Pietro Del Sorbo
email: pietro.delsorbo@ensam.eu

Jeremie Girardot
email: jeremie.girardot@ensam.eu

Frederic Dau
email: frederic.dau@ensam.eu

Ivan Iordanoff
email: ivan.iordanoff@ensam.eu

Hyperelastic modelling of yarn structures for dynamic applications

Dry fabrics comprised of high performance polymeric fibers have been widely used as protection layers in structures submitted to high velocity impacts (HVI). Their outstanding impact energy dissipation ability combined with an high strength-to-weight ratio make them a preferable choice in different applications such as bullet vests or blade containment systems over standard materials. Among the different approaches adopted to study these structures numerical methods assume a central role. Thanks to their reduced costs and the related possibility of evaluating the effects of single phenomena, they are often used to predict the structure ballistic limits or to study the physical events which occur during the penetration. Among the different strategies adopted to model a fabric, mesoscopic models have been largely adopted by different authors. These models assume the yarns as a continuum body while the fabric geometry is explicitly described. Nowadays yarn material models are universally assumed to be linear elastic and orthotropic. This modelling approach mostly focuses on the longitudinal behaviour of the yarn, however fiber-scale analyses and experimental results shows the importance of three-dimensional stress state on the ballistic limit. In order to obtain a three-dimensional description of the yarn strain state during the impact, a novel hyper-elastic model for yarn structures here is developed. In a first step, fiber-level preliminary analyses have been performed to obtain the effective behaviour of these structure under the projectile collision. In the second step, the hyperelastic model has been implemented and identified thanks to microscopic elementary tests. Finally, a continuum model of the yarn have been perfomed. First results show the relevance of the hyperelastic model compared to the fiber-level observation and enhance the limit of the classical linear elastic material model.

Introduction

High performance aramid and polyethilene fibres such as Kevlar and Spectra are widely used for impact protection systems due to their high strength and strength-to-weight ratio. Usually woven in flexible fabrics, they are used as main material in soft body armors or secondary layers in ceramic protections. Mechanical behaviour of these materials under high velocity impacts has been largely studied and determined using different methods. Classical solutions include analytical [1], semiempirical [2] and numerical approaches [3]. Within this group, numerical approaches are one of the most promising since they usually relies on less hypotheses compared to the analytical ones and do not require large investments in materials and time as experimental campaigns. Different numerical models have been proposed for fabrics under high velocity impact and they are historically classified according to the minimum scale individually modeled in the textile.

Macroscopic models assume single and multilayered textiles as a continuum body [4]. This approach tends to be preferable in terms of computational costs but it lacks of a correct representation of the complex physics behind the failure of the system which is intrinsically related to the weaving geometry and yarn to yarn interaction [3].

In mesoscopic models, textile yarns are individually modelled as a continuum body. Here the weave geometry is explicitly reproduced and phenomena as yarn pullout, yarns failure and friction dissipation due to yarn relative motion are naturally taken into account. Classical yarn models mostly focus on the correct representation of the filament longitudinal behaviour, then they are not able to correctly model yarn failure related to multiaxial loads [5].

Finally, microscopic or multifilament models descent into the scale of fibers. In this case, yarns which comprise the fabric are modeled as an assemble of real or equivalent fibers [6] in order to take into account fiber-fiber friction dissipation and yarn transverse behaviour. Obviously this type of models considers the major-ity of the physical aspects which contribute to define the structure ballistic properties, anyway they are related to a significant, usually unacceptable, computational cost even for a single textile layer model.

In order to improve the global response of the actual mesoscopic models and extend their ability in representing the yarn transverse response, a novel yarn continuum model based on an hyperelastic constitutive law here is employed. The ability of the proposed model have been assessed for the case of transverse impact on a single yarn. The results of the new mesoscopic approach are compared with those obtained by the same simulation performed at the microscale. In the first part of the paper the physical configuration of the impact test is presented. Secondly microscopic and mesoscopic models are described with their specific peculiarities and discretization. Finally, results of both models are discussed and compared.

Test Set up

The impact scenario consists in a single 25.4 mm length Kevlar KM2 600 yarn clamped at the extremities (Fig. 1) and impacted transversely in the centre by a cylindrical projectile. The 400 filaments which compose the yarn are assumed to be straight and circular with a constant diameter equal to 12 µm. A cylindrical projectile with a the mass of 9.91 mg and a diameter φ of 2.2 mm is located in the centre of the yarn with contact condition at the initial time. The initial speed have been set equal to 120 m s -1 . Due to the nature of the problem, symmetry conditions are applied for both the analyses.

Fiber Material Properties

Kevlar KM2 fibres exhibit a purely elastic strain-rate insensitive behaviour in the longitudinal direction and non-linear elastoplastic behaviour in their transverse direction [7,8].

Longitudinal Young Modulus E and density ρ have been assumed equal to 84.62 GPa and 1.44 g cm -3 respectively [7] while transverse behaviour of the single fiber has been neglected. This last assumption is reasonably justified by the fact that yarn transverse kinematic is mostly related to fibers rearrangement within the cross section rather than single fibers transverse deformation.

Maximal strain in the longitudinal direction is assumed as failure criterion for the single fiber as for the yarn, with a strain limit lim equal to 0.0452 This choice is motivated by the fact that few experimental information are available nowadays for the multiaxial failure of polymeric fibres and yarns.

Microscopic model using Discrete Element Approach

In the present application, a revisited version of the discrete element method inspired by the work of Wang [9] is applied to model yarn fibres and explore the microscopic phenomena which have place during the impact. All the 400 fibres which compose the yarn are individually modeled as a series of equally spaced DEs relatively linked by truss elements, Fig. 2. These particles carry out the fiber inertial properties and the numerical treatment of contact. Here the fibres will be assumed rigid in the transverse direction, while the longitudinal elastic properties are provided by the truss constitutive behaviour. Spherical DEs with a constant diameter of 12 µm are used to discretize the fibres. Relative distance among joined discrete elements has been set to 12 µm in the initial configuration, to provide fibres continuity. Since all the fibres are equally discretized, the global mass of the yarn has been homogeneously distributed within the particles.

DE couple

Mesoscopic model using Finite elements

In opposition to the microscopic model, here the yarn is modeled as a continuum body.

It is assumed to be straight with an elliptical cross section which does not vary along its length. The major and minor semi-axes of the section are taken equal to 0.0575 mm and 0.267 mm which results in a yarn volume fraction ν = 0.88. A discretization of twelve elements per cross section has been assumed which results in 1200 four nodes linear solid elements for the whole yarn. A density of 1.267 g cm -3 has been computed for the equivalent continuum multiplying the original Kevlar density for the yarn volume fraction.

Hyperleastic constitutive law

A revisited version of the material model proposed by Charmetant [10] has been employed for the yarn. It is based on an additive decomposition of the strain energy density function Eq 1. Each one of the three terms is purely dependent by a single physical invariant I e , I tc or I td which is intrinsically related to a specific deformation mode: longitudinal elongation, transversal compaction and transversal distortion respectively.

W i = f (I e ) + g(I tc ) + h(I td ) (1) f (I e ) = 0.5k e I 2 e
(2) Transverse and spreading waves are observed in both the analyses. The transverse wave consist in the propagation of a vertical displacement field out of the impact zone. This wave firstly moves leftwards to the clamped edge in the period between 0 µs and 20 µs, it is reflected and then moves rightwards to the impact point, 20 µs-30 µs. When it reaches the impact point, yarn failure is observed in the microscopic model.

g(I tc ) = k tc |I tc | p (3
The spreading wave is related to the yarn section rearrangement.

When the yarn gets in contact with the projectile, the different fibres spread under the charge and yarn section is arranged into a new configuration. This rearrangement of the section travels in the form of a wave with the same propagation direction and the same speed of the transverse one, Fig. 5.

The propagation of the spreading wave is naturally modeled at the microscale, since fibers rearrangement is explicitly taken into account, however is not so obvious to observe it in a continuous media. Here for the first time, according to the authors knowledge, this wave is observed into a mesoscopic model. This important novelty is related to the yarn hyperelastic constitutive law which does not require the classical hypothesis of null Poisson ratios currently assumed in linear elastic anisotropic models. Fig. 6 reports a comparison among the projectile velocity history in the two models. A very good correlation is obtained to the instant in which microscopic model fails. This clearly indicate the ability of the homogeneous model in reproducing the mechanical response of the fibrous media. From the physical point of view, the projectile velocity trend is intrinsically related to the way in which its energy is stored into the impacted structure, kinetic and internal energy. For this reason it is possible to assert that microscopic and mesoscopic models are also equivalent from the energetic point of view.

A second observation concerns the failure criteria. In this impact scenario, failure is only observed in the DEM model while continuous yarn keeps on absorbing energy even after the second reflection of the transverse wave. This clearly indicate that a pure longitudinal failure criteria is not sufficient to establish the equivalence among the two models. In the current work a new mesoscopic model for yarn structures have been presented and validated under the case of transverse impact. The validation has been performed comparing the results with those obtained by the modelisation of the same test at the microscopic scale. All the principal kinematic aspects of the impact observed in the microscopic analysis, including spreading wave, have been captured by the mesoscopic model. The two models are even equivalent from the quantitative point of view up to the failure of the microscopic one. If the coherence of the pre-failure phase reassures on the constitutive law adopted, the the difference after the failure phase pose an accent on the failure criteria here adopted. This critical point will be addressed in the future works and finally this constitutive behaviour will be adopted in the yarns at the fabric level.

Figure 1 .

 1 Figure 1. Transverse impact scenario.

Figure 2 .

 2 Figure 2. Fibre model using DEs

2 td ( 4 )Fig. 3

 243 Fig. 3 and 4 reports the yarn deformation at 0 µs(a), 10 µs(b), 25 µs(c) and 40 µs(d) for the microscopic and mesoscopic model respectively.Transverse and spreading waves are observed in both the analyses. The transverse wave consist in the propagation of a vertical displacement field out of the impact zone. This wave firstly moves leftwards to the clamped edge in the period between 0 µs and 20 µs, it is reflected and then moves rightwards to the impact point, 20 µs-30 µs. When it reaches the impact point, yarn failure is observed in the microscopic model. The spreading wave is related to the yarn section rearrangement. When the yarn gets in contact with the projectile, the different fibres spread under the charge and yarn section is arranged into a new configuration. This rearrangement of the section travels in the form of a wave with the same propagation direction and the same speed of the transverse one, Fig.5. The propagation of the spreading wave is naturally modeled at the microscale, since fibers rearrangement is explicitly taken into account, however is not so obvious to observe it in a continuous media. Here for the first time, according to the authors knowledge, this wave is observed into a mesoscopic model. This important novelty is related to the yarn hyperelastic constitutive law which does not require the classical hypothesis of null Poisson ratios currently assumed in linear elastic anisotropic models.

Figure 3 .

 3 Figure 3. Impacted Yarn using DEM

Figure 4 .Figure 5 .

 45 Figure 4. Impacted Yarn using FEM

Figure 6 .

 6 Figure 6. Projectile velocity comparison for a transverse impact at 120 m s -1 .


Mahdia Ali Pasha

Abdallahi Ibn Muhammad

Muhammad Ahmad

Abdallah Al-Mahdi

Charles Gordon

Ismaïl Pasha

Jaafar Nimeiry

Keywords: Sudan, Turkiyya, Mehemet refugees, unplanned settlements

est destinée au dépôt

Text :

Khartoum, the present capital of the republic of Sudan, was founded in 1824, in the aftermath of the conquest of Sudan by a Turkish-Egyptian army sent in 1820 by the viceroy of Egypt, Mehemet Ali Pasha (1768 ?-1849), under the command of his son Ismaïl. The fort and its garrison which were established at the confluence of the Blue and White Niles soon became the siege of the administration of the new Sudanese provinces of the Ottoman Empire. It is not before the reign of Khedive Ismail Pacha (1830-1895) that the Sudan turned into a profitable economic asset, and that Khartoum asserted itself as the political center of the conquered territories. But the rebellion launched in 1881 by Muhammad Ahmad ibn Abdallah al-Mahdi in Kordofan overran Khartoum despite the helpless resistance of the besieged British Governor-General, Charles Gordon (1833-1885). Instead of settling in Khartoum, which was abandoned and razed, the Mahdi decided to strengthen his military encampment in the small fishermen's village of Omdurman, on the western shore of the Niles' confluence. This settlement was to develop as the capital of his successor, the khalifa Abdallahi (1846-1898), who attracted there his kinsmen of the Taaisha tribe of Darfur. The central quarters of Omdurman still recall the memory of this period : they still bear the names of their activities or inhabitants ("Al-Mulazimin", who were the personal guard of the khalifa in his final years of reign, "Al-Masalma", the Christian who remained under the Mahdist' islamic regime, "Beit al-Mal", the location of the Treasury, "Wad Nubawi", etc.), around the Central Mosque, the Mahdi's Tomb, the khalifa's simple "palace" and the Central Suq. The center of Omdurman, the "native city" therefore presents a "traditional" aspect, with curved and narrow lanes and raw clay blind walls, and still works as a gateway of the capital towards the Sahelian belt of Sudan, from the White Nile to Kordofan and Darfur. On 1st september 1898, at Kereri, north of Omdurman, was fought the last battle of the khalifa 's reign. The victorious British-Egyptian expedition led by General Horatio Kitchener (1850Kitchener ( -1916) ) opened the British-Egyptian Condominium period , in which Khartoum was to recover its primacy, flanked by Omdurman and by a new town, Khartoum-North, built to accommodate the new industrial activities of the metropolis. The British-Egyptian Condominium over Sudan (1898Sudan ( -1955) ) witnessed a tremendous growth of the capital of what was to become the largest country in Africa. Total population rose from 245 000 inhabitants in 1956 to 750 000 in 1973, 1.34 million in 1983, 2. 9 million in 1993 to approximately 6 million in 2017, thus doubling its population every decade. By the eve of the XXIst century, it broadly covers a square of 1600 sq km, expanding on 40 km from west to east and north to south, from the alluvial plain of the Niles to the sandy soils of the Goz Abu Dulu to the west to the clay soils of the Jezira to the South.

Despite their gathering in the frame of a "Khartoum State", entrusted with the management and planning of the capital's growth, within the institutional frame of Sudan as a Federal State after the military seizing of power in June 1989, the Three Towns still present very distinctive features : -Khartoum, the "modern city", retains the political and administrative functions (Presidential palace, Ministries, Government offices and foreign Embassies), and most intellectual and cultural institutions (foremost University of Khartoum, the former British Gordon College, founded in 1902 and the Khartoum Branch of the University of Cairo, founded in 1955), while the Sudan Armed forces Headquarters are located at the eastern outskirts close to the international Airport. While the city center remains a commercial hub, around the Great Mosque, residential quarters extend toward the south : "colonial" villas in Khartoum 2, multi storey buildings in Amarat, and a square streets frame extending far south with middle-class developments of Sahafa and Jabbana... The agricultural land further south have been squattered by huge amounts of refugees and displaced people following the drought and wars since the 1970's. Unplanned extensions (Hillet Mayo, Mandela...) have thus developed on and behind the "Green Belt" deemed at protecting the city from the seasonal dust storms ("haboob"). The official policy of expulsion or forced relocation ("kasha") has proven a failure on the long run, and the new generations of rural origin, Arabs or non-Arabs of all brands, have become city dwellers with a deep sense of belonging to the urban world, and reject any idea of returning to their homeland. So the two axes of urban extension toward the south, along the Wad Medani or Jebel Aulia roads, entail a huge mix of population, with very different cultural features than the economic and political dominant community originating from the riverine Arabized tribes of the Nile valley.

-Omdurman presents more "traditional" Arab, Islamic and "African" features, despite the fact that it hosts the National Assembly and the National Radio and TV broadcasting premises : it is the most populated of the three cities, with over 2.5 million inhabitants, having received most of drought and war hit people from Western Sudan since the 1970's. It has extended deeply into the Bayuda desert on the N-W, while reaching along the Nile the military airbase of Wad Sayyidna. Its main activity is the trade of goods through the vast reaches of the steppic and desertic areas of the West : cattle, arabic gum and other traditional products are exchanged again consumer goods imported and dispatched in thriving popular suqs, like the famous "Suq Libya" which long used to be the entrance gate of Omdurman from the desert. The industrial zone consists mainly of slaughterhouses, which work for the internal market but also for the Arabic peninsula affluent market.

-Khartoum-North (in arabic "Bahri" which means "Nilotic" or by extension "Northern") was originally home to Egyptian (along them Christian Copts) and Nile riverine Sudanese workers and technicians. This professional and human background remains till today. The city entails an important industrial zone (building material, small industry of transformation of imported goods). It is linked to the Main Nile valley and to the major eastern towns of Gedaref, Kassala and Port-Sudan by tarmac roads through the Butana desert. If the railway does not play any more a major role as the link between Khartoum and the Sudanese provinces, a pipeline from the Kordofan and Southern Sudan oil fields feeds the oil refinery of Geili, 60 km north of Khartoum-North, on its way to the terminal of Bashaïr, near Port Sudan on the Red Sea. .If Omdurman remains the stronghold of the Mahdi's movement, Khartoum-North quarter of Hay Khogali holds the siege of the Mirghani family, heir of the founder of the Khatmiya (or Mirghaniya) rival brotherhood on the Sudanese political scene, who traditionally keeps close ties with Egypt. But this original human settings has been completed by the inflow of large amounts of displaced people originated from the impoverished Central Sudan and war torn South from the 1970's to the end of the XXth century. The makeshift camps of Hillet Kuku, Hajj Yousif or Cartoon Kassala have now been integrated into the urban fabric, but they are still economically and socially marginalized.

The dramatic spatial extension of the Khartoumese metropolis since its foundation has been accompanied by deep socio-cultural transformations. This was attested by a series of events which became landmarks of contemporary Sudanese history. Among them, are to be recalled two popular and pacific intifada-s, who resulted in the ousting of two military dictators, with huge demonstrations of people taking to the street : Marshall Ibrahim Abboud (1900-1983) in October1964, Marshall Jaafar Nimeiry (1930-2009) in April 1985. Also bloodless had been the seizing of power by the then Colonel Jaafar Nimeiry in May 1969, and would be the coup d'Etat of Brigadier-General Omer al-Bashir (1944-) on the 30th of June 1989. Khartoum has from then on been the siege of military regime inspired by an islamic thinker, Dr Hassan al-Turabi ; this regime has consistently tried to maintain the previous ethnic, religious and social homogeneity of the capital's population. It has thus re-shaped the urban planning in order to strengthen the control over land use, resorting as the previous governments to mass expulsion of displaced dwellers originating from Southern Sudan or Nuba Mountains, but also from Western Sudan, namely Darfur. But the all out counter-insurrection launched against rebel movements has in return triggered a mass exodus toward the capital. The independence of Southern Sudan has not led to the return home of all natives of the new State : the capital keeps its human diversity, enriched by the settling of a large and active community of Eritreans and Ethiopians since the wars and famines which hit these neighboring countries during the 1970's and 1980's. But the start of oil exports in 2000 gave the government the means to embark in an ambitious campaign of modernization and refurbishing of Khartoum, with a new Central Business District at the confluence of the two Niles ("Al-Mogren"). New industrial districts have developed as satellite cities at a distance in the north (Geili) and south (Al-Massid) . But the oil bonanza has been shortlived, due to the lasting instability and internal warfare, after the independence of Southern Sudan.in July 2011. Khartoum is one of the most extended and populated African metropolises ; it still commands a vast national territory, without competitors in terms of population or functions. But this huge concentration still lacks basic infrastructure and services accessible to all. Despite the above mentioned trend to urban integration, it still retains a distinct rural feature in the way of life and culture of most of its inhabitants.


David Espinel Sarmiento

Adrien Lebre
email: adrien.lebre@inria.fr

Lucas Nussbaum
email: lucas.nussbaum@loria.fr

Abdelhadi Chari
email: abdelhadi.chari@orange.com

Distributing

Distributing connectivity management in Cloud-Edge infrastructures : Challenges and approaches

Keywords: VIM, Cloud, virtualization, IaaS, overlay network

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Internet of Things (IoT) applications, Network Function Virtualization (NFV) services, and Mobile Edge Computing will require to deploy IaaS services within the backbone in a distributed fashion to respect delay or legal requirements [START_REF] Bousselmi | Towards a massively distributed iaas operating system : Composition and evaluation of openstack[END_REF]. One way to deploy such a Cloud-Edge infrastructure/Distributed Cloud Infrastructure (DCI) is enabling existing network points of presence (PoPs) to be used as micro DCs (potentially reaching several thousands of deployments) using Virtual Infrastructure Managers (VIM) like OpenStack, as proposed in the DISCOVERY initiative [START_REF] Lebre | Revising openstack to operate Compas[END_REF]. While this approach could better fit the requirements and constraints of the emerging needs, it raises new questions from a management point of view [START_REF] Cherrueau | Edge computing resource management system : a critical building block ! HotEdge[END_REF]. In order to provide the capacity of managing connectivity in a native way among several VIMs, a solution should answer the following Edge-Cloud challenges : -Scalability : The Cloud-Edge infrastructure must allow an increasing number of instances without affecting performance.

Compas'2019 : Parallélisme / Architecture / Système LIUPPA -IUT de Bayonne, France, du 24 au 28 juin 2019 -Resiliency : A Cloud-Edge infrastructure should be able to maintain control logic in case of network partitions without affecting the general behavior of the non-disconnected part and also being capable of providing local services in the isolated sites. -Locality awareness : VIMs should have autonomy for local domain management. This implies that locally created data should remain local as much as possible, and only shared with other instances if needed, thus avoiding global knowledge. This also implies the capacity to peer with other instances to establish networking services and send information only when demanded as the sharing of global network information could be restricted or forbidden, and only allowed for certain cases. -Abstraction : Configuration and instantiation of inter-site networking services should be kept as simple as possible to allow the deployment and operation of complex networking scenarios. The management of the involved implementations must be fully automatic and transparent for the users. Among the required features, the capacity to interconnect virtual networking constructions belonging to several independent VIMs is an important one. As VIMs have been conceived to work in a pretty stand-alone way managing a single deployment, it is necessary to have a networking solution that enables the control of both intra-PoP and inter-PoP infrastructure services connectivity. In the case of OpenStack, if having one OpenStack instance by site is considered, the main issue will rely on the networking module (i.e., Neutron), that has not been designed to interact with other instances. This paper aims at initiating the debate on how inter-site connectivity challenges can be addressed. In that sense, our work contributes (i) to provide an analysis of the requirements and challenges raised by the connectivity management in a Cloud-Edge infrastructure managed by several VIMs, ii) to present an overview of the shortcomings of the current solutions aiming to addressing those challenges, and (iii) to provide a discussion of the research directions in this field. The rest of this paper is organized as follows. Section II gathers a list of networking services and features expected in a Cloud-Edge infrastructure. Section III describes the challenges that need to be addressed to provide those services. Section IV presents ongoing works. Possible approaches to overcome the challenges are discussed in Section V. Finally, Section VI concludes and discusses future works.

Inter-Site Connectivity Requirements

There are several requirements and constraints that a solution should guarantee or provide in a Cloud-Edge infrastructure. Among the required networking services that need to be deployed in such infrastructure, the following four could be considered as the cornerstones for the architecture [START_REF] Chari | Approaches for on-demand multi-VIM infrastructure services interconnection. -Rapport technique[END_REF]

Inter-Site Connectivity Challenges for a Cloud-Edge Infrastructure

Several questions arise in order to provide the aforementioned Layer 2 extension feature in a Cloud-Edge infrastructure. This feature should be provided while satisfying the general requirements of scalability, locality awareness, resiliency, and abstraction. This section aims to explain some of the challenges.

Challenge 1 : Standard automatized and Distributed Interfaces

Due to the centralization, VIMs only present a user-oriented interface to provide local services. This is a management integration challenge which implies that the interface which faces the user (user side or north-side as traffic flows in a vertical way) and the interface which faces other VIMs (VIMs-side or east-west-side as traffic flows in a horizontal way) have to be smoothly bridged among them. This integration needs to be done in order to provide the necessary user abstraction and the automation of the VIMs communication process. Consequently, this necessitates the specification and development of well-defined north-and east-west-bound interfaces. The initial information exchanges among VIMs should take into account the identification of the mechanism to use (could be a pair of VLANs on an interconnection box, BGPVPN RT identifiers, VXLAN ids, etc.). This later, due to the fact that the user should not be aware of how these networking constructions are configured at the low-level implementation. Since a Cloud-Edge infrastructure could scale up to hundreds of sites, manual networking stitch techniques like [START_REF]Neutron bgpvpn interconnection[END_REF][11] will be simply not enough. Thus, how to design an efficient interface for bot north-bound and east-west-bound communication is an important problem in the research of inter-site connectivity management tools. The use of a centralized DataBase (DB) by all participants can be leveraged to avoid the need to request the Layer 2 extension service. In that case, the information of a Layer 2 segment created at VIM1 and the local MAC/IP addresses attached to it will be available to other VIMs. The problem with this approach lies in the locality awareness as we need that locally created data remains local as far as possible and the use of a centralized DB does not respect this point. Even more, in network partitioning cases, if the DB is not accessible by a site, the VIM will not be capable of providing even local services, thus impacting the desired resiliency of the system.

Compas'2019 : Parallélisme / Architecture / Système LIUPPA -IUT de Bayonne, France, du 24 au 28 juin 2019

Challenge 2 : On-Demand States Sharing

VIMs need to be able to share states among them only when requested. The MAC/IP addresses and network identifiers of a local network in VIM2 do not need to be shared with VIM1 and VIM3 unless the user requests the L2 extension of this network. How to deal with requests demanding to extend Layer 2 segments with already deployed VMs presenting address overlapping presents as an important problem that need to be studied. Overlapping addresses could also be presented in network partitioning cases and should be treated as well. If a Layer 2 segment is shared among the three VIMs of Figure 1 because of a network failure VIM2 is isolated from the others, the user may do the provisioning of a new VM in VIM2 with an IP address already granted to a VM in VIM1. Once the network failure is restored, VIM2 will notify the other VIMs about the VM information creating a conflict with the overlapping addresses. Such class of conflict resolution must be addressed minimizing the incoherence states and preserving local autonomy.

Challenge 3 : Dynamic Notification and Reconfiguration

Dynamic reconfiguration of networking services on each VIM needs to be done automatically according to (1) the requested service and (2) taking into account the explicit and implicit operations. For the first point, if a Layer 2 extension is requested between VIM1 and VIM2 and does not concern VIM3, there is no reason to notify or to reconfigure VIM3 network services. For the latter, for an already provisioned Layer 2 extension present at the three sites, if a new VM is attached to the segment in VIM3, it must execute implicit operations to notify the other VIMs about the reachability information of the new VM. Depending on the implementation, the solution needs be able to do this reconfiguration at the underlay level which implies the ability to talk to some physical equipment like the Edge site gateway ; or to do it at the overlay level which implies the ability to reconfigure virtual forwarding elements like GoBGP instances [START_REF][END_REF], Open vSwitch switches [START_REF] Foundation | Openvswitch[END_REF] or Linux bridges [START_REF] Foundation | Linux bridges[END_REF].

Ongoing works for Cloud-Edge infrastructures

The management of Cloud-Edge infrastructures has already been studied in the literature at different levels but without addressing the totality of the aforementioned challenges. We can distinguish two categories : the distributed cloud management solutions that do not consider the inter-site networking services, and the solutions proposing networking services.

Distributed Cloud solutions without networking services

A few works [START_REF] Bousselmi | Towards a massively distributed iaas operating system : Composition and evaluation of openstack[END_REF][START_REF] Cherrueau | Edge computing resource management system : a critical building block ! HotEdge[END_REF][START_REF] Lebre | Revising openstack to operate Compas[END_REF][START_REF] Soares | Re-designing cloud platforms for massive scale using a p2p architecture[END_REF] have investigated distributed approaches to deal with Cloud-Edge resource management challenges. However, they did not take into account the inter-site connectivity features. In [START_REF] Lebre | Revising openstack to operate Compas[END_REF] the authors make a complete analysis of the main limitations for OpenStack scalability, showing that the most critical points are the SQL Database and the messaging queue. Although the connectivity issue is mentioned, it is not studied and it is left as future work. In [START_REF] Bousselmi | Towards a massively distributed iaas operating system : Composition and evaluation of openstack[END_REF], the author experiments with several deployment configurations of OpenStack to provide a fully native DCI. The study concludes that using the regions feature, a deployment having an isolated communication bus and a shared database for all services could be a good start for future works. However, it presented network connectivity issues because the shared database did not respect the data locality and autonomy constraints, allowing remote instances to access private network information and trying to make non desired local changes. The challenge is left as future work.

Compas'2019 : Parallélisme / Architecture / Système LIUPPA -IUT de Bayonne, France, du 24 au 28 juin 2019

Solutions proposing networking services

This section gathers a set of solutions differing in their architecture designs but that provide some kind of multi-site networking services.

Cloud-enabled networking solutions without distribution

Several works have proposed ways to manage a Cloud-Edge infrastructure connectivity services adopting a centralized or hierarchical architecture [START_REF] Brasileiro | Fogbow : A middleware for the federation of iaas clouds[END_REF][START_REF] Moreno-Vozmediano | Cross-site virtual network in cloud and fog computing[END_REF][START_REF]OpenStack. -Kingbird project[END_REF][START_REF]Tricircle project[END_REF]. The major drawback of these kinds of solutions is the fragility exposed by the root or central element controlling the entire architecture, as it can experiment troubles that can make the entire infrastructure inaccessible. In [START_REF]Tricircle project[END_REF] Tricircle project is proposed, it achieves network automation in a multi-region deployment of OpenStack using a Central Neutron Service (the only exposed Neutron API to the user) and a series of modified Neutron Core plug-ins. Tricircle does not fit well in network partitioning cases as isolated sites are completely useless without communication with the Central Neutron.

Distributed networking solutions without Cloud-awareness

In this category we gather networking solutions like DISCO [START_REF] Phemius | Disco : Distributed multi-domain sdn controllers[END_REF] that presents a distributed architecture but that are unable to manage a Cloud-Edge infrastructure. DISCO (stands for DIstributed SDN COntrol Plane) is an SDN controller for overlay networks. It relies on a perdomain organization where each controller is in charge of an SDN domain. Every controller has an intra-domain part that gathers the main functionalities like managing virtual switches, and an inter-domain part that manages communication with other DISCO controllers to make reservations, topology state modifications or monitoring tasks. DISCO provides an inter-controller channel using a message-oriented communication bus implemented using AMQP in federation mode, every controller has at the same time an AMQP server and a client.

Summary

As might be seen, the capability of establishing inter-site networking services among several VIMs instances has been left aside in the literature. Although it is still an important element that needs to be studied and addressed in order to deploy a DCI architecture where users resources can effectively communicate among them.

Research Directions to Decentralize Connectivity Management

As we stated in the last section, our community should propose effective connectivity management mechanisms among VIMs. Knowing the challenges that need to be addressed, it is possible to present some approaches that will allow us to overcome the limitations and propose a new way to interconnect Cloud-Edge infrastructures. Inspired by the aforementioned DISCO architecture, we propose to leverage a physically and logically distributed inter-site connectivity solution. This solution will be by itself the interdomain part of the VIMs main networking component, analogous to the inter-domain and intra-domain parts of DISCO. In case of network partition this architecture will provide full autonomy to isolated sites since only the inter-site part will be unavailable while local services are still provided. For the rest of the network, multi-site operations will remain available without affecting the normal behavior of the system. Such kind of autonomy for VIMs functionalities will allow to create a resilient system without the need for heavy synchronization. The solution should leverage the use of E-VPNs and IP-VPNS based on BGPVPN [START_REF] Rosen | Using bgp as an auto-discovery mechanism for layer-3 and layer-2 vpnss[END_REF] technologies to grant virtual routes exchanges among VIMs. In consequence, an easy extension of Compas'2019 : Parallélisme / Architecture / Système LIUPPA -IUT de Bayonne, France, du 24 au 28 juin 2019 Layer 2 local segments in several sites will be allowed. In this sense, the work presented in [START_REF]Neutron-neutron interconnections[END_REF] is a promising start since it allows to create a two sites-related "interconnection" resources. The first resource references a local resource (e.g. network A in VIM1) and a remote resource (e.g. network B in VIM2) having the semantic informing that connectivity is desired between the two. The proposition then leverages the use of BGPVPNs at both sides to create an overlay network connecting the two local segments. In all cases, user has to define the interconnection at each VIM. The future work should focus in a solution combining the distributed architecture from DISCO and using BGPVPN technologies. DISCO-based architecture will allow VIMs networking components to peer among them for communication purposes ; at the same time, BGPVPN will allow to span overlay networks among the requested sites involving the possibility to create Layer 2 extensions. The use of a physically and logically distributed architecture for inter-site networking services among several VIMs while providing full autonomy to each one, presents itself as a good approach for the DCI case. Such approach will allow to achieve a distribution of connectivity management accomplishing a scalable, locality-aware, resilient, and easy to use infrastructure.

Conclusions

Leveraging each PoPs in Telcos's architecture as part of a Cloud-Edge infrastructure is an approach that gives answers to the many constraints posed by services like NFV, IoT, and MEC. Although there are some proposals for the management of such infrastructure, provide interdomain networking services in a distributed fashion is still a challenge to be addressed. In this paper, we explained some possible ways to allow peering among several VIMs in order to provide networking services among sites. Then, we reviewed some related works aiming at leveraging a management system for a DCI and explained the problems of its designs. We then explained different approaches to tackle down those limitations in order to provide a distributed connectivity management. We conclude that there is an enormous potential using a physically and logically distributed architecture composed by an inter-site connectivity module leveraging some already existing overlay network technologies in order to achieve a distributed network automation among several VIMs.

Traffic filtering, policy and Quality of Service (QoS) : be

  able to enforce traffic policies and QoS rules for traffic between several VIMs.

	: -Layer 2 network extension : be able to have a Virtual Network (VN) that spans several VIMs. This is the ability to plug into the same VN, virtual machines (VMs) that are deployed in different VIMs. -Routing function : be able to route traffic between a user A's VN on VIM 1 and a user B's VN on VIM 2. across several VIMs : this means infor-ming each of the VIMs that it must extend a local virtual network to another site. -A mechanism to learn MAC/IP VMs ad-dresses between the interested VIMs (in our example VIM1, VIM2, and VIM3) : e.g. Allows VIM1 to learn VIM2's and VIM3's MAC/IPs and know how to reach them and vice versa. -Some switching instances located at every VIM that will use this learned MAC/IPs to forward L2 packets between the inter---A way to request the Layer 2 extension connected VIMs.

-Service Chaining : Service Function Chaining is the ability to specify a different path for traffic in replacement of the one provided by default. A user needs to be able to deploy a service chaining spanning several VIMs, that means the possibility to have parts of the service VMs placed in different VIMs. FIGURE 1 -Layer 2 extension feature