Jonatan Krolikowski
email: jonatan.krolikowski@telecom-paristech.fr

Anastasios Giovanidis
email: anastasios.giovanidis@lip6.fr

Marco Di Renzo
email: marco.direnzo@lss.supelec.fr

Fair distributed user-traffic association in cache equipped cellular networks

Caching of popular content on wireless nodes is recently proposed as a means to reduce congestion in the backbone of cellular networks and to improve Quality of Service. From a network point of view, the goal is to offload as many users as possible from the backbone network to the wireless caches while at the same time offering good service to cacheunrelated users. Aggressive offloading can lead to an unbalanced user association. Some wireless nodes can be overloaded by cacherelated traffic while the resources of others remain underused.

Given a fixed content placement, this work proposes an efficient distributed algorithm to control and balance the association of cache-related traffic among cellular cache memories. The algorithm allows the network to achieve the globally optimal solution and can be executed on base stations using a limited amount of information exchange between them. It is based on a novel algorithm we call Bucket-filling. The solution limits the cache-users per node by balancing the total load among the nodes in a fair way. The improvement compared to common user assignment policies is highlighted for single-as well as for multi-tier random networks.

I. INTRODUCTION

By 2020, wireless data traffic is estimated to reach roughly the 8-fold of its volume of 2015 [START_REF]Cisco visual networking index: Global mobile data traffic forecast update[END_REF]. Such increase in data demand will be satisfied by densifying the network with new tiers as well as by allowing cooperation among stations. However, this increase of wireless traffic can pose new problems to the wireless backhaul network that are related to congestion. A trending strategy to ease the backhaul is to equip wireless nodes with large cheap cache memories [START_REF] Poularakis | Mobile data offloading through caching in residential 802[END_REF]. Content can be stored on them based on some knowledge of the popularity of the content requested by the users in the cellular network. The content is thereby brought closer to the user and the costly usage of backhaul bandwidth is reduced.

Since not all requests can be served by the caches, wireless traffic will be divided into (1) cache-related and (2) cacheunrelated traffic. The former can retrieve the requested content from the cache of a node whose signal can be sufficiently received. The latter will typically connect to the node with the strongest signal. As a result, wireless nodes with popular content could be overloaded with cache-related traffic, leaving no resources for cache-unrelated users. At the same time, other nodes with less popular content could be underused.

A solution for such imbalance can be to limit the maximum cache-related load per wireless node and redistribute, when possible, the remaining load among neighboring nodes. This way, resources can be kept available for cache-unrelated traffic which is less predictable. Note that although multicasting of cached content could reduce the effective traffic load, this approach also has its limitations due to service delay tolerance [START_REF] Poularakis | Exploiting caching and multicast for 5g wireless networks[END_REF]. Thus, the solution of the above association problem remains necessary.

The existing literature has not adequately dealt with such questions yet. It focuses on how to determine good content placement policies with respect to certain optimality criteria such as the hit ratio or user delays. User association is handled in different ways: In [START_REF] Borst | Distributed caching algorithms for content distribution networks[END_REF], the authors use caching to minimize bandwidth cost in a tree-like network. The routing decisions of users are, however, independent of each other. The authors of [START_REF] Shanmugam | Femtocaching: Wireless content delivery through distributed caching helpers[END_REF] associate users to any covering station that caches their requested content without balancing the traffic loads. In other works [START_REF] Blaszczyszyn | Optimal geographic caching in cellular networks[END_REF] [START_REF] Bastug | Cache-enabled small cell networks: Modeling and tradeoffs[END_REF], users are associated to the closest base station, not knowing if the requested content is stored in the cache or not. The authors of [START_REF] Poularakis | Approximation algorithms for mobile data caching in small cell networks[END_REF] maximize the hit ratio by means of integer optimization. They introduce a bandwidth constraint limiting the amount of users that can be connected to each cellular station. While this model avoids overloading cellular stations, it cannot guarantee a balanced routing among them. In [START_REF] Dehghan | On the complexity of optimal routing and content caching in heterogeneous networks[END_REF], user association is balanced between a cached and an uncached path. Association to the individual caches is modeled by shortest distance, again not allowing control over the use of the separate resources. The model in [START_REF] Naveen | On the interaction between content caching and request assignment in cellular cache networks[END_REF] includes both fractional content placement and routing variables and allows for the balancing of user traffic loads at the cache-equipped base stations. In the solution of the problem, however, the convergence to an optimal routing is dependent on iterative fractional content placement updates, which is decided for the entire network.

In this paper, we model the problem of associating users to stations with given cached content by introducing a utility function per station which puts soft limitation on the served user load. The related optimization problem allows to enforce a load fairness criterion between caches. We further develop a policy to optimally solve this problem in a distributed way. For a given cache placement, the resulting policy guarantees that all resources are used as evenly as possible. The calculations can be executed on the individual stations requiring a limited amount of information exchange. We show that the policy is beneficial both in single-and in multi-tier networks.

The remainder of this paper is organized as follows: Section II presents the network model and the problem formu-lation. In Section III, we introduce the solution techniques: Augmented Lagrangian, Diagonal Quadratic Approximation and the novel Bucket-filling algorithm. Numerical evaluations of the resulting policy are presented in Section IV for random networks (single-tier and 2-tier) with varying coverage or node density. Finally, Section V concludes our work.

II. SYSTEM MODEL AND PROBLEM STATEMENT

Consider the downlink of a cellular communications network with a finite set M = {m 1 , . . . , m M } of Cached Base Stations (CBSs). Every CBS is equipped with a cache memory in which content files from a finite catalog F are stored. Note that other base stations not equipped with caches (UBSs) can be part of the network (not considered in M). Each CBS has a coverage area, and areas of different CBSs can overlap.

A user arrives in a position on the plane and requests a file f ∈ F. The user will be covered (or not) by some CBS. In case he/she is covered by some CBS with the requested content in the cache, the user will be served from the caches. This traffic is called cache-related. The user association is assumed unique in the sense that an association to two or more CBSs is not allowed. When a user request occurs in the overlap of two or more coverage areas, it can be associated to any one of the covering CBSs. The exact distance of the user from the covering station (e.g. near the center or at the edge of the cell) is not taken into consideration. The users who do not find their requested content cached, and the users not covered by any CBS at all, constitute the cache-unrelated traffic. This traffic will be served either from covering CBSs or UBSs. In this work, we will not treat the question how to distribute its load among the stations. The boundaries of the overlapping coverage areas of the CBSs partition the plane into a set of disjoint regions: Two points are in the same region if and only if they are in the coverage areas of exactly the same subset of CBSs. Let S denote the set of all regions covered by at least one CBS.

The cache placement is given apriori. Tuples of region s and file f are called region-files q = (s, f ) if there is a CBS covering s with f in its cache. We denote the complete set of region-files by Q. Not included in Q are requests for files not stored in a covering CBS. The subset of CBSs that cache content f and cover region s is denoted by M(q) ⊆ M. Conversely, Q(m) ⊆ Q are the region-files which can be served by the cache of m.

For delay and backhaul congestion reasons, it is always more beneficial to serve a request from a cache than through the backhaul network. Therefore, in an optimal solution of the routing problem, all traffic of q ∈ Q is served from the cache of a CBS: For each region-file q = (s, f ) ∈ Q there is a station covering s with f in its cache. As a consequence, all user requests realted to region-files in Q (and only they) are cache-related traffic.

For each region-file q ∈ Q, the expected number of user requests is denoted by N q ∈ R + . The vector of these popularity values is denoted by N := (N q ), q ∈ Q. The information on file popularity is considered locally available at each covering CBS. Note that the model does not assume spatially uniform traffic and that the vector N is general.

We introduce the routing variable y m,q ≥ 0 for all m ∈ M, q ∈ Q(m). Each y m,q with q = (s, f ) denotes the part of expected traffic for content file f in region s associated to CBS m. The vector of all routing variables is denoted by y. For each q ∈ Q, the sum of all routing variables towards the covering CBSs must be smaller than or equal to N q . Formally, for every feasible solution:

m∈M(q) y m,q ≤ N q , ∀ q ∈ Q. ( 1
)
The total traffic volume associated with CBS m depends on the partial vector y m := (y m,q ), q ∈ Q(m) and can be expressed as follows:

v m (y m ) := q∈Q(m) y m,q .
The aim of our model is to put a soft limit on the maximum traffic associated with a CBS while balancing the cache-related traffic volume among the CBSs. This approach also guarantees the usefulness of each cache. We measure the usefulness of a CBS m by the utility function U m which takes the traffic volume routed to the CBS as its argument.

Following the concept of diminishing returns, U m is increasing and concave as well as continuously differentiable. Additionally, we can choose the utility function such that for volumes greater than a certain V m , the derivative of U m becomes close to zero. Such soft limitation entails that it is not beneficial to further route users to this station. The overall objective is to maximize the sum of utilities subject to routing constraints. The Convex Program formulation of the Cache Routing Problem is

(CRP) max 0≤ym≤Nm,m∈M m∈M U m (v m (y m )) s. t. m∈M(q) y m,q = N q , ∀ q ∈ Q,
where N m := (N m,q ), q ∈ Q(m) is the vector of expected requests for the region-files covered by m. Note that we introduce an equality constraint instead of the inequality in (1), since the utility functions are increasing. There is, thus, no cache-related traffic in the optimal solution that remains unrouted. Traffic association is balanced if the available resources are used in a fair way. Some notions of fairness are maxmin, αand proportional fairness. Each of them is achieved by appropriate choice of the utility functions (see [11][12]). E.g. for proportional fairness, utilities could be chosen as (weighted) logarithms, depending also on the soft limit we want to achieve.

In the next section, we derive the procedure that achieves the solution to the CRP for general utilities, leaving their specific choice to the network designer.

III. SOLUTION

The CRP is solved with a distributed algorithm which consists of three nested loops.

A. Dual method for the Augmented Lagrangian

The CRP is solved using the dual method on the Augmented Lagrangian (see [START_REF] Bertsekas | Parallel and Distributed Computation: Numerical Methods[END_REF], Section 3.4.4). We use the Augmented instead of the regular Lagrangian to achieve a distributed solution. In our case, the regular Lagrangian is not appropriate since it is not strictly concave in the primal variables and hence the primal solution is not unique. This creates conflicts when different stations compete for the same users and convergence cannot be guaranteed. Like the regular Lagrangian, the Augmented one relaxes constraints of the CRP and introduces a price λ q for the violation of each constraint. The difference between them is an additional quadratic term penalizing the violation of each constraint together with a factor > 0. This penalty guarantees strict concavity in the primal variables. Denoting the Augmented Lagrangian by L ( ) , we get

L ( ) (y, λ) = m∈M U m (v m (y m )) - q∈Q λ q (N q - m∈M(q) y m,q ) -2 q∈Q (N q - m∈M(q) y m,q ) 2 , (2)
where λ := (λ q ), q ∈ Q is the price vector. The domains of the dual variables are λ q ∈ R for all q ∈ Q, since the respective constraints are equalities. The Duality theorem (see [START_REF] Bertsekas | Parallel and Distributed Computation: Numerical Methods[END_REF], Appendix C) applies, which means that the duality gap is 0, and the dual method can be used. The objective function of the dual problem is

D ( ) (λ) := max 0≤ym≤Nm,m∈M L ( ) (y, λ) = L ( ) (y * (λ), λ),
where

y * (λ) = arg max 0≤ym≤Nm,m∈M L ( ) (y, λ) (3)
is the primal maximum of (2) for a given price vector λ. The dual problem is then defined as

(CRP-dual) min λ∈R Q D (λ).
Starting from an arbitrary initial dual vector λ(0), the dual vector is iteratively updated according to

λ q (t + 1) = λ q (t) + m∈M(q) N q -y * m,q (λ(t)) , (4)
where the steplength > 0 is the penalty used in [START_REF] Poularakis | Mobile data offloading through caching in residential 802[END_REF]. The convergence of this method is well known (see [START_REF] Ruszczyński | On convergence of an augmented lagrangian decomposition method for sparse convex optimization[END_REF] or Section 3.4.4 of [START_REF] Bertsekas | Parallel and Distributed Computation: Numerical Methods[END_REF]).

For practical implemetation issues of each update step of the region-file price λ q , q ∈ Q, only the primal solutions of the covering CBSs need to be known. Thus, for a distributed implementation, exchange of such information among neighboring stations is sufficient.

The next subsection presents the distributed solution for the primal problem [START_REF] Poularakis | Exploiting caching and multicast for 5g wireless networks[END_REF], which needs to be found for every iteration of the dual algorithm.

B. Distributed solution for the primal problem

The solution for (3) is unique since the domain of y is convex and compact and, for any fixed feasible vector λ, the Augmented Lagrangian L ( ) is strictly concave. We use the Diagonal Quadratic Approximation Method (DQA) [START_REF] Ruszczyński | On convergence of an augmented lagrangian decomposition method for sparse convex optimization[END_REF] to derive seperate problems which can be solved by each cache. A limited amount of exchanged information between neighboring caches is required.

The DQA overcomes the problem that the objective function L ( ) (y, λ) of ( 3) is not easily separable among the variables related to the different CBSs, since it contains quadratic terms combining different variables y m,q (see ( 2)). To achieve this, we introduce the functions L ( )

m : R Qm × R m Q m × R Q → R for all m ∈ M: L ( ) m (y m , ỹ, λ) := U m (v m (y m )) + q∈Q(m) λ q y m,q -2 q∈Q(m) ( N m q (ỹ) -y m,q ) 2 ,
where N m q (ỹ) := N q -m∈M(q) m =m ỹ m,q is the number of requests in q not associated with caches other than m in the routing vector ỹ = (ỹ m,q ), m ∈ M, q ∈ Q(m) which is here seen as a parameter. The primal problem to be solved by each cache m is defined as

(CRP-primal-m) max 0≤ym≤Nm L ( ) m (y m , ỹ, λ). (5)
Since L ( ) m (y m , ỹ, λ) is strictly concave in y and the domain is compact, CRP-primal-m has a unique solution which we call ỹ * m . The vector containing the solutions of CRP-primal-m for all caches is ỹ * .

The DQA method consists of parallel execution of CRPprimal-m at the caches with consecutive update of the vector ỹ in the fashion of a nonlinear Jacobi algorithm. It produces a succession of vectors ỹ(0), ỹ(1), ỹ(2), . . .. Starting from some given vector ỹ(0), the vector ỹ(τ +1) is defined as the convex combination of ỹ(τ ) and ỹ * (τ ). Given a constant 0 < α ≤ 1, we get

ỹ(τ + 1) = ỹ(τ ) + α(ỹ * (τ ) -ỹ(τ )). (6)
In [START_REF] Ruszczyński | On convergence of an augmented lagrangian decomposition method for sparse convex optimization[END_REF] it is shown that the DQA method converges. Observe that the convergence depends on the uniqueness of the primal solutions ỹ * (τ ). For every update [START_REF] Blaszczyszyn | Optimal geographic caching in cellular networks[END_REF], each station only requires results from its neighboring stations that cover a common region-file.

C. Bucket-filling

What is left is to find an efficient solution to CRP-primal-m (5) running on each CBS separately: In order to do so, we develop a novel technique we call Bucketfilling. First, we can simplify our notation since the problem is separated by cache, and the vectors ỹ and λ are parameters. In this subsection, y := y m , U := U m , N := N m , v := v m , Q := Q(m), Nq := N m q (ỹ). Then, the solution to (5) can be rewritten as

y * = arg max 0≤y≤N U(v(y)) + q∈Q λ q y q -2 q∈Q ( Nq -y q ) 2 = arg max 0≤y≤N U q∈Q y q - q∈Q 2
y 2 q -(λ q + Nq )y q .

The last step comes from the development of the quadratic term and from omitting the additive constants which do not affect the optimal solution. Further defining a q := λ q + Nq , the CRP-primal-m can be stated as

y * = arg max 0≤y≤N g(y) (7)
with g(y) := U q∈Q y q -q∈Q 2 y 2 qa q y q . We will now show that one known value in the optimal routing vector is sufficient to derive the entire solution of CPR-primal-m. This observation allows to develop the Bucketfilling technique.

Given the optimal vector y * , we define the function g q (y) : [0, N q ] → R for q ∈ Q as

g q (y) := U y + q =q y * q -2 y 2 -a q y - q =q 2 (y * q ) 2 -a q y * q .
The maximum of this function is the optimal solution y * q . In other words, arg max 0≤y≤Nq g q (y) = y * q . Furthermore, note that g q is continuously differentiable, strictly concave and defined on a compact set which implies that it has a unique maximum. We denote the unique root of its derivative

g q (y) = U y + q =q y * q -[ y -a q ] (8)
by y q . Then we get 0 ≤ y q ≤ N q =⇒ y * q = y q , y q < 0 =⇒ y * q = 0, (9) y q > N q =⇒ y * q = N q . Now, we can formulate the following key lemma:

Lemma 1. Let y * be defined as in [START_REF] Bastug | Cache-enabled small cell networks: Modeling and tradeoffs[END_REF]. Let i, j ∈ Q with 0 < y * i < N i , 0 < y * j < N j . Then

y * i = a i -a j + y * j .
Proof. From (9) we know that g i (y * i ) = 0 and g j (y * j ) = 0 and thus g i (y * i ) = g j (y * j ). From ( 8), we get

y * i -a i = y * j -a j
The statement follows from a simple calculation.

The Lemma allows us to characterize the entire optimal solution just from one value 0 < y * q < N q .

Corollary 1. The steepest increase of g (as in [START_REF] Bastug | Cache-enabled small cell networks: Modeling and tradeoffs[END_REF]) is achieved by increasing the region-file q with the highest value a q . For two different q, q ∈ Q, the gradients of g q and g q become equal once y q is increased by the value (a qa q )/ .

We can now describe the novel Bucket-filling algorithm that efficiently finds the optimal solution to CRP-primal-m: Algorithm 1 Bucket-filling 1: Sort Q by a q non-increasingly. 2: Declare all q ∈ Q with maximum a q as active.

3: Increase y q of active q equally (because of Lemma 1) until

• another q becomes active by Corollary 1,

• a q becomes inactive by y q reaching N q , or • g (y) = 0 for all active region-files q. 4: If the last condition is fulfilled, or y q = N q for all q, then terminate. Otherwise, go to step 3.

The algorithm is illustrated in Fig. 1. It terminates and returns the optimal solution y * defined in [START_REF] Bastug | Cache-enabled small cell networks: Modeling and tradeoffs[END_REF].

a) b) c) d) e) 0 a1-a2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 a1-a2 + N 2 a1-a3 + N 3 N 1 a1-a3
Fig. 1. Illustration of the Bucket-filling algorithm. Each bucket q is placed with its bottom at level amax-aq and has the height Nq. The buckets are filled to a common level -or until they are full. The algorithm halts when further increasing the water levels starts decreasing the objective value.

Observe that step 1 can be done in O(|Q| log(|Q|)) operations with a sorting algorithm such as quicksort. Step 2 runs in O(|Q|). Step 3 is executed up to 2 |Q| times, since every region-file is activated and deactivated no more than one time each. Assuming that f can be evaluated in O(1), this implies O(|Q|) as the asymptotic runtime for steps 3 and 4. This shows that the overall runtime is dominated by sorting in step 1 and thus is O(|Q| log(|Q|)).

This algorithm is executed in every inner loop of the DQA method, which is why its efficiency is paramount.

D. Algorithm

To sum up, the complete algorithm that findes the globally optimal solution to the CRP is Algorithm 2 Solve CRP 1: Choose dual vector λ(0), t = 0, ε > 0. 2: while λ(t)λ(t -1) > ε do 3:

Choose ỹ(0), τ = 0.

4:

while ỹ(τ )ỹ(τ -1) > ε do 5:

Find ỹ * m (τ ) with Algorithm 1 at every m ∈ M separately.

6:

Exchange results among neighboring stations, set ỹ(τ + 1) as in [START_REF] Blaszczyszyn | Optimal geographic caching in cellular networks[END_REF], τ = τ + 1.

7:

end while 8:

Exchange results among neighboring stations, set λ(t + 1) as in (4) , t = t + 1. 9: end while

The choice of the first dual vector λ(0) in line 1 is arbitrary. The first primal vector ỹ(0) in line 3 can be chosen as the last primal vector of the iteration before.

IV. NUMERICAL EVALUATION

For the simulation of the algorithm, we consider an urban area of 2.5 km × 2.5 km with uniform user distribution. A catalog of 6 files of equal size is known. The popularity of the files follows a Zipf distribution with parameter 1. Throughout the simulations, CBSs are placed in the area following a Poisson Point Process (PPP) with density 8 CBS km 2 . This means that their total number in each run is a random Poisson realization, and their position is uniform in the simulation window. In this way we avoid the bias of testing only particular network topologies. We run two simulation scenarios, the first for single-tier and the second for two-tier netowrks. Each scenario consists of 1000 simulation runs and we consider the averaged results over the runs. Coverage follows the Boolean model where a disc area is centered on each wireless station with some defined radius. The surface of different overlapping areas is found in each run by the Monte-Carlo method. The users are routed to the CBSs following three different policies:

1) The policy from Algorithm 2 with logarithmic utility function for each cache. This policy guarantees a proportionally fair (and also max-min fair) solution. We call this policy fair.

2) The closest-available policy, which associates each user with the closest CBS that both covers its position and has the requested content cached. 3) The unsplittable policy which associates all users in a region requesting the same file with a unique random CBS among all covering CBSs having this content. We want to evaluate the proportion of user traffic served by different CBSs over the total traffic routed to CBSs for each policy. In this way we can compare the policies based on how (un)equally they associate traffic load among the available CBSs. Observe that for all three policies, the total traffic volume associated to CBSs is the same, because in all scenarios the CBSs store the same cached content, and traffic is routed to a CBS whenever possible. Hence, the comparison is fair.

A. Single-tier Networks

In an ideal situation, all stations would serve exactly the same amount of traffic. This, however, is normally not possible in a random network. A routing policy is better than another, when the maximum load of a CBS is lower and at the same time the minimum load share is higher than in the other policy. This way, an overload of the stations is avoided while the usefulness of all stations is achieved. Simulating single-tier networks, we want to verify that the fair policy provides a more balanced distribution of traffic to CBSs than the other two. The coverage radius of the CBSs is varied between 62.5 m and 500 m. This can be translated to an expected number of covering CBSs per user between 1 and 6. This mapping comes from the Boolean model [START_REF] Blaszczyszyn | Optimal geographic caching in cellular networks[END_REF]. Two different sets of content files with different popularities are placed uniformly randomly into the caches. Since we are only interested in traffic associated with CBSs, we disregard users not covered by any CBS. The results show that with an increasing average number of covering stations, the fair policy achieves a lower maximum load as well as a higher minumum load. Since the overall traffic routed to the CBSs is the same for all policies, we can conclude that the fair policy makes the most balanced use of the available resouces. The resources which remain available for potential cache-unrelated traffic are spread evenly across the network.

B. Two-tier Network

In a second scenario, we simulate an area covered by two tiers [START_REF] Di Renzo | Average rate of downlink heterogeneous cellular networks over generalized fading channels: A stochastic geometry approach[END_REF]: one of large and one of small coverage. We show that the fair policy is better at offloading traffic from larger to smaller CBSs than the other policies (see Fig. 3). While the fair policy burdens the small stations with a higher load, we demonstrate that it distributes the load more evenly among them so that no individual station is overburdened (see Fig. 4). The first tier consists of large CBSs having a 187.5 m coverage radius while the second tier of small CBSs has 62.5 m coverage radius. The large CBSs are equipped with caches and the two most popular files are stored in all of them. The smaller CBSs get one of these two files assigned uniformly randomly in their cache.

In Fig. 3, we show the percentage of all traffic routed to large CBSs for each of the three policies. The x-coordinate increases with the ratio of small stations over large stations in the network. When less traffic is routed to the large CBSs, then the policy provides a more efficient offloading of traffic towards the small CBSs. The figure shows that, increasing the amount of small CBSs, the fair policy offloads significantly more traffic to the small stations than the unsplittable policy, and slightly more than the closest-available policy. Fig. 4 shows (as in Fig. 2) the maximum and minimum traffic load routed to a small CBS depending on each policy. Even though for the fair policy more users are routed to the small CBSs overall, the maximum load share that one small CBS takes is almost the same for all policies. The increase in traffic load by the fair policy is distributed to the less loaded small CBSs. This is indicated by the higher minimum load among the stations. When applying either the closest-available or the unsplittable policy these CBSs are underused. Thus, the fair policy utilizes the available resources better.

V. CONCLUSIONS

We propose a distributed algorithm that optimizes cacherelated user traffic association among cache-equipped cellular stations for a given content placement. The main novelty of the approach is the balancing of cache-related traffic load to evenly use all available resources. The solution procedure makes use of the Augmented Lagrangian to solve a strictly concave problem. The novel Bucket-filling subroutine takes optimal routing decisions locally at each station. With limited information exchange, our policy achieves a fair distribution of users among the stations. The efficiency of the algorithm allows for large networks with different sizes of coverage areas and different cache sizes to be solved optimally. Simulations of single-tier and multi-tier networks show that our policy is superior to conventional user traffic association policies in balancing cache-related user traffic among stations.

Fig. 2 Fig. 2 .

 22 Fig. 2. Minimum and maximum load share of a CBS in the network depending on the mean coverage number.

Fig. 3 .

 3 Fig. 3. Aggregate traffic share of large CBSs depending on the amount of small CBSs.

Fig. 4 .

 4 Fig. 4. Minimum and maximum load share of a small (2nd tier) CBS depending on the ratio of small CBS number over large CBS number.


Florence Colbère-Garapin

Bruno Blondel

Aure Saulnier

Isabelle Pelletier

Karine Labadie

SILENCING VIRUSES BY RNA INTERFERENCE

Post-transcriptional gene silencing (PTGS) makes possible new approaches for studying the various steps of the viral cycle. Plus-strand RNA viruses appear to be attractive targets for small interfering RNAs (siRNAs), as their genome functions as both mRNA and replication template. PTGS creates an alternative to classic reverse genetics for viruses with either negative-strand or double-stranded RNA genomes and for those with a large genome.

PTGS allows modification of the expression of a given cellular gene as a means to elucidate its role in the viral cycle and in virus-host cell interactions, and to investigate cellular pathways involved in viral pathogenesis. It also allows the creation of new animal models of human diseases. In addition, PTGS already appears to be a promising new therapeutic tool to fight viral multiplication and dissemination through the host and to prevent inflammation and virus-induced pathogenesis, including virus-induced tumorigenesis.

Introduction

Small noncoding RNAs have important roles regulating a wide range of cellular pathways associated with developmental programs and the protection of the genome against mobile genetic elements. In particular, small interfering RNA (siRNA) molecules mediate post-transcriptional gene silencing (PTGS), a natural biological phenomenon discovered in plants [START_REF] Matzke | Reversible methylation and inactivation of marker genes in sequencially transformed tobacco plants[END_REF] and Caenorhabditis elegans [START_REF] Fire | Potent and specific genetic interference by double-stranded RNA in Caenorhabditis elegans[END_REF]. In plants, it is a natural, conserved mechanism of antiviral immunity. PTGS is mediated by siRNAs produced by the type III endoribonuclease Dicer processing double-stranded RNA precursors [START_REF] Zamore | RNAi: double-stranded RNA directs the ATP-dependent cleavage of mRNA at 21 to 23 nucleotide intervals[END_REF]. T. Tuschl and coll. [START_REF] Elbashir | Duplexes of 21-nucleotide RNAs mediate RNA interference in cultured mammalian cells[END_REF] demonstrated that synthetic 21 nucleotide (nt)-long RNA duplexes transfected into cultured cells silenced genes in a sequence-specific manner. These synthetic siRNAs, with 2 nucleotide 3' overhangs, mimic those produced by the ribonuclease Dicer by digestion of large double stranded (ds) RNAs. Duplexes of RNAs shorter than 30 base pairs (bp) generally do not activate non-specific suppression by double stranded (ds) RNA-dependent protein kinase [START_REF] Elbashir | Duplexes of 21-nucleotide RNAs mediate RNA interference in cultured mammalian cells[END_REF][START_REF] Stark | How cells respond to interferons[END_REF]. After incorporation into the RNA-induced silencing complex (RISC), one of the siRNA strands acts as guide and selects the homologous target in the mRNA, which is then cleaved and degraded by RNases (Fig. 1). The efficiency of siRNAs is generally greater than that of short antisense RNAs. One characteristic of siRNAs is that for activity, they must be perfectly base-paired to their target in the corresponding RNA. However, up to 3 G:U wobble base pairs do not alter target specificity [START_REF] Saxena | Small RNAs with imperfect match to endogenous mRNA repress translation. Implications for off-target activity of small inhibitory RNA in mammalian cells[END_REF], probably because they have the same thermodynamic stability as Watson-Crick base pairs [START_REF] Gautheret | U base pairing motifs in ribosomal RNA[END_REF]. Other small duplex RNAs, named micro RNAs (miRNAs), are also dependent on Dicer for processing, but do not require perfect complementarity of the mRNA target and block gene expression through translational inhibition [START_REF] Zeng | MicroRNAs and small interfering RNAs can inhibit mRNA expression by similar mechanisms[END_REF][START_REF] Doench | siRNAs can function as miRNAs[END_REF]. This mechanism therefore differs from that of PTGS, which is highly sequence-specific. It has been recently shown that after transfection, small duplex RNAs displaying one or few mismatches with their target sequence sometimes behave like miRNAs, inhibiting translation of the mRNA, which remains intact [START_REF] Doench | siRNAs can function as miRNAs[END_REF].

Preferably, siRNA target sequences should be chosen outside of RNA regions predicted to be highly structured [START_REF] Elbashir | Duplexes of 21-nucleotide RNAs mediate RNA interference in cultured mammalian cells[END_REF]. Guidelines for the choice of siRNA sequences have been published [START_REF] Ui-Tei | Guidelines for the selection of highly effective siRNA sequences for mammalian and chick RNA interference[END_REF][START_REF] Schwarz | Asymmetry in the assembly of the RNAi enzyme complex[END_REF][START_REF] Khvorova | Functional siRNAs and miRNAs exhibit strand bias[END_REF]; they include a G:C bp at the 5' end of the sense strand of the siRNA, an A:T bp and an A-T rich sequence at the 5' end of the antisense strand of the siRNA, and no G-C stretch longer than 9 bp. Enzymatically prepared siRNAs have been synthesized in several ways to improve their efficiency and to lower the cost. In one approach, a large duplex RNA is cleaved in vitro by a cloned Dicer, as occurs in cells [START_REF] Yang | Short RNA duplexes produced by hydrolysis with Escherichia coli RNase III mediate effective RNA interference in mammalian cells[END_REF]. This has the advantage of producing a large panel of siRNAs covering a long segment of the mRNA, thereby enhancing efficiency and, in the case of viruses, avoiding the emergence of escape mutants. Another method involves using the T7 polymerase to transcribe siRNAs from short DNA templates encoding siRNAs downstream from a T7 promoter [START_REF] Milligan | Oligoribonucleotide synthesis using T7 RNA polymerase and synthetic DNA templates[END_REF]. One of the limitations of chemically or enzymatically synthesized siRNAs is their transient effect in transfected animal cells.

Chemically-protected siRNAs and viral vectors have been used to circumvent this problem [START_REF] Gitlin | Short interfering RNA confers intracellular antiviral immunity in human cells[END_REF][START_REF] Rubinson | A lentivirus-based system to functionally silence genes in primary mammalian cells, stem cells and transgenic mice by RNA interference[END_REF][START_REF] Zhao | Specific gene inhibition by adenovirus-mediated expression of small interfering RNA[END_REF].

The siRNA technology is so powerful that it is leading to a revolution in molecular virology. It makes possible new approaches for studying the various steps of the viral cycle, not only for plus-strand RNA viruses (Fig. 2), but also for all kinds of viruses. PTGS creates an alternative to classic reverse genetics for viruses with either negative-strand or doublestranded RNA genomes and those with a large genome. PTGS allows modification of the expression of a given cellular gene as a means to elucidate its role in the viral cycle and in virus-host cell interactions, and to investigate cellular pathways involved in viral pathogenesis. It also allows the creation of new animal models of human diseases. In addition, PTGS already appears to be a promising new therapeutic tool to fight viral multiplication and dissemination through the host and to prevent inflammation and virus-induced pathogenesis, including virus-induced tumorigenesis (see below). The literature on PTGS is already substantial and this review is far from exhaustive. A few examples have been chosen among RNA and DNA virus families to illustrate the possibilities already offered by this new technology. Most retroviruses will not be considered because they will be the subject of a separate review in this journal.

SiRNA transfer and siRNA-encoding vectors.

SiRNAs are negatively charged and do not readily cross cell membranes. They can be introduced into cells by electroporation. Alternatively, delivery vehicles of two classes can be used: synthetic carriers such as cationic lipids, peptides and cationic polymers (reviewed in [START_REF] Han | Development of biomaterials for gene therapy[END_REF]); and viral vectors. Non-viral carriers present fewer safety concerns than viral vectors, but are generally less effective for delivery.

The effect of both chemically and enzymatically-synthesized siRNAs is generally transient and typically does not last more than a week [START_REF] Tuschl | Expanding small RNA interference[END_REF]. To prolong the effects, RNA polymerase III-driven small RNA expression vectors have been constructed to induce longlasting RNA silencing in mammalian cells [START_REF] Brummelkamp | A system for stable expression of short interfering RNAs in mammalian cells[END_REF]. SiRNAs are transcribed from H1 or U6 RNA polymerase III promoters through to a stretch of five T residues acting as a transcription termination signal. Positive and negative-strands of siRNAs are obtained from either tandemtype or hairpin-type transcripts. These constructs have been inserted into several types of vectors, including lentivirus, adenovirus and adeno-associated virus (AAV) vectors [START_REF] Rubinson | A lentivirus-based system to functionally silence genes in primary mammalian cells, stem cells and transgenic mice by RNA interference[END_REF][START_REF] Zhao | Specific gene inhibition by adenovirus-mediated expression of small interfering RNA[END_REF][START_REF] Pinkenburg | Inhibition of NF-kappaB mediated inflammation by siRNA expressed by recombinant adeno-associated virus[END_REF]. Long-term expression of si-or shRNAs, lasting several weeks, has thereby been obtained. Note that lentiviruses are suitable vectors for use in non-dividing cells, and in particular in certain primary cell cultures [START_REF] Nishitsuji | Expression of small hairpin RNA by lentivirus-based vector confers efficient and stable genesuppression of HIV-1 on human cells including primary non-dividing cells[END_REF]. Episomal vectors have also been designed. One of them contains the ori P origin of replication, a coding sequence for EBNA-1 protein that is required for episome maintenance and two H1 tandem promoters that drive the synthesis of each of the siRNA strands [START_REF] Wilson | RNA interference blocks gene expression and RNA synthesis from hepatitis C replicons propagated in human liver cells[END_REF].

Methods commonly used in vivo include electroporation of siRNAs into the neural tube of chick embryos [START_REF] Hu | Inhibition of retroviral pathogenesis by RNA interference[END_REF] and hydrodynamic injection into the tail vein of mice [START_REF] Lewis | Efficient delivery of siRNA for inhibition of gene expression in postnatal mice[END_REF].

SiRNAs have also been delivered intranasally [START_REF] Tompkins | Protection against lethal influenza virus challenge by RNA interference in vivo[END_REF] and subcutaneously [START_REF] Chen | RNA interference targeting VP1 inhibits foot-and-mouth disease virus replication in BHK-21 cells and suckling mice[END_REF]. Viral vectors are routinely used in vivo.

SiRNA targets in the genome of plus strand RNA viruses.

Most regions of viral genomes have been assayed as targets for PTGS. Plus strand RNA viruses appear to be attractive targets for siRNAs, as their genome functions as both mRNA and replication template [START_REF] Kanda | Interference of hepatitis A virus replication by small interfering RNAs[END_REF]. A pioneer study by Gitlin et al. [START_REF] Gitlin | Short interfering RNA confers intracellular antiviral immunity in human cells[END_REF], targeting the capsid protein region or the 3D RNA polymerase region of the poliovirus (PV) genome, has shown that the viral yield of a one step growth cycle was about 100-fold lower when cells were transfected by specific antiviral siRNAs before infection. Antiviral siRNAs interfered with viral multiplication early after infection, but were not dependent on viral replication, and induced specific post-transcriptional cleavage and degradation of viral RNAs. Cell protection was slightly extended when both anti-capsid and anti-polymerase siRNAs were used together.

Neither interferon (IFN) nor either of its dsRNA-activated effectors, PKR or RNAse L, was required for suppression of PV replication by siRNAs. Interestingly, escape PV mutants rapidly emerged when cells treated with single siRNAs were infected at a high multiplicity of infection (MOI=10) while they rarely emerged at lower MOIs, suggesting that they were already present in the initial viral population [START_REF] Gitlin | Short interfering RNA confers intracellular antiviral immunity in human cells[END_REF].

A DNA-based human hepatitis A virus (HAV) replicon has been used in a hepatoma cell line to investigate whether HAV replication is inhibited by siRNAs targeting regions of the replicon encoding nonstructural proteins [START_REF] Kanda | Interference of hepatitis A virus replication by small interfering RNAs[END_REF]. Specific inhibition but not complete suppression of HAV replication was demonstrated. As for PV [START_REF] Gitlin | Short interfering RNA confers intracellular antiviral immunity in human cells[END_REF], combinations of siRNAs were more effective than single siRNAs for suppressing viral replication [START_REF] Kanda | Interference of hepatitis A virus replication by small interfering RNAs[END_REF]. Unexpectedly, two HAV-specific siRNAs induced increased replicon expression [START_REF] Kanda | Interference of hepatitis A virus replication by small interfering RNAs[END_REF]. Thus, PTGS was ineffective in this case, probably because of the secondary structure of target RNA that may influence the efficiency of PTGS.

A similar phenomenon has also been observed in the case of a human hepatitis C virus (HCV) replicon and an siRNA specific for the first nucleotides of the HCV 5' noncoding (NC) region, which exhibits a stem-loop structure [START_REF] Yokota | Inhibition of intracellular hepatitis C virus replication by synthetic and vector-derived small interfering RNAs[END_REF]. Given the medical importance of HCV infections, several laboratories have investigated the possibility of inhibiting the replication of HCV in cell lines of hepatic origin [START_REF] Wilson | RNA interference blocks gene expression and RNA synthesis from hepatitis C replicons propagated in human liver cells[END_REF][START_REF] Kapadia | Interference of hepatitis C virus RNA replication by short interfering RNAs[END_REF][START_REF] Seo | Small interfering RNA-mediated inhibition of hepatitis C virus replication in the human hepatoma cell line Huh-7[END_REF][START_REF] Sen | Inhibition of hepatitis C virus protein expression by RNA interference[END_REF]. Since no efficient cell culture system for growth of HCV is available, these studies were performed with HCV replicons harboring a reporter gene and/or a selective marker. Only some of the HCV-specific siRNAs were effective (inhibiting HCV replication at least 10 fold) in an IFN-and cell cycle-independent manner [START_REF] Kapadia | Interference of hepatitis C virus RNA replication by short interfering RNAs[END_REF]. A protocol involving two to three successive transfections with endonucleaseprepared siRNAs was highly effective [START_REF] Krönke | Alternative approaches for efficient inhibition of hepatitis C virus RNA replication by small interfering RNAs[END_REF]. In mice, an siRNA targeting the viral polymerase NS5B region reduced expression from a HCV NS5B-luciferase chimera by 75%, and inhibition was more than 90% when DNA templates encoding small hairpin RNAs (shRNAs) were used [START_REF] Mccaffrey | RNA interference in adult mice[END_REF]. In a hepatoma-derived cell line that already harbors autonomously replicating subgenomic HCV RNA, luciferase activity was reduced by up to 85% in a dose-responsive manner after transfection of cells by a specific siRNA targeting the 5' NC region of HCV [START_REF] Seo | Small interfering RNA-mediated inhibition of hepatitis C virus replication in the human hepatoma cell line Huh-7[END_REF]. Prolonged siRNA effects were obtained with bicistronic plasmids expressing complementary siRNAs [START_REF] Wilson | RNA interference blocks gene expression and RNA synthesis from hepatitis C replicons propagated in human liver cells[END_REF]. Wilson et al. [START_REF] Wilson | RNA interference blocks gene expression and RNA synthesis from hepatitis C replicons propagated in human liver cells[END_REF] used a self-contained episomal expression vector that extended the duration of siRNA activity to three weeks. Introduction of siRNAs targeting another nonstructural protein, NS5A, resulted in the inhibition of NS5A and NS5Amediated activation of the IL-8 promoter, as well as the inhibition of core protein expression [START_REF] Sen | Inhibition of hepatitis C virus protein expression by RNA interference[END_REF]. SiRNA targeting the core region also resulted in dose-dependent and specific HCV RNA silencing [START_REF] Randall | Clearance of replicating hepatitis C virus replicon RNAs in cell culture by small interfering RNAs[END_REF]. SiRNAs reduced the levels of both (+) and (-) strand RNA [START_REF] Randall | Interfering with hepatitis C virus RNA replication[END_REF] and could clear replicating HCV RNA from >98% of cells. The HCV NS3-1 gene also appears as a good target for PTGS [START_REF] Takigawa | Suppression of hepatitis C virus replicon by RNA interference directed against the NS3 and NS5B regions of the viral genome[END_REF].

Dengue virus (DENV) is another plus strand RNA virus of great medical importance: it causes dengue hemorrhagic fever and it is responsible for dengue shock syndrome. AAV vectors encoding siRNAs specific for a 3' NC sequence common to all dengue serotypes reduce dengue infection in dendritic cells and decrease the dengue-induced apoptosis of these cells [START_REF] Zhang | Attenuation of dengue virus infection by adeno-associated virus-mediated siRNA delivery[END_REF].

A novel coronavirus (CoV), responsible for severe acute respiratory syndrome (SARS), spread worldwide in early 2003. This virus (SARS-CoV), like other members of the Coronaviridae family, is enveloped and has a large genome of positive polarity. SiRNAs targeting the SARS-CoV RNA polymerase blocked cytopathic effects of the virus on Vero cells, blocked viral RNA and protein synthesis, and reduced virus production [START_REF] Wang | Inhibition of severe acute respiratory syndrome virus replication by small interfering RNAs in mammalian cells[END_REF].

SiRNAs: an alternative to classic viral genetics.

Molecular genetics is difficult with viruses having either a negative-strand RNA genome, or a segmented genome, or a very large genome. For these viruses, the siRNA technology offers a potentially valuable alternative strategy to modulate viral gene expression.

Negative-stranded RNA viruses include important human pathogens. Among them, pediatric disease caused by human respiratory syncytial virus (hRSV) claims about a million lives annually. The nonsegmented genomic and antigenomic RNAs of hRSV escape siRNAs, probably because they are tightly wrapped with the nucleocapsid protein N, which makes them inaccessible [START_REF] Bitko | Phenotypic silencing of cytoplasmic genes using sequence-specific double-stranded short interfering RNA and its application in the reverse genetics of wild type negative-strand RNA viruses[END_REF]. Unlike the full-length genomic and anti-genomic RNA, the mRNAs do not bind N protein. Two types of hRSV-specific siRNAs have been designed: the first is specific for the P protein, involved in the formation of a complex responsible for sustained RNA elongation during transcription. The second is specific for the fusion protein F. At nanomolar concentrations, the siRNAs specific for viral P and F mRNAs abolished expression of the corresponding mRNAs and proteins, and produced the expected mutant phenotype. Targeting the P mRNA substantially diminished all viral protein production, reduced viral progeny yield by up to 10 4 fold, and inhibited cell fusion. In contrast, targeting the F mRNA did not inhibit cytopathic effects completely but prevented syncytia formation.

Therefore, hRSV-specific siRNAs allow functional genomic studies, attenuated infection, reverse genetic analysis and studies of host-virus signaling pathways [START_REF] Bitko | Phenotypic silencing of cytoplasmic genes using sequence-specific double-stranded short interfering RNA and its application in the reverse genetics of wild type negative-strand RNA viruses[END_REF].

Influenza viruses are another group of major human pathogenic viruses causing particularly severe respiratory infections in the elderly and immunocompromized individuals.

One of the advantages of an siRNA treatment is that it does not require a functional immune system [START_REF] Ge | Inhibition of influenza virus production in virus-infected mice by RNA interference[END_REF]. The genome of influenza virus A is composed of 8 RNA segments of negative polarity. Ge et al. [START_REF] Ge | Inhibition of influenza virus production in virus-infected mice by RNA interference[END_REF] designed 20 siRNAs targeting regions of the viral genome that are conserved among different subtypes and strains of virus from human and animal species.

Most viral genes were targeted, except the hemagglutinin and neuraminidase genes, because of the extensive diversity in these genes. SiRNAs targeting nucleocapsid protein NP and two proteins of the transcriptase complex (PA and PB1) were effective, even when cells were infected with virus a few hours prior to siRNA introduction. In addition, siRNAs inhibiting influenza virus production in vitro also inhibited virus production in chicken embryos [START_REF] Ge | Inhibition of influenza virus production in virus-infected mice by RNA interference[END_REF].

Interestingly, the same authors demonstrated that the target of siRNA was either mRNA, or complementary (+) strand cRNA, or both, but not viral (-) strand RNA. However, targeting NP and PA genes resulted in overall inhibition of viral RNA transcription. Influenza virus matrix protein-encoding RNA has also been successfully targeted [START_REF] Hui | Inhibition of influenza virus matrix (M1) protein expression and virus replication by U6 promoter-driven and lentivirus-mediated delivery of siRNA[END_REF].

Rotaviruses are the leading etiologic agents of severe diarrheas in young children worldwide. They consist of three concentric layers of protein that enclose a genome of 11 segments of double-stranded (ds) RNA. Dimers of VP4 form 60 spikes at the surface of triple layered particles (TLPs) that are involved in virus attachment to the cell surface. SiRNAs corresponding to the VP4 gene efficiently inhibited VP4 synthesis, and the synthesis of other viral proteins was not affected. Most of the viral particles were TLPs, but lacked VP4. The results reported by Dector et al. [START_REF] Dector | Rotavirus gene silencing by small interfering RNAs[END_REF] indicate that VP4 was not required for the budding of double-layered particles (DLPs) into the endoplasmic reticulum or for the enveloped intermediate particles to lose their lipid envelope. VP4 was not required for the assembly of VP7 into the third protein layer, but VP7 assembled in a loose manner under these conditions, and formed spike-less TLPs. The resulting particles were poorly infectious. These findings confirm the essential role of VP4 in the infectivity of rotavirus [START_REF] Dector | Rotavirus gene silencing by small interfering RNAs[END_REF]. Interestingly, the viral transcripts involved in virus genome replication do not seem to be susceptible to siRNAs [START_REF] Arias | RNA silencing of rotavirus gene expression[END_REF][START_REF] Silvestri | Rotavirus replication: plus-sense templates for double-stranded RNA synthesis are made in viroplasms[END_REF]. They may either be protected within electron-dense inclusions (viroplasms) or by RNA-binding proteins in the cytoplasm. Synthesis of VP4 was silenced even when the corresponding siRNA was added 4 h post-infection [START_REF] Arias | RNA silencing of rotavirus gene expression[END_REF]. Silencing the VP7 gene prevented the formation of TLPs, and caused DLPs to accumulate [START_REF] Silvestri | Rotavirus replication: plus-sense templates for double-stranded RNA synthesis are made in viroplasms[END_REF]. Silencing the viral polymerase, VP1, and the nonstructural protein, NSP5, blocked the secondary transcription of the virus, with the concomitant inhibition of the synthesis of all viral proteins (reviewed in [START_REF] Arias | RNA silencing of rotavirus gene expression[END_REF]).

Another potential target is NSP4, since this viral enterotoxin contributes to diarrhea (reviewed in [START_REF] Arias | RNA silencing of rotavirus gene expression[END_REF]). In the absence of a reverse genetics system, PTGS should be very useful for functional genomic studies in rotaviruses [START_REF] Arias | RNA silencing of rotavirus gene expression[END_REF].

Herpesviruses are large DNA viruses that typically infect their host latently after an acute phase. Reactivation of the lytic virus cycle may occur following induction by various agents. Two human gammaherpesvirus, Kaposi's sarcoma associated herpesvirus (KSHV) and Epstein-Barr virus (EBV), are associated with several types of malignancies. Jia and Sun [START_REF] Jia | Inhibition of gammaherpesvirus replication by RNA interference[END_REF] targeted the Rta gene of a murine gammaherpesvirus, herpesvirus 68 (MHV68), encoding an immediate-early viral protein responsible for the switch between the latent and lytic phases. They also targeted ORF45, a gene that is conserved among all gammaherpesviruses making it a good target. Anti-Rta siRNA cotransfected with virus DNA into permissive cells significantly blocked Rta expression. It also blocked the expression of other viral proteins. Cells cotransfected with either anti-Rta-or anti ORF45-siRNA grew better than controls and produced only 1 to 2% of the virus progeny at 4 days posttransfection [START_REF] Jia | Inhibition of gammaherpesvirus replication by RNA interference[END_REF]. Herpes simplex virus type 1 (HSV-1) is an alphaherpesvirus that infects epithelial and neuronal cells. Glycoprotein E (gE) from HSV-1 is essential for cell-to-cell spread. When human keratinocytes were transfected with gE-specific siRNAs and then infected with HSV-1, Bhunyan et al. [START_REF] Bhuyan | Short interfering RNA-mediated inhibition of herpes simplex virus type 1 gene expression and function during infection of human keratinocytes[END_REF] observed small plaques, corresponding to the phenotype of a gE-deletion mutant of HSV-1.

The human polyomavirus JC, which is responsible for a demyelinating disease (progressive multifocal leukoencephalopathy), has been successfully blocked by PTGS in human astrocytic cells [START_REF] Radhakrishnan | Intracellular approach for blocking JC virus gene expression by using RNA interference during viral infection[END_REF].

Hepatitis B virus (HBV) causes both acute and chronic infection of the human liver, which can lead to the development of liver cirrhosis and hepatocellular carcinoma. In stable HBV-producing hepatoma cell lines, siRNAs targeting the polyadenylation, precore and HBV surface antigen (HBsAg) significantly decreased the abundance of the corresponding HBV RNAs [START_REF] Giladi | Small interfering RNA inhibits hepatitis B virus replication in mice[END_REF][START_REF] Konishi | Inhibition of HBV replication by siRNA in a stable HBV-producing cell line[END_REF][START_REF] Li | Genome-wide expression profiling of RNA interference of hepatitis B virus gene expression and replication[END_REF]. In particular, the small HBsAg has been selected as a target for siRNAs because the major transcripts synthesized from this genomic region during HBV replication overlap and include the pregenomic RNA, which serves both as the template for reverse transcription and the synthesis of viral DNA and mRNA. In mice, injection of either HBsAgspecific siRNAs or plasmids encoding shRNAs, together with a plasmid encoding the entire HBV genome, resulted in the decline in HBV serum marker levels [START_REF] Giladi | Small interfering RNA inhibits hepatitis B virus replication in mice[END_REF][START_REF] Mccaffrey | Inhibition of hepatitis B virus in mice by RNA interference[END_REF]. Concomitantly, antiviral siRNA treatment greatly reduced the number of HBsAg-and core-positive hepatocytes. SiRNA treatment did not cause inflammatory infiltrate in liver tissue [START_REF] Giladi | Small interfering RNA inhibits hepatitis B virus replication in mice[END_REF].

Targeting cellular factors involved in viral multiplication

The first cellular molecules to be involved in viral multiplication are receptors responsible for virus binding and entry into the cell. These receptors are particularly interesting targets for silencing, because the absence of such receptors blocks all subsequent steps of the viral cycle. Gaggar et al. [START_REF] Gaggar | CD46 is a cellular receptor for group B adenoviruses[END_REF] used CD46-specific siRNAs to demonstrate the role of CD46, a ubiquitously expressed complement regulatory protein, as a cellular attachment receptor for most group B adenoviruses. Similarly, the role of the ubiquitous glucose transporter GLUT-1 as a component of the receptor for the human T cell leukemia virus (HTLV) has been demonstrated by down modulating endogenous GLUT-1 expression with siRNAs specific for the 3' NC region of GLUT-1 mRNA [START_REF] Manel | The ubiquitous glucose transporter GLUT-1 is a receptor for HTLV[END_REF]. Caveolin-1 knockdown by PTGS reduced human coronavirus 229E infection, because this virus binds to CD13 in rafts and enters the cell through caveolae [START_REF] Nomura | Human coronavirus 229E binds to CD13 in rafts and enters the cell through caveolae[END_REF].

SiRNAs encoded by Adenovirus vectors have been used to confirm the role of putative cellular cofactors for HCV, since viral replication in Huh-7 hepatoma cells was substantially blocked by silencing either La (a protein potentially involved in HCV internal initiation of translation), polypyrimidine tract binding protein (a protein interacting with both 5'-and 3'-NC regions), or subunit gamma of eukaryotic initiation factors 2B (a cofactor of HCV cap-independent translation) [START_REF] Zhang | Down-regulation of viral replication by adenoviral-mediated expression of siRNA against cellular cofactors for hepatitis C virus[END_REF]. Similarly, targeting the human RNA helicase p68 by specific siRNAs caused a reduction in the transcription of negative strand HCV RNA [START_REF] Goh | Cellular RNA helicase p68 relocalization and interaction with the hepatitis C virus (HCV) NS5B protein and the potential role of p68 in HCV RNA replication[END_REF].

Inhibition of viral dissemination within a host and inhibition of pathogenesis by siRNAs.

Dengue virus (DENV) serotypes 1-4 are transmitted to humans by the mosquitoes Aedes aegypti and Aedes albopictus. A Sindbis virus expression vector was used to study the role of mosquito genes in determining mosquito competence and virus dissemination.

Sanchez-Vargas et al. [START_REF] Sanchez-Vargas | RNA interference, arthropod-borne viruses, and mosquitoes[END_REF] engineered a Sindbis virus genome such that it contains the coding region for early trypsin (TrypEarl) protein, a regulator of the proteolytic cascade in the midguts of blood-fed mosquitoes. The recombinant Sindbis virus transcribed a 500 bp region of the TrypEarl gene. TrypEarl-siRNAs were produced in mosquito midguts, leading to degradation of TrypEarl mRNA. Importantly, this affected dissemination of DENV-2 to tissue in the head. PTGS can thus be used to identify cellular genes involved in viral dissemination in mosquitoes.

A baculovirus, Autographa californica nucleopolyhedrosis virus, has caused severe economic losses in the silk industry over many years. Interfering with genes essential for baculovirus virulence, such as a major nucleocapsid gene or an early transcriptional activator, inhibits viral infections and prevents the death of over 95% of insects [START_REF] Flores-Jasso | Silencing structural and nonstructural genes in baculovirus by RNA interference[END_REF].

Foot-and-mouth disease virus (FMDV) is a picornavirus and the etiological agent of a devastating disease of cloven-hoofed animals, foot-and-mouth disease. W. Chen et al. [START_REF] Chen | RNA interference targeting VP1 inhibits foot-and-mouth disease virus replication in BHK-21 cells and suckling mice[END_REF] engineered plasmids encoding capsid protein VP1-specific siRNAs and injected them subcutaneouly into the neck of suckling mice. This treatment rendered mice less susceptible to FMDV and promoted their survival. Interestingly, preadministration of a plasmid encoding the VP1 transcript contributed to the protection of animals. This result is in agreement with the observation that the effect of siRNA may be long-lasting if target mRNA is continually available [START_REF] Song | Sustained small interfering RNA-mediated human immunodeficiency virus type 1 inhibition in primary macrophages[END_REF].

The murine model has also been used to show that siRNAs specific for highly conserved regions of the nucleoprotein (NP) or acidic polymerase (PA) of influenza A virus inhibit viral replication in vivo [START_REF] Tompkins | Protection against lethal influenza virus challenge by RNA interference in vivo[END_REF]. The intravenous and intranasal routes of inoculation were used successively. Virus-specific siRNAs reduced virus titers in the lung and protected mice against lethal challenge with highly pathogenic avian influenza A viruses of the H5 and H7 subtypes [START_REF] Tompkins | Protection against lethal influenza virus challenge by RNA interference in vivo[END_REF]. IFN could not have been responsible for the inhibition of virus replication, because H5 viruses are resistant to the antiviral effects of IFNs. In addition, Ge et al. [START_REF] Ge | Inhibition of influenza virus production in virus-infected mice by RNA interference[END_REF] have shown that siRNAs given after influenza virus infection reduce virus replication in the lungs of mice, demonstrating a therapeutic effect of siRNAs.

SiRNAs and the recovery from virus-induced abnormal cell proliferation.

Over 90% of human cervical cancers harbor a human papillomavirus (HPV) genome and co-operative effects of the HPV E6 and E7 genes drive cell transformation. E6 and E7 interact with key tumor suppressors, p53 and the retinoblastoma protein pRb, respectively.

Silencing the E6 gene in cervical carcinoma cells positive for HPV16 resulted in selective E6 mRNA degradation and p53 nuclear accumulation. Stabilization of p53 was accompanied by induction of the expression of a cell cycle control protein, p21 (a protein targeted by p53), and reduced cell growth, although no substantial G1 arrest was observed [START_REF] Jiang | Selective Silencing of Viral Gene E6 and E7 Expression in HPV-Positive Human Cervical Carcinoma Cells Using Small Interfering RNAs[END_REF]. SiRNA specific for E6 did not induce significant cell death. In contrast, silencing the E7 gene induced selective loss of hyper-phosphorylated cellular pRb and caused the cells to round up and to undergo apoptosis. Therefore, in the case of HPV-positive human carcinoma cells, treatment with E7specific siRNA leads to selective killing of the cancer cells [START_REF] Jiang | Selective Silencing of Viral Gene E6 and E7 Expression in HPV-Positive Human Cervical Carcinoma Cells Using Small Interfering RNAs[END_REF].

Furthermore, in a squamous carcinoma model in New Zealand White rabbits infected with a cottontail rabbit papillomavirus, the role of specific cellular genes in cell invasion has been shown by PTGS [START_REF] Huber | Gene profiling of cottontail rabbit papillomavirus-induced carcinomas identifies upregulated genes directly Involved in stroma invasion as shown by small interfering RNA-mediated gene silencing[END_REF].

Rous sarcoma virus (RSV) causes abnormal proliferation and tissue disorganization in chick embryos. A plasmid encoding a derivative of RSV modified for use as a retroviral vector and either RSV Gag-specific siRNAs or a nonspecific siRNA control have been introduced into the neural tubes of chick embryos by electroporation two days after fertilization [START_REF] Hu | Inhibition of retroviral pathogenesis by RNA interference[END_REF]. The effects were assessed three days later. All embryos electroporated with RSV plus control siRNAs were dead by this time, with abnormal misplaced proliferative cells, whereas those receiving RSV plus Gag-specific siRNAs were indistinguishable from uninfected embryos. Therefore, RSV-induced abnormal cell proliferation and tissue disorganization can be reversed by PTGS [START_REF] Hu | Inhibition of retroviral pathogenesis by RNA interference[END_REF].

The limits of RNA interference

Although RNA interference is an extremely powerful tool, this new technology has several limits. RNA viruses show a high degree of sequence diversity between different genotypes; and there is rapid evolution of quasi-species, by mutation and recombination, and the generation of reassortant genomes in the case of segmented genomes. These are major problems for the development of siRNA-based gene therapies [START_REF] Krönke | Alternative approaches for efficient inhibition of hepatitis C virus RNA replication by small interfering RNAs[END_REF]. In addition, large sections of highly structured, untranslated regions of viral RNA genomes are resistant to PTGS [START_REF] Krönke | Alternative approaches for efficient inhibition of hepatitis C virus RNA replication by small interfering RNAs[END_REF]. A few siRNAs even enhance expression instead of having a silencing effect. Others have an offtarget effect and therefore silence the wrong genes [START_REF] Saxena | Small RNAs with imperfect match to endogenous mRNA repress translation. Implications for off-target activity of small inhibitory RNA in mammalian cells[END_REF][START_REF] Jackson | Expression profiling reveals off-target gene regulation by RNAi[END_REF][START_REF] Kawasaki | siRNAs generated by recombinant human Dicer induce specific and significant but target site-independent gene silencing in human cells[END_REF]. SiRNAs may also cross-react with targets of limited similarity [START_REF] Jackson | Expression profiling reveals off-target gene regulation by RNAi[END_REF]. Escape mutants have emerged after treatment of cells with a single virus-specific siRNA, in particular when cells are infected at high MOI [START_REF] Gitlin | Short interfering RNA confers intracellular antiviral immunity in human cells[END_REF][START_REF] Boden | Human immunodeficiency virus type 1 escape from RNA interference[END_REF][START_REF] Das | Human immunodeficiency virus type 1 escapes from RNA interference-mediated inhibition[END_REF]. The design of multiple siRNAs targeting different regions of the viral genome, in particular well-conserved regions, reduces the probability of generating escape mutants. In addition, some studies have shown that transfection with siRNAs results in IFN-mediated activation of the Jak-Stat pathway and general upregulation of IFN-stimulated genes [START_REF] Bridge | Induction of an interferon response by RNAi vectors in mammalian cells[END_REF][START_REF] Sledz | Activation of the interferon system by short-interfering RNAs[END_REF].

The effect was mediated by dsRNA-dependent protein kinase, PKR, and depended on the concentration of siRNAs [START_REF] Sledz | Activation of the interferon system by short-interfering RNAs[END_REF]. Bridge et al. [START_REF] Bridge | Induction of an interferon response by RNAi vectors in mammalian cells[END_REF] also noted that some shRNAs produced by a lentiviral vector induced an IFN response whereas homologous chemically synthesized siRNAs did not. However, some synthetic siRNAs do induce an IFN response [START_REF] Sledz | Activation of the interferon system by short-interfering RNAs[END_REF]. SiRNAs caused Toll-like receptor 3 to induce type 1 IFN and sequence-independent mRNA degradation in the course of acute herpes simplex virus type 1 infection of keratinocytes [START_REF] Kariko | Exogenous siRNA mediates sequence-independent gene suppression by signaling through toll-like receptor 3[END_REF].

It is therefore recommended to use the lowest effective dose of siRNAs or siRNA-encoding vectors [START_REF] Bridge | Induction of an interferon response by RNAi vectors in mammalian cells[END_REF][START_REF] Sledz | Activation of the interferon system by short-interfering RNAs[END_REF][START_REF] Kariko | Exogenous siRNA mediates sequence-independent gene suppression by signaling through toll-like receptor 3[END_REF].

PTGS suppressor proteins have been identified in plant and animal viruses, although the molecular mechanisms of silencing inhibition are still poorly understood [START_REF] Lichner | Double-stranded RNA-binding proteins could suppress RNA interference-mediated antiviral defences[END_REF]. Flock house virus (FHV), which belongs to the Nodaviridae family, encodes a B2 protein exhibiting a potent silencing-suppression activity in transgenic plants [START_REF] Li | Induction and suppression of RNA silencing by an animal virus[END_REF]. B2 is essential for FHV accumulation in Drosophila cells. Li et al. [START_REF] Li | Induction and suppression of RNA silencing by an animal virus[END_REF] demonstrated that FHV triggers strong virus RNA silencing and that the same virus is equipped with an effective silencing suppressor. It has been suggested that dsRNA-binding proteins, such as the reovirus outer shell protein sigma 3, could suppress PTGS-mediated antiviral defenses [START_REF] Lichner | Double-stranded RNA-binding proteins could suppress RNA interference-mediated antiviral defences[END_REF]. Vaccinia virus and human influenza virus each encode an essential protein that suppresses the RNA silencing basedantiviral response in Drosophila. The respective suppressors, E3L and NS1, are dsRNAbinding proteins inhibiting the IFN-regulated innate antiviral response [START_REF] Li | Interferon antagonist proteins of influenza and vaccinia viruses are suppressors of RNA silencing[END_REF]. These results suggest that PTGS can play a role in nucleic acid-based antiviral immunity in mammalian cells [START_REF] Li | Interferon antagonist proteins of influenza and vaccinia viruses are suppressors of RNA silencing[END_REF].

Conclusions

Most of our knowledge about the molecular mechanisms of PTGS comes from studies in plants, C. elegans and drosophila. In mammals, the mechanisms and the tissue-specific characteristics of PTGS still need to be investigated in greater detail. The role of PTGS as a natural antiviral response in mammalian cells has yet to be confirmed, and the transmission of interference from one cell to another remains an interesting question that should be investigated. The identification of viral proteins as PTGS suppressors in mammalian cells has just started [START_REF] Li | Interferon antagonist proteins of influenza and vaccinia viruses are suppressors of RNA silencing[END_REF] and the various effects of viruses on PTGS in cells need to be studied. Nevertheless, PTGS is already extremely useful as a new approach in viral functional genomics and is already widely used to characterize the role of cellular proteins in the cycles of many viruses. The possibility of partial silencing allows the role of proteins required for cell vability to be studied.

For both preventive and therapeutic effects of siRNAs, it may be useful to reinforce some of the cellular pathways involved in PTGS. In animals, disease prevention by virusspecific siRNAs may be useful. In humans, the therapeutic properties of siRNAs will probably be developed before preventive applications. Today, there remain many problems concerning how to deliver the appropriate amounts of the desired siRNAs to the appropriate tissue, at the right time. These siRNAs, after testing for the absence of toxicity, will have to be stabilized, probably by chemical modifications, in order to obtain long-lasting effects. Despite these current limitations, the siRNA technology, targeting either viral or cellular genes, is very promising for the development of treatment for diseases for which neither vaccines nor efficient therapy are currently available. 1 A schematic model of gene silencing by synthetic siRNAs. Once transfected into cells, synthetic siRNAs are phosphorylated and a helicase, which may be associated with the RNAinduced silencing complex (RISC), leads to siRNA unwinding. The antisense strand of siRNA guides the complex towards the cognate mRNA. The target RNA is cleaved by an endoribonuclease in the RISC in a homology-dependent manner, resulting in mRNA degradation (see [START_REF] Zamore | RNAi: double-stranded RNA directs the ATP-dependent cleavage of mRNA at 21 to 23 nucleotide intervals[END_REF][START_REF] Elbashir | Duplexes of 21-nucleotide RNAs mediate RNA interference in cultured mammalian cells[END_REF] and references in the text).

Legend to Figure

Figure 2

 2 Figure 2

Acknowledgements

The authors are very grateful to Laurent Blondel for his precious help with the figures. This work was supported by grants from the Institut Pasteur.


Jérôme Boéro

Franck Schoefs
email: franck.schoefs@univ-nantes.fr

Bruno Capra
email: bruno.capra@oxand.com

Nicolas Rouxel
email: nicolas.rouxel@equipement.gouv.fr

Jérôme Boero
email: jerome.boero@oxand.com

Risk management of French harbour structures. Part 1: Description of built assets

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

Introduction

Maintenance of harbour assets is a major economic and tourist stake. The challenge of the owners consists in guaranteeing the ageing structures operation (wharves, dry docks, dikes, etc.) with good safety, reasonable costs and availability conditions (AIPCN, 2001;AIPCN, 2008). Moreover, the harbour development opportunities are more and more limited in front of increasing environmental constraints and decreasing available space for low cost development. Currently, the decisions about maintenance are often taken without an overall view of the associated risks. That is why they give place to long and difficult meetings between managers who have various priorities: technical, strategic, financial, etc. Most of the time, maintenance is curative (after unforeseen events) or preventive, with a high cost (anticipation of predictable events) and more rarely, predictive (evolutionary predictions). Decisions are generally based on budgetary, operation and safety constraints. Furthermore, in some cases, structures are operated in more severe service conditions than initially forecasted. In these conditions, owners could face two major risks: uncontrolled maintenance costs or uncontrolled safety and unavailability costs. To deal with this problem, the GEROM project (Risk Management of maritime and river structures in harbours) was created within the GIS MRGenCi (Grouping of Scientific Interest "Risk management in Civil Engineering") and lies on a partnership between Oxand and the Research Institute in Civil and Mechanical engineering of Nantes. The GEROM project was undergone from 2006 until 2009. It aims to: a) Collect all the elements necessary for the development of an optimized methodology of technical management. b) Help owners draw and optimize their decisions concerning the durable management of their structures. In the first phase, with the support of the CETE de l'Ouest (Ministry of ecology, energy, sustainable development and town and country planning), a national inquiry was carried out with owners about the technical management of the maritime harbour structures. This national inquiry's preparation was based on the FMECA method (Failure Mode Effects and Criticality Analysis) [START_REF] Villemeur | Sûreté de fonctionnement des systèmes industriels. Fiabilité, facteurs humains, informatisation[END_REF]HALDI, 1997) that is more and more developed for hydraulic or coastal infrastructures [START_REF] Sorensen | Risk-based optimization and reliability levels of coastal structures[END_REF][START_REF] Peyras | Étude de la sûreté de fonctionnement d'un aménagement hydraulique de génie civil. Application à des ouvrages de protection contre les inondations de la ville de Nîmes. Fiabilité des matériaux et des structures, analyse de risques[END_REF]BILLARD et al., 2006;BILLARD et al., 2007;BOERO et al., 2006), in particular to define maintenance programs (inspection, common maintenance and repair). Our objective was then to identify and acquire information which can be integrated into a risk analysis applied to harbour structures. Due to the multiple topics addressed during the national investigation, results are presented in two parts. This paper deals with the first part and is focused especially on: a) The structures' functions (dikes, locks, dry docks, quays, landing stages, bridges, buildings, roads, etc.) and the position of the structures in the system (functional analysis).

b) The strategic importance for economic and touristic developments, national defence, etc., safety of the installations, security of the persons, environmental protection, control of the direct costs (maintenance) and indirect costs (availability, public image) (consequences, stakes analysis). c) The construction techniques, ages, materials, geometry, environment (factors affecting the frequency of failure modes).

Progress of the national inquiry on the harbour assets management

Objectives

The inquiry objectives were to: a) Facilitate an experience sharing between owners of harbour structures and the various participants of this project. b) Compile an overview of the existing French national built assets, current maintenance practices (maintenance politics and strategies, experience feedback on the harbours' pathologies, efficiency of technical repair, etc.) and needs in this domain.

Spatiotemporal perimeter

This inquiry was performed from January 24 th to May 12 th 2006, and was completed in the first quarter 2007. The geographical perimeter covers a total amount of 7 Autonomous Harbours (AH), 16 National Interest Harbours (NIH) and 3 Military Harbours (MH) located along the French metropolitan coast. The status of AH have changed since the law of July 4th, 2008 and since its implementing decrees, in particular those of October 9th, 2008. The 532 harbours, that have been decentralized since 1984, and managed by the General Councils of departments or Municipalities, were not integrated in this study because of their large number. However, some of them were interviewed (without inquiry's support) in order to have an overall view. Further to the recent decentralization of the NIH since January 1 st 2007, the status of NIH no longer exists. In this article, this status was preserved to make the distinction with harbours already decentralized in 1984. The referees are technical managers of harbour structures, and the following sources were used to contact them: a) The partners of the GEROM project. b) The maritime structures' club (meeting reports). c) The AITPE 2005 (directory of the Association of the State Public Works Engineers). d) The harbours websites.

Inquiry's process

The inquiry's process comprises several steps starting with researching potential contacts, phoning to confirm contacts and mailing a short questionnaire for an interview of approximately 2 hours. This process obtained a very good level of return. In fact, of the 23 contacted harbours (AH, NIH, MH), 19 returned the filled questionnaire and were interviewed, that represents approximately 85% of the targeted owners.

Themes

The various selected themes correspond to the different stages of the built assets management cycle: a) Know: which built assets have to be managed? b) Organize: what are the available resources and how must they be structured? c) Estimate: what is the performance of the built assets with regard to their functions and what are the associated risks? d) Forecast: how to predict the evolution of risks? e) Evaluate: what are the acceptable risks over the short and long-term? f) Define: what are the actions to control risks? g) Plan: which are the actions to do first, considering the maintenance constraints (financial, technical and exploitation)? h) Capitalize: what information must be capitalized to optimize the management cycle of the built assets?

Role and importance of the French harbour system

The French harbour system has an essential role: on the one hand for French business, tourism and industry; and on the other hand for European defence.

Military harbours

Along with Great Britain, France is the only State member of the European Union that owns a navy with world vocation: it should be able to be present on all the seas of the world and to deploy nuclear deterrence (MARINE NATIONALE, 2006). In addition, military naval sector (ships construction and maintenance) is an important activity for the balance sheet of France's foreign trade. In metropolitan France, the main naval bases are: Brest, Cherbourg and Toulon.

Commercial harbours: goods, passengers

Three quarters of world trade occurs by sea. Sea transport is in perpetual growth, especially since it remains the most economical (between 0.3 and 1.6% of the final price of the product) and ecological method of transport (CLUSTER MARITIME FRANCAIS, 2006).

France is the 5 th commercial world power (5 th exporter and 6 th importer) based on the value of the goods. Two-fifth of the tonnage (40.6%) and one fifth of the value (20.2%) of France's foreign trade were transported through a seaport (DGMT, 2006). Classification of French ports among the European ports is presented in figure 1. Autonomous Harbours treat more than 80% of sea traffic goods. National Interest Harbours treat the rest and more than 80% of the passenger's traffic. Consequently, stakes associated with military and commercial harbours rest on a set of installations for which maintenance is necessary.

Functional analysis

The studied system includes all the installations which fulfil the harbours' functions relative to ships, or to the ground operations (primary activities). The part of the built assets which contributes to the development of secondary activities (industries, tourism, town planning and service, etc.) is also considered. All installations that are likely to interact with the primary and secondary activities are presented in figure 3.

The role of the system can be assured only if all the functional domains are successful.

In example, for a commercial harbour: a) The ship must be able to fasten quickly and easily to its berthing and mooring structure. For this reason, the ship is sometimes obliged to cross diverse docks, sluice and locks before arriving alongside the quay.

b) The goods must be able to be quickly transhipped or, if necessary, stored for a more or less long time in the port with the aim of its forwarding, all of this with the lowest cost. c) Finally, goods either go into an industrial transformation process inside the ports boundaries, or have to pass in transit through the port to connections with the outside transport networks by ground transportation (roads, railroads) and\or ways of inner navigation.

Quantitative patrimonial analysis

In this paper, we focus on the berthing and mooring works. Cranes, pavements, warehouses and sheds are not included in our analysis. Note that built assets belong mainly to public authorities and only some wharves are owned by private companies. In this analysis, only the length of the structures is considered as an indicator for the ranking of built assets. This allows for the comparison of berthing and mooring works realized with various construction techniques. Note that the "height × length" area is more adapted than the length, but this information was not available at the time of the inquiry.

Typological analysis

This information was not available from military harbours, and therefore this analysis only considers AH and NIH. The distribution, in linear kilometres, of the construction techniques used for the berthing and mooring's structures is presented in figure 4. They are classified from right to left in order of chronological appearance but, after the six first ones, techniques coexist. The great majority of the structures are masonry, followed by concrete blocks, reinforced-concrete caissons, steel piles supported wharves, steel sheet piles seawalls and diaphragm walls. This figure illustrates the inventiveness of engineers confronted with the challenges of designing maritime structures; however it also means that owners are faced with delicate management decisions with regards to the principles of mechanical functioning and multiple failure modes.

A part of the answer is in the monitoring (survey) of structures and the instrumentation of the more recent ones (DELATTRE & MESPOULHE, 1999;GATTERMANN et al., 2001;[START_REF] Schoefs | Stratégie d'instrumentation pour la gestion optimisée des ouvrages portuaires[END_REF]YANEZ-GODOY & SCHOEFS, 2006;YANEZ-GODOY et al., 2008), especially to re-evaluate their reliability (YANEZ-GODOY et al., 2006). This double level of heterogeneity (concept and material) is one of the issues that the GEROM project wishes to address.

Age analysis

The distribution of harbour infrastructure ages is presented in figure 5 for the three types of owners. Even if the main part of the structures was built more than 25 years ago, the owners don't have equivalent built assets: a) NIH manage built assets for the main part dating before the twentieth century (essentially in masonry). b) MH have built assets essentially bound to the reconstruction period after the Second World War, and thus previous to 1955. c) AH have more recent built assets that appeared mainly between 1955 and 1980. This can be explained by a more recent status and a growth strongly linked to economic development. To compare the economic role of these structures, we consider the weight of goods as published by DGMT (2006). Through the ratio of million tons of raw goods by linear kilometre (Mt / km), the inquiry supplied interesting data: a third of NIH treats a very weak tonnage under 100 t / km, another third, a ratio of the order of 0.5 Mt / km, and the rest a 1 Mt / km ratio; AH have a ratio exceeding 2 Mt / km with 3 Mt / km in average. One National Interest Harbour has a very particular profile due to the Trans-Channel traffic fluidity and dynamism and reaches 6 Mt / km. The economic analysis needs specific studies in every harbour and it is not discussed here. This information could be completed by a more specific analysis that considers the value and nature of goods for instance. However, as this information is highly likely to vary, the authors prefer not to conduct further investigation along these lines.

Conclusions

This article presents the first part of the results of the national inquiry of the technical management of maritime harbour structures undertaken in 2006-2007. Results show a significant heterogeneity between the structures in age and in construction technique.

The great majority of the structures are in masonry which corresponds to the oldest part of the built assets. After the Second World War, other construction techniques were used due to the characteristics of ships, site conditions and economic factors.

Consequently the built assets are varied.

To perform a more detailed analysis, indicators other than length can be quantified in order to specify the maintenance requirements. For instance, the surface in square kilometres could be selected in future works as a more accurate factor to quantify maintenance stakes.

Figure 1 .

 1 Figure 1. Classification of the main European ports according to their raw tonnage (millions tons) in 2000 (Atlas permanent de la Mer et du Littoral n°5-Littoral français 2000, p38, CNRS et Géolittomer -LETG UMR 6554).

Figure 2 .

 2 Figure 2. French ports traffic in 2000 (Trafic 2000 des ports maritimes métropolitains et des DOM -TOM, ISEMAR, July 2001).

Figure 3 .

 3 Figure3. Activities in interaction with the structures composing the harbour system.

Figure 4 .

 4 Figure 4. Distribution of construction techniques of berthing and mooring structures.

Figure 5 .

 5 Figure 5. Age distribution of berthing and mooring structures.

  These results can be further analyzed by studying the amount of investment in nonmilitary harbour facilities published in March 1994 by the Economic Observatory of

	Transport Statistics. Even if investments concern all harbour infrastructures, the trend is
	the same: in constant francs (year for reference: 1980), approximately 1400 million
	francs (213 million euros) were invested from 1957 to 1970, then investments increase
	strongly until 1975 with 2500 million francs (381 million euros) in average, exceeding
	even 3000 million francs (457 million euros) in 1975 and levelling out at the end of the
	80s at a value of 700 million francs (107 million euros).
	5.3 Economic analysis
	Roughly 205 km of berthing and mooring structures were analyzed during the inquiry;
	64% (130 km) are managed by AH, 24% (50 km) by NIH and 12% (25 km) by MH.

Acknowledgements

This study is led within GEROM (contact: franck.schoefs@univ-nantes.fr), project financed by the company OXAND and led within the Grouping of Scientific Interest MRGenCi. The authors thank the CETE de l'Ouest for its contribution to the inquiry phase and all the owners who were kind enough to grant time to this project. AIPCN (2001)