sections rather than experimentally measuring it.

The equivalent radius R b of a cylinder containing all the fibres of the original bundle without any void can be written as a function of the linear density Λ of the bundle and the specific weight ρ of the material :

R b = Λ πρ (2)
The total surface of the section after twisting this compact cylinder is given by Leech [START_REF] Leech | The modelling and analysis of the mechanics of ropes[END_REF] and its radius R 0 f at rest is :

R 0 f = R b 1 + (πN 0 R b ) 2 (3)
where N 0 is the twist. Assuming that the fibres are incompressible, so their volume remains constant over their extension, allows the evolution of the radius R f of the equivalent cylinder containing all fibres without void to be expressed as a function of the yarn deformation y :

R f ( y ) = R 0 f 1 1 + y (4)
Finally, knowing the theoretical total surface S T h f = πR 2 f of the fibre sections and the experimentally measured total surface S Exp y = πR 2 y of the yarn section as shown in Fig. 1d, the packing factor µ can be expressed as :

µ( y ) = S T h f S Exp y ( 5
) (a) (b) (c) (d)

Theoretical Background

In the following part, yarn mechanics will be developed on the basis of Leech's work [START_REF] Leech | The modelling and analysis of the mechanics of ropes[END_REF] and linked with the theories involving a first key parameter : the orientation density functions which describe the yarn structure in a statistical manner. From these derivations, another key parameter is underlined : the fibre deformation which depends on the fibre angle and on yarn lateral contraction. An expression is developed for the latter and unknown coefficients will be found by our experiments.

Yarn Mechanics

The energy functional per unit length U f of a fibre should depend on its strain , its twist per unit length dθ ds and its curvature χ. Following Liu [START_REF] Liu | Mechanical Modeling of Singles Yarn[END_REF] who showed that the contribution of fibre torsion and fibre bending in the total yarn stored strain energy are negligible compared to fibre tension and Leech [START_REF] Leech | The modelling of friction in polymer fibre ropes[END_REF] who neglected the energy dissipation due to friction, assuming that slippage between fibres remains very small in extension tests, we only take into account fibre tensile energy to derive the relationships. Hence, the energy functional U f of a simple fibre can be written as :

U f ( , dθ ds , χ) = U f ( ) (6)
If we deal with little portions of fibre being small enough to be considered as straight segments, we can sort each angle θ between fibre segments and the yarn axis (this angle will be called fibre orientation) into different intervals of an arbitrary width ∆θ in order to obtain the relative frequency (probability) P of fibre orientations :

P(θ, ∆θ) = n(θ,∆θ) N s
where n(θ, ∆θ) is the number of angles falling into the range θ ± ∆θ 2 and N s the total amount of fibre segments. The Orientation Density Function (ODF) ω(θ) is defined by making the interval size dθ tend to zero as :

ω(θ) = P(θ, dθ) dθ (7)
The structural strain energy per unit length for a yarn characterized by a distribution n(θ, ∆θ) of fibre orientations can be written as a function of U f (energy/unit length) :

U s = π 2 0 n(θ) sec(θ)U f ( f ) (8)
where sec(θ) appears because of the obliquity of the fibres, increasing the volume of matter and thus, the stored fibre strain energy per unit length of yarn. In the continuous case, the previous relationship can be expressed in terms of the orientation density function ω(θ) :

U s = N f π 2 0 ω(θ) sec(θ)U f ( f )dθ ( 9
)
This expression is the same as those developed first by Hearle and Sakai [START_REF] Hearle | On The Extended Theory of Mechanics of Twisted Yarns[END_REF], and then by Komori and Makishima [START_REF] Komori | Mechanics of Large Deformation of Twisted-Filament Yarns[END_REF],

who used a different definition of the orientation density function, but showed the equivalence with Hearle and Sakai.

Considering a yarn sample of initial length L 0 submitted to a tensile load F, the variation L 0 dU s of its strain energy induced by an infinitesimal increment of displacement dL can be calculated as:

L 0 dU s = F • dL. (10)
The tensile force F can therefore be expressed as a function of the strain energy U s as:

F = L 0 dU s dL . ( 11
)
As U s is defined as a function of f , the derivation of can be decomposed into:

dU s dL = dU s d f d f dL . ( 12
)
Assuming a relation between the deformation of a fibre f , and the axial strain of the yarn s , one can write:

dU s dL = dU s d f d f d s d s dL . ( 13
)
Denoting L the current length of the yarn, and defining its axial strain by:

s = L -L 0 L 0 , (14)
one obtains:

d s dL = 1 L 0 , (15)
hence:

F = dU s d f d f d s . (16)
Then, introducing Eq. 9, the tensile force can be expressed as:

F = N f π 2 0 ω(θ) sec(θ) dU f d f d f d s dθ. ( 17
)
We assume that the strain energy (energy/unit length) U f of a fibre is equal to the strain energy of the bundle made of those fibres divided by their number N f :

U f ( f ) = 1 N f f 0 F b ( )d (18)
Where F b is the expression of the tensile force applied to the bundle as function of its elongation, which is experimentally identified. Whereas dispersion is expected in the experimental identification of the tensile response of individual fibres, approximating this response from a test performed on a bundle amounts to averaging the tensile behaviour over all fibres in the bundle, and is simpler than carrying out tests on single fibres. Finally, using the expression 18 in Eq.17, the total force F as a function of yarn deformation y is :

F( y ) = π 2 0 ω(θ) sec(θ)F b ( f ) d f d y dθ (19)
Sibellas et al. [START_REF] Sibellas | Experimental study of the fiber orientations in single and multi-ply continuous filament yarns[END_REF] investigated the experimental orientation density functions of various kinds of yarns (1 to 3 plies) and compared them to existing models. The same experimental setup was used with the same methodology to track the fibres in the single yarns studied here. The next section deals with the derivation of the expression of fibre deformation as a function of the yarn deformation taking into account yarn lateral contraction.

Fibre Deformation

The deformation of the fibre f has to be expressed as a function of the yarn deformation y . Considering sufficiently small portions of fibre so that they can be seen as straight segments, Hearle and Sakai [START_REF] Hearle | On The Extended Theory of Mechanics of Twisted Yarns[END_REF] derived the deformation of these segments in space as a function of the initial fibre angle θ, the yarn deformation y and the lateral contraction λ(r) of the fibre segment:

f = (1 + y ) 2 cos 2 (θ) + (1 -λ(r) y ) 2 sin 2 (θ) -1 (20)
The radial lateral contraction λ is defined as the ratio between the relative variation of radial position of the fibre and the axial deformation of the yarn :

λ(r) = - 1 y r r 0 -1 (21)
where r 0 and r are the radial position of the fibre in the initial configuration and after extension respectively. Assuming, for the sake of simplicity, a uniform contraction in the yarn cross-section, this lateral contraction can be expressed as a function of the yarn radius in the initial state R 0 and after deformation R :

λ = - 1 y R R 0 -1 (22)
The yarn packing factor µ is defined as the ratio between the surface of fibre sections and the total surface of the yarn section. This definition easily leads to the following relationship between the yarn radius and its packing factor at rest and under extension :

R R 0 = µ 0 µ( y ) 1 1 + y (23)
Hence, Eq. 20 can be rewritten as a function of the yarn packing factor :

f = (1 + y ) 2 cos 2 (θ) + µ 0 µ( y )(1 + y ) sin 2 (θ) -1 (24)
From this equation, we can derive f in order to get the partial derivative in Eq. 19 :

∂ f ∂ y = 1 2(1 + f )        2(1 + y ) cos 2 (θ) + sin 2 (θ) µ 0 (1 + y ) 2 dµ( y ) d y (1 + y ) -µ( y )        (25)

Yarn Rupture

The yarn mechanical model presented before will be used to evaluate the initial part of the tensile curves and does not aim at predicting their breaking point. Nevertheless, the rupture mechanism in the yarn is handled considering individually each class of orientations obtained in the experimental identification, and assuming a rupture criterion expressed in terms of the axial strain rupt at the breaking point of the extension of the original bundle of parallel fibres (before being twisted). The axial strain f of each individual class of orientation centred on a value θ is expressed as function of the axial strain of the yarn y by means of Eq. 24. When this axial strain f exceeds rupt the tensile force for the corresponding class of orientations is set to zero.

Tensile Curve of the Initial Fibre Bundle

Experimental tensile curves of the initial fibre bundles (0 tpm) are difficult to obtain because of the lack of fibre cohesion. Moreover, single fibre tensile tests were not performed and their non-negligible variability would be a strong questionable aspect of the results. Instead, we performed tensile tests on the yarns twisted at 100 tpm and used the theory in an inverse manner to find an estimation of the bundle tensile curves. Taking the mean orientation angle θ from the experimental orientation density functions at 100 tpm, we can rewrite Eq. 19 :

F 100tpm ( y ) = F b ( f ) sec( θ) d f d y ( 26
)
which gives :

F b ( f ) = F 100tpm ( y ) sec( θ) d f d y -1 (27)
For each value of y of the yarn at 100 tpm, we will find the value of F b for the corresponding deformation f = f ( y ).

It should be noted that using the complete equation involving the orientation density function instead of the average angle θ adds much more complexity in the determination of the tensile curve of the initial fibre bundle.

Experimental Measurements of the Evolution of the Packing Density

For each type of yarn (see table 1), measurement of their radius under extension was carried out with the help of the X-ray microtomography and the results are reported in Fig. 2a for the yarns made of polyester fibres and in Fig. 2b for the ones with aramid fibres. These figures show a non-negligible decrease of the yarn radius (about 10 % for the different cases) during the yarn extension. The corresponding evolution of packing density for each kind of yarn is depicted in Fig. 3 where its increase with the yarn extension is clearly observed. The slope of the curve representing the evolution of the packing factor can be seen as a rate of contraction which is always the highest at the beginning of the deformation. This could be related to a high rearrangement of the fibres filling the empty spaces or straightening their curved parts instead of taking part in the yarn extension by elongating themselves. In addition, this rate of contraction is higher for aramid yarns which could be explained by the ratio between axial and flexural stiffness and the more important number of aramid filaments of a lesser size of radius. This combination tends towards a higher transverse pressure in the aramid yarn cross-section leading to a higher rate of contraction. The evolution of the packing density µ as a function of the yarn extension y can be empirically fitted by the following expression :

µ( y ) = µ c + (µ 0 -µ c )e -κ µ y (28)
where µ 0 is the initial value of packing density, µ c the value of the packing density at infinite strain and κ µ , a coefficient governing the rate of change of the packing density. The values of these parameters are adjusted so that the packing density function fits experimental data. For simplicity, it has been chosen to assume they are independent of the initial twist N 0 , and to adjust them to fit the average of the experimental packing density curves obtained for three different twists (see Fig. 3). These adjusted values are summarized in table 2 and will be used in the following.

The Orientation Density Function

The orientation of a fibre represents the angle between its tangent (on a specific point of the fibre trajectory) and the yarn axis. Because of the stochastic character of the fibre arrangement and the consequent difficulty of deterministic models to describe the fibre trajectories in a realistic manner, orientation distributions are used to represent the Nature of fibres µ 0 µ c κ Polyester 0,69 0,85 40 Aramid 0,65 0,87 35 yarn structure. Accurate orientation distributions for single-ply and multi-ply yarns made of continuous fibres were obtained using X-ray microtomography by the same authors [START_REF] Sibellas | Experimental study of the fiber orientations in single and multi-ply continuous filament yarns[END_REF]. With the same experimental setup, yarns studied in this paper were scanned and their orientation distributions are depicted on Fig. 4b where the effect of twist increasing the obliquity of the fibres is clearly observed. These experiemental results will be used as input in the mechanical model described previously.

Calculations of the Yarn Mechanical Properties

Tensile behaviour with a constant packing density

The forces developed by the yarns under extension were calculated with the orientation distributions described in the previous section and compared to experimental tensile curves. In order to firstly capture this influence independently of the lateral contraction (analysed in the next paragraph), the cross-sectional packing density of fibre µ is prescribed to be constant and equal to µ 0 in this first calculation. The results are reported in Fig. 5a for aramid yarns and in Fig. 5b for polyester yarns. We observe that each of the models can capture the decrease of stiffness with the twist but does not show an agreement with the experimental tensile tests. Thus, fibre orientations along with a constant packing factor cannot explain the total decrease of rigidity of the yarn studied. Furthermore, the use of a distribution causes fibres with small orientation angles to break prematurely initiating cascading breaks of each of the class of fibre angle. The model described in this paper does not aim at modelling the last part of the tensile curve because it does not take into account the different phenomenons occuring before yarn rupture.

Tensile behaviour with a variable packing density

This last part is devoted to the calculation of the theoretical tensile curves with a variable fibre packing density determined experimentally (parameters are given in table 2). The results are reported on Fig. 6. In both case, very good agreements between the theoretical and experimental curves are obtained. Moreover, the strong non-linearity (arising from twist) of the yarn made of aramid fibres appears to be correctly predicted.

This variable fibre packing density allows fibres to take place in the empty spaces in the yarn cross-section during its extension, thus increasing the packing density. Consequently, the fibres can reduce their orientation angle towards the yarn axis and limit their own deformation. This induce a lower involvement of the fibres to the total longitudinal force developed and a lower overall rigidity of the yarn.

Conclusions

A model of the mechanical response during extension of single continuous-filament yarns based on the fibre orientation density function and a variable fibre packing density was presented. Those two key parameters were experimentally measured using X-ray microtomography, an in-situ tensile setup especially designed for yarns and different image processing techniques. Polyester and aramid fibres were twisted to produce yarns at 100, 200 and 300 turns per meter. The model showed that the fibre orientations and a constant packing density do not explain the total decrease of yarn rigidity. Taking into account the experimental variable fibre packing density through its theoretical derivation in the model led to very good agreements between theoretical and experimental curves and could predict the strong non-linearity of the tensile curves of yarn made of aramid fibres.

Figure 1 :

 1 Figure 1: (a) Image of a single yarn cross-section obtained with X-ray microtomography. (b) Median filter applied to the first image. (c) Binarization of the cross-section with an adapted threshold. (d) A function "fill holes" is applied to fulfil every blank hole between the binarized fibres.

Figure 2 :Figure 3 :

 23 Figure 2: Evolution of yarn radius under extension in the case of (a) polyester fibres and (b) aramid fibres.

Figure 4 :

 4 Figure 4: Orientation density functions of (a) polyester yarns and (b) aramid yarns.

Figure 5 :

 5 Figure 5: Influence of the orientation density function on (a) the whole tensile curve of aramid yarns and at (b) the beginning of the loading.

Figure 6 :

 6 Figure 6: Influence of the orientation density function on (a) the whole tensile curve of aramid yarns and at (b) the beginning of the loading.

Table 1 :

 1 Single yarns produced and their geometrical parameters.

	Type of fibre Twist (tpm) Diameter (mm) α ( • )
		100 (108)	0,48	9,2
	Polyester	200 (195)	0,48	16,4
		300 (294)	0,48	23,9
		100 (105)	0,55	10,3
	Aramid	200 (197)	0,55	18,8
		300 (297)	0,53	26,3

Table 2 :

 2 Experimental parameters defining the evolution of the yarn packing density as a function of yarn extension.


Sofiene Jelassi
email: sofiene.jelassi@univ-rennes1.fr

Gerardo Rubino
email: gerardo.rubino@inria.fr

Toward Operative QoE Models using Virtual Multimedia IP-based Streaming Services

Keywords: IP-based multimedia streaming, Modeling of Quality of Experience, QoE monitoring and reporting

The measurement of the Quality of Experience (QoE) of multimedia streaming services (MMSS) over IP networks may be realized thanks to objective QoE models. They are mathematical functions transforming metrics from technical to user domains. An interesting category of QoE models predicts QoE scores of MMSS at runtime, letting use them for the monitoring operation. This requires integrating them inside the production environments, i.e., where the actual MMSS are consumed by end-users. This aspect is often neglected by QoE modelers that focus mainly on the accuracy and fitness of their designed models with respect to a given set of settings and conditions. As a consequence, a considerable technical effort should be made in order to bring them from the laboratory to the production environments. This obviously discourages MMSS providers to easily accept and adopt them. For the sake of enhancing QoE models integration, we propose Mesukal, a software-layer ensuring portability of QoE models over a variety of underlying MMSS, e.g. YouTube or Netflix. Specifically, Mesukal acts as a Java Virtual Machine (JVM) enabling to build portable applications over different OS, e.g. Windows, Linux or MacOS. Mesukal can be considered as a virtual MMSS that is able to seamlessly interact with QoE models, on the one hand, and arbitrary real MMSS, on the other hand. Each considered MMSS over IP networks is appropriately virtualized by a dedicated Mesukal App. Besides real MMSS, Mesukal can be used to instantiate experimental MMSS where the accuracy and portability of QoE models may be inspected and checked under controlled conditions. The inputs needed by the concerned QoE models are fetched from each real MMSS using probes that are tailored following the technology used by the considered multimedia service. In addition, Mesukal includes a rich GUI dashboard that enables to inspect QoE results.

I. INTRODUCTION

QoE measurement is nowadays a well-established research topic. Since its inception, two decades ago, huge steps forward have been made to define, measure, model and standardize it [START_REF] Barman | QoE Modeling for HTTP Adaptive Video Streaming A Survey and Open Challenges[END_REF]. In contrast to technical metrics, QoE measurement considers human perception and behavior in order to rate a given service. This is actually very insightful to promote a considered technology. A lot of attention has been paid to model QoE using mathematical functions allowing to (a) avoid redundant, costly and time-consuming subjective in-lab testing and (b) extend the application scope of QoE measurement, with some partial successes. We call "in-the-box" a QoS model developed by the concerned service provider, and "outof-the-box" those developed by third parties (see Fig. 1). Mesukal is concerned basically by the latter. They can be actually segregated into media-and equipment-based. The former category, denoted sometimes as black-box approach, examines the processed media, e.g. audio, image or video solely at the end-points of a considered media processing chain. However, the latter category, denoted sometimes as glass-box approach, examines the effects of each individual physical element, e.g. microphone, encoder, network, playback algorithm, or echo canceler, located in the media processing chain between end-points. Each QoE model defines tailored inputs that should be provided in the right format and margin in order to get faithful outcomes. In this work, we consider QoE models that require only data gathered at the exit point of MMSS given that our focus on monitoring.

Out-of-the-box models are built for baseline "abstracted" MMSS under certain settings, e.g. H.265 or VP9 and conditions, e.g. outdoor or indoor, that may be likely encountered in the production environment. This choice is made for increasing their application scope, and thus improving their added-value. This implies that MMSS developers should select suitable out-of-the-box QoE models before plugging them inside their special development and production environments. This is well-recognized to be tedious and time-consuming processes needing thorough knowledge about the QoE area coupled with a cumbersome technical effort. Moreover, the out-of-thebox QoE models should be maintained and upgraded with respect to each MMSS release that is a supplementary source of troublesome and confusion. These embarrassing features explain, to certain extent, why MMSS developers are more and more reluctant to include out-of-the-box QoE models. Indeed, this is often judged as an accessory incurring an unnecessary significant overhead. That is why, service developers prefer building their own in-the-box QoE models, such as Netflix and YouTube. The resulting in-the-box QoE models can be easily maintained and integrated within the service universe in an agile fashion. Hence, for the sake of supplying hands-on outof-the-box QoE models, they should be portable in the sense that they should be operative over different underlying MMSS service technologies, again such as Netflix and YouTube, to Moreover, they should be pluggable in the sense that they can be changed, updated or replaced without interfering with the underlying MMSS. This is the main goal of our work, and our focus in this demo.

This work addresses the issue of making portable and pluggable out-of-the-box QoE models over distinguished underlying MMSS. We actually used directive ideas followed by the popular JVM (Java Virtual Machine) built in order to execute a unique source code over different computing machines. This is basically performed by inserting a specialized virtualization software layer, denoted to as Mesukal, that abstracts the underlying real MMSS over IP (see Fig. 1). The goals of our demo are then twofold: (1) to illustrate for beginners in which way Mesukal should be setup, configured and used through two case studies and (2) demystify Mesukal for proficients by going through its internal components and their interactions. We strongly believe that Mesukal will be a useful instrument enabling continuous integration, a.k.a. DevOps, of QoE models inside production environments. Please note that as previous text suggests, Mesukal should be installed like a JVM by the user, but obviously a service provider should probably be included in the development of a Mesukal software layer.

The rest of the paper is organized as follows. In Section 2, we give an overview about workflow and architecture of Mesukal. In Section 3, we present two QoE case studies using Mesukal. We conclude in Section 4.

II. MESUKAL OVERVIEW

The schema plotted in Fig. 1 highlights the general Mesukal workflow and its basic interactions with QoE models and real MMSS. As we can see, the virtual MMSS instantiated by Mesukal fetch appropriate QoE model inputs by calling real MMSS using their provisioned API, e.g. YouTube or Vimeo API, and/or by inspecting suitable transport ports and media channels. The QoE models to invoke and their parametrization are specified in the settings that may be given in a manual or scripted way. Please note here that one or several QoE models may be invoked with respect to the intended goals; let's say comparing the accuracy of two QoE models or the alpha and beta versions of the same one. Once inputs are received and their correctness is validated, virtual MMSS transmit them, after an optional supplementary processing, toward the concerned models. The latter compute QoE scores and send them to the virtual MMSS. Typically, the received QoE scores are sent to the real-time plotting and/or saving components according to the specified settings.

To handle the technological variety of MMSS, we created one Mesukal App per enclosed MMSS that instantiates the corresponding virtual MMSS. Basically, a Mesukal App can be seen as an orchestrator that consolidates many software components, which may be classified into data and control planes. The data plane includes all software components required to actively accede and retrieve locally media content delivered by a given MMSS. Moreover, it includes software components offering VCR-like commands, which enable to play and/or record fetched media content for further processing. Needless to say, software components in the data plane are highly dependent on the technology used by the MMSS. On the other hand, the control plane includes all software components required to fetch the QoE model inputs and to deliver the computed QoE scores to the appropriate programs, namely the plotter and the logger. The fetching process relies on a set of probes customized with respect to the parametrization used by each MMSS, e.g. media format, transport protocol or port numbers. The included probes search information from three main sources: statistics and meta data returned by the MMSS API, captured NDU (Network Data Unit) and captured ADU (Application Data Unit). The available probes are activated according to the required inputs of each QoE model. Two case studies of Mesukal App will be discussed in Section III.

III. MESUKAL CASE STUDIES

The prevailing Mesukal App supported by Mesukal may be coarsely split into three categories: Experimental, Live TV channels, and social and commercial VoD services. We note that Mesukal has been mainly developed in Python and Tkinter. The following case studies discuss relevant operations that may be achieved with our tool.

Case Study A: This case study seeks to compare and examine the behavior and the accuracy of three QoE models of Digital Video Broadcasting (DVB) sessions over IP networks. The first one is specified in the ITU-T Rec. P1201.2 [START_REF] Cruz | A survey of standardized approaches towards the quality of experience evaluation for video services: An itu perspective[END_REF], and the second and third ones are proposed in [START_REF] Hernando | Evaluating quality of experience in iptv services using mpeg frame loss rate[END_REF]. Please note that we manipulated our implementation of those QoE models that may be slightly different than the original ones. All considered QoE models use as input a list of NDU and need several metadata about the configuration of the receiver end-point. These specifications led us to design a DVB Mesukal App as follows:

The data plane instantiates an experimental MMSS composed of a VLC-based streaming server and client sides. They are created and managed programmatically using python-vlc library. The streaming server is configured in order to actively transmit MPEG-2 video content using Transport Stream (TS) over RTP/UDP to a set of predefined streaming clients. The time-varying network impairment conditions are applied using the Traffic Control (TC) utility. They are specified using packet loss ratio, one way delay and jitter incurred during a DVB session. The control plane includes one probe that captures NDU including TS packets. A second probe is used in order to dissect tables belonging to program-specific information (PSI), namely Program Association Table (PAT) and Program Mapping Table (PMT). The computed QoE scores are sent to the plotter that displays them at runtime. For sake of clarity, we give in Fig. 2 a snapshot of GUI implemented by this Mesukal App.

Case Study B: This case study seeks to check the behavior and accuracy of the QoE model proposed in [START_REF] Kotropoulos | A no-reference modular video quality prediction model for h.265/hevc and vp9 codecs on a mobile device[END_REF], denoted as PAL QoE model, which has been designed to automatically assess QoE of services using Google VP9 Codec, e.g. YouTube or Netflix. To do that, we need to establish an interaction between PAL QoE model and the real service. This is actually what for instance YouTube Mesukal App provides. It has been designed as follows: the data plane includes components enabling to acceding and retrieving arbitrary YouTube video content at runtime. The user can manually specify the URL where YouTube video content is located. Moreover, it enables selecting a specific video format among available ones. The loading process of media content relies basically on ffmpeg, which pulls video segments and buffer them in a dedicated pipe. In order to play received video content at runtime, we implement a simple streaming video player using OpenCV library. It follows a static playback policy where video frames are fetched at a regular frequency. On the other hand, the control plane includes three kinds of probes. The first one relies on the public provisioned YouTube API accessible via Restful API. It returns stats about displayed video content, such as numbers of likes and views, video duration and size, etc. The second probe collects needful meta-data found at the application-layer using ffprobe, which are bitrate, resolution and frame rate. Finally, the third probe intercepts NDU including video content and puts them in a PCAP file. This operation relies essentially on Tshark. Our preliminary inspection shows that the PAL QoE model achieves reasonably good results, but we believe that more profound experiments are needed for a better judgment.

IV. DEMO EQUIPMENT AND ORGANIZATION

A Beta Mesukal version is maintained by our research team Dionysos at Inria. We also maintain a ready-to-use VM where a stable version of Mesukal is configured and installed. A link will be given to the participants in order to download Mesukal VM that runs over VirtualBox. A detailed guideline will be provided in order to reproduce various showcases, explained remotely, on their personnel computing machine.

V. CONCLUSION

Mesukal is a step toward building operative and portable QoE models over a variety of MMSS. It consolidates a collection of software components inside Mesukal App in order to virtualize experimental or existing MMSS. It will help in improving and extending the use of QoE models inside MMSS in production environments. Moreover, it offers a way of analyze QoE models as they appear and evolve.

Of course, it is required a full understanding of the service in order to extract the suitable inputs required by a set of models. Moreover, a Mesukal App should follow the evolution of the service to keep capturing those input parameters. Moreover, mechanisms for protecting user privacy should be be considered.

Fig. 1 .

 1 Fig. 1. Mesukal overview

Fig. 2 .

 2 Fig. 2. A controlled streaming experiment