Y H Shen
email: yhshen@city.ac.uk

S Pal

J Mandal

T Sun

K T V Grattan

S A Wade

Stephen F Collins

Gregory W Baxter

Bernard Dussardier

Gérard Monnom

; J Mandal

; S Pal

; T Sun

V Grattan

; G Monnom

Investigation of the photosensitivity

Keywords: Fiber Bragg Grating (FBG), fluorescence spectra, crystallization

Introduction

UV-induced Fiber Bragg Gratings (FBG) have been shown to be very important components for use in both the telecommunications and fiber optic sensing fields, especially over the past ten years. A number of comprehensive reviews of the principles, performance and applications of these devices have been published recently [START_REF] Othonos | Fiber Bragg Gratings: Fundamentals and applications in telecommunications and sensing[END_REF][START_REF] Kashyap | Fiber Bragg Gratings[END_REF]. In addition, considerable effort has been expended on the study of the issue of the thermal stability of FBGs and the consequent effects on performance [START_REF] Erdogan | Decay of ultraviolet-induced fiber Bragg gratings[END_REF][START_REF] Baker | Thermal decay of fibre Bragg gratings written in boron and germanium codoped silica fiber[END_REF][START_REF] Dong | Thermal decay of fiber Bragg gratings of positive and negative index changes formed at 193 nm in a boron co-doped germanosilicate fiber[END_REF][START_REF] Kannan | Thermal stability analysis of uv-induced fiber Bragg gratings[END_REF][START_REF] Chisholm | Effects of thermal annealing on Bragg fibre gratings in boron/germania co-doped fibre[END_REF], which is key to many of the practical applications that have been demonstrated. These researchers have considered the characteristic differences seen between FBGs written into various fiber types. For example, writing FBGs into Sn-doped silica fiber, which has an enhanced photosensitivity, results in a FBG able to sustain temperatures as high as 800 0 C [START_REF] Brambilla | Photorefractive index gratings in SnO2:SiO2 optical fibers[END_REF], while FBGs written in Boron/Germanium (B/Ge) co-doped silica fiber had a much lower highest sustainable temperature, typically only 300 0 C [START_REF] Erdogan | Decay of ultraviolet-induced fiber Bragg gratings[END_REF].

Photosensitive fiber with additional fluorescent ion doping, such as Er 3+ , is valuable both in the sensing field and in laser applications. The combination of the peak wavelength interrogation technique in the reflection spectrum of an FBG written into a fiber when the important fluorescence characteristics are examined, such as the fluorescence lifetime and the fluorescence intensity ratio, has enabled fiber probes to be designed and used for the simultaneous measurement of temperature and strain [START_REF] Forsyth | Dual temperature and strain measurement with the combined fluorescence lifetime and Bragg wavelength shift approach in doped optical fiber[END_REF][START_REF] Pal | Bragg grating performance in Er-Sn-doped germano-silicate 16 fiber for simultaneous measurement of wide range temperature (to 500 C) and strain[END_REF].

It is likely that any structural change within the glass of the doped fiber will result in a shift of the fluorescence spectrum, and work by Henderson and Imbush has shown that a process of crystallization of the glass material will result in the narrowing of this spectrum [START_REF] Henderson | Optical spectroscopy of inorganic solids[END_REF]. For optimum applications in sensing, it is important to understand comprehensively the possible structural changes in the fiber that occur during the process of high temperature annealing and UV exposure.

To the authors" knowledge, no detailed investigation has been published into the structural transformations that occur in the fiber or of the silica glass from which it is fabricated using fluorescence-based spectral analysis, although the techniques of electron spin resonance (ESR) analysis [START_REF] Griscom | Defect structure of glasses: Some outstanding questions in regard to vitreous silica[END_REF] and Raman spectroscopy [START_REF] Dianov | UV-irradiation-induced structural transformation of germanosilicate glass fiber[END_REF] have previously been used to explore the defects, the structural transformations and the photosensitivity mechanisms in the UV-exposed photosensitive fibers.

As it is relatively easy to excite fluorescence from an Er doped fiber by using light from a comparatively inexpensive laser diode (LD), and then record its emission spectrum for analysis using an optical spectrum analyzer (OSA), the approach of fluorescence spectral analysis would seem to be both a relatively simple and practically valuable mechanism to reflect such changes of the matrix structure in the glass fiber. Potentially, therefore, it could be used to indicate the onset of a possible crystallization processes, and this approach is thus used in this work. The aim has been to monitor the fluorescence under the situation where there is a change in the crystallization process occurring in the photosensitive silica fibers at high temperatures and to explore both the effects of UV exposure and high temperature annealing, again through examining the fluorescence characteristics of the fibers. Thus, in this paper, an investigation into the effects of the changes in the fluorescence spectrum, when exposed to high temperatures, has been carried out. To do so, the fluorescence spectra of three Er 3+ -doped fibers at high temperatures were recorded and the results were related to the onset and subsequent characterization of the changes occurring in the fiber material. The effect of total UV exposure was also taken into account, by comparing the spectral characteristics of the same sample fiber both with and without UV exposure to the laser radiation, at a familiar grating wavelength of 248 nm. When comparing these results with the highest sustainable temperatures of the FBGs written into these fibers, it was found that there is a close relation between the temperature at which the process of crystallization began, and the highest sustainable temperature for FBG operation.

High temperature sustainability of FBG

Optical fiber used in this work

A number of FBGs were written into a range of doped fibers for use in this work. To do so, the FBGs inscribed into several such different photosensitive fibers were fabricated by exposing them to UV emission from a KrF excimer laser (Braggstar-500 supplied by Tuilaser AG) at 248 nm through a phase-mask (pitch period:1060 nm, supplied by OE-Land Inc., Canada). A cylindrical plano-convex lens (focal length 20 cm) was used to converge the laser beam onto the photosensitive fiber, where the phase-mask was placed immediately in front of the fiber to form a light interference pattern between the 1st positive and negative orders of the diffraction pattern. The fibers used were both from commercial sources and specially fabricated and included boron/germanium co-doped fiber (B/Ge fiber, fiber type: PS1250/1500, supplied by Fibercore Ltd., UK), Er doped high germanium fiber (Ge/Er fiber, type A021, specially fabricated at the University of Nice, France, with a nominal doping concentrations of Er ~2700 ppm and GeO 2 ~20 mole%) and Sn/Er co-doped germansilicate fiber (Sn/Er fiber, type A022, made also at the University of Nice, France, with a nominal doping concentrations of Er ~1000 ppm, GeO 2 ~10 mole% and SnO 2 of ~ 0.2 mole%). This Sn/Er fibre was fabricated with a Ge concentration of ~10 mole% (as the main cause of the refractive index increase, where n is in the range 0.016 -0.018) and also it contained ~ 4 times as much Al as Er (respectively about 4000 and 1000 mol ppm). The writing times of the FBGs were controlled for each sample until the FBG achieved a high level of reflectivity and this was monitored using an optical spectrum analyzer (OSA-Agilent HP86140A). For the B/Ge co-doped fiber, a time of about 50 seconds was required for the FBG to reach its highest reflectivity, of over 99.9%, when a laser repetition rate of 100 Hz and an energy per pulse of 12 mJ was used. For the Ge/Er co-doped fiber, the time needed was about 2 minutes to reach the highest value of about 96%.

Finally, for the Sn/Er co-doped fiber, it took about 12 minutes of exposure to achieve the maximum reflectivity of 91.5%. All the fibers from the University of Nice contained the same amount of Al, this being ~ 4-5 times the concentration of Er. In Figure 1, a typical transmission spectrum of the FBG written into the B/Ge fiber is shown.

Calibration

The gratings fabricated in this way were then placed loosely in a silica tube and put into a Carbolite tube oven in order to observe their thermal decay characteristics over a period of time, taking results in a series of isothermal steps starting from 100 0 C, with increments in steps of initially 100 0 C, and then 50 0 C. At each temperature, a fast decay of the grating characteristic was seen, followed by a substantial slow decay being observed. At low temperatures, this decay was so slow that there was almost no observed change in the reflectivity, and thus of the modulation of the refractive index of the FBG after annealing for 24 hours. The reflectivity decays of the FBGs studied after annealing are illustrated in Figure 2.

It is obvious from the data produced that the highest sustainable temperatures for the different kinds of FBGs studied are quite different one from another. The grating effectively disappeared on reaching a temperature of 350 0 C for B/Ge fiber and at 600 0 C for Ge/Er fiber, but the equivalent temperature for the loss of grating reflectivity was over 850 0 C for Sn /Er fiber. To examine why this occurs, it is important to consider any effects that may arise from the fiber fabrication process. A valid explanation appears to be that a matrix structure transformation has occurred in the glass due to the process of cation hopping occurring during UV exposure [START_REF] Shen | High temperature sustainability of the strong FBGs written into Sb/Ge co-doped photosensitive fiber and its decaying mechanism involved during annealing[END_REF], and that such a transformation could cause the difference in the highest sustainable temperature for the various kinds of FBGs used in this work. This has also been considered from the viewpoint of the enhanced photosensitivity of the B/Ge co-doped fiber [START_REF] Williams | Enhanced UV photosensitivity in boron codoped germanosilicate fibres[END_REF].

Fluorescence spectral shifting in the Er doped photosensitive fibers after annealing at high temperatures

As mentioned above, the fluorescence spectral shift that occurs after annealing and UV exposure, may be explored as a means to reflect the change in the matrix structure of the fiber. This fluorescence spectral analysis approach was used in this work, with the aim of monitoring the change processes occurring in the photosensitive silica fibers, exploring in particular the effects of UV exposure and high temperature annealing on the fibers. The method is advantageous to use as it is comparatively easy to excite the fluorescence from the Er doped fiber wherever it is installed or in the laboratory by using instrumentation based on a readily available commercial LDs and recording the emission spectrum -optical filters may be used to isolate specific spectral components for comparative measurements.

Spectra shifting measurement on the non-UV exposed fiber

The three kinds of Er doped fibers discussed were used in the experiments carried out to monitor the fluorescence spectra, these being the Ge/Er and Sn/Er fibers, using another Er doped low germanium fiber (Er fiber, Er concentration: 200 ppm, core codopant: Ge-Al-Si) for comparison. All the fibers used were single mode (SM) on the 1500 nm band. For the measurement of the fluorescence spectra, a LD working at 980 nm with a fiber pigtailed power output of 20 mW was used to excite the fluorescence of the fiber, this being recorded in this work by using the OSA.

Initially the fibers (of length for each fiber of 150 mm) were spliced to conventional SM "telecom" fibers at both ends, put into a silica tube and then placed in the middle of a well-characterized and calibrated tube oven. The fibers were then annealed at temperatures from 500 0 C to 1050 0 C, using incremental steps of 100 0 C. For consistency, the annealing time at each temperature was controlled and stabilized for 2 hours. After that time, the oven power was turned off and the fibers were allowed to cool naturally in the oven to room temperature. The fluorescence spectra of the fibers (before and after annealing at each of the annealing temperatures), covering the wavelength range of 1450 nm to 1650 nm, were recorded at room temperature. In addition, fluorescence spectra were also obtained at the beginning and at the end of the annealing process, at each of the annealing temperatures used.

The fluorescence spectral shift with the annealing temperature is depicted in Figure 3. In Figure 3(a), the spectra of the Ge/Er fiber (after annealing) are presented, where a spectral shift with the changing annealing temperatures can be clearly seen. These shifts were mainly discernible through the change of the spectral width and the relative intensity of the smaller spectral peak at ~1550 nm. From 500 0 C to 900 0 C, it was found that the spectral width gradually became larger and the initially smaller peak stronger. However, beyond 900 0 C, the spectrum remained almost unchanged until a temperature of 1050 0 C was reachedthe upper temperature limit of these experiments, set by the characteristics of the oven used in the work.

In Figure 3(b), the fluorescence spectra for the Sn/Er fiber, before and after annealing, are presented. Similar spectral shifts to those above could be seen. However, in this case it was at 1050 0 C, (a temperature which was 150 0 C higher than for the former case), the spectral width was found no longer to be increasing, but became narrower and with that the intensity of the smaller peak became weaker. For comparison, the spectral shift of the third Er fiber is presented in Figure 3(c). It was found that the spectral narrowing occurred at a much lower temperature than for the other two fibers, at a temperature of around 600 0 C.

Spectral shifting measurement on the UV-exposed fiber

A further series of experimental measurements was performed on the UV-exposed fibers. In order to create the same conditions in the material to those when the FBGs were written, similar fibers (using the same length of 150 mm for each fiber) as were used in the experiments discussed above in Section 3.1(for non-UV-exposed fiber) were then exposed to UV laser emission, before they were annealed in the oven. This was done by irradiating the fibers, piece by piece, with intense UV laser emission (using the same laser as was used for writing the FBGs) so that the whole fiber was exposed to the UV radiation from the laser in this process. For each segment of fiber of 6 mm length, the total UV energy dose from the laser was 48 J (8 mJ per shot, frequency 100 Hz, exposure time 60 seconds). The fluorescence spectra of the UV-exposed fiber, together with the spectrum before UV exposure, are presented in Figure 4, with Figure 4(a) showing the situation for the Ge/Er fiber and Figure 4(b) for the Sn/Er fiber. It is interesting to note that the spectral width of the fluorescence spectrum of the Ge/Er fiber did not change, but the intensity of the smaller peak did. However, no observable spectral change was found for the Sn/Er fiber, which may explain the different experimental phenomena discussed in the next section on the spectral shifting of the UV exposed fibers, when they were annealed at high temperatures.

In Figure 5(a), the spectral shifting of the Ge/Er fiber, after annealing is presented. The conditions used for annealing are the same as those for the non-UV exposed fiber. It can be seen that beyond 900 0 C, the spectrum reached its greatest width and the smaller peak its highest intensity and beyond that temperature, it became narrower in width and the smaller peak weaker, at both 1000 0 C and 1050 0 C. This is quite different from the result obtained from similar but non-UV-exposed fibers of this type. However, for the Sn/Er fiber, the spectral shifting is almost the same as that for the non-UV-exposed fiber (see Figure 5(b)).

The shift of the full width of half maximum (FWHM) of the fluorescence spectra, based on the data above, is shown in with Figure 6(a) for the Ge/Er fiber and Figure 6(b) for the Sn/Er fiber. It is evident that the change of FWHM that is observed strongly depends on the annealing temperature and the prior history of UV exposure of the fiber.

Interpretation of the fluorescence spectra shifting of the Er doped photosensitive fiber

It is important to consider carefully the likely origin of the fluorescence spectral shift of the Er-doped photosensitive fibers used, after the high temperature annealing and UV exposure has been carried out. These spectral shifting phenomena that have been observed mainly relate to the change of the spectral width and the smaller peak intensity observed in these experiments.

For non-UV-exposed Ge/Er fiber, the spectral width increase occurred after annealing had been carried out at temperatures below 900 0 C. Such an increase may be attributed to stress relief within the fiber during annealing, as stresses arise from the optical fiber drawing process and this effect has been previously documented [START_REF] Young | Analysis of composites using Raman and fluorescence microscopy -A review[END_REF]. Beyond 900 0 C, the spectral width remained almost unchanged, which suggests that the stress had been fully relieved (before the annealing temperature exceeded 900 0 C) and no significant change occurred above that temperature. However, it would appear that there was no evidence of a crystallization process occuring during the annealing, at least until a temperature of 1050 0 C was reached, as prior work implies that the crystallization of the glass would normally result in a narrowing of the fluorescence spectrum [START_REF] Henderson | Optical spectroscopy of inorganic solids[END_REF] that was not observed.

For the UV-exposed Ge/Er fiber, a similar spectral widening phenomenon could be found with annealing at temperatures below 900 0 C, which likely resulted from the same type of stress relief process discussed above. The main difference observed from the case of the non-UV-exposed fiber arose in the fluorescence spectrum becoming narrower after annealing at 1000 0 C and 1050 0 C (see Figure 6a). This narrowing phenomenon is indicative of the suggestion that the fiber had experienced, to some extent, a process of crystallization during annealing [START_REF] Henderson | Optical spectroscopy of inorganic solids[END_REF]. It is reasonable to believe that the UV-exposure process for this Ge/Er fiber did result in some structural transformation of the photosensitive fiber which, as a result, made it more susceptible to crystallization. This viewpoint is also supported by the observed change of smaller peak in the fluorescence spectrum, after the Ge/Er fiber was exposed to the UV laser emission, as is illustrated in Figure 4(a).

In the case of the Sn/Er fiber, the UV-exposure seemed to have little (or no) effect on the fluorescence characteristics of the fiber, as no real difference could be observed in the spectrum of the UV-exposed and non-UV-exposed fibers after they both experienced high temperature annealing.

The fluorescence spectra became wider at temperatures below 1000 0 C, which could indicate that the expected stress relief process was occurring within the fiber. However, as discussed earlier, the spectral narrowing in this temperature region may also result from the crystallization process occurring in the fiber.

Compared with the Ge/Er and Sn/Er fibers, the Er fiber showed a much greater susceptibility to these temperature effects. This may most likely be attributed to its composition, as the fiber data sheet showed Al was the main co-dopant within the fiber and only a low concentration of Ge (< 3%) and no Sn was used in its fabrication.

Based upon the data and analysis above, a likely explanation for the effects seen is that the fluorescence spectral shifting that was observed has mainly resulted from the process of the stress relief, followed by crystallization of the fiber during the high temperature annealing process. The different compositions of the fiber, as well as the UV-exposure before annealing, appear to relate in a consistent way to the occurrence of crystallization of the fiber at these high temperatures.

Effect of the crystallization process on the high temperature sustainability

An analysis of the fluorescence spectral shifting, considered above, can shed light on the different temperature sustainability of the Ge/Er and Sn/Er fibers. This is particularly relevant for high temperature FBG-based sensors. Comparing the temperature (Tc), at which the crystallization process begins, and the highest sustainable temperature (Ts) of the FBG, a relationship can be deduced. For the Ge/Er fiber (UV-exposed), the crystallization process appeared to begin at 900 0 C, and for the Sn/Er fiber, it began at above 1000 0 C. The corresponding maximum sustainable temperatures for the FBGs written in the fiber were 700 0 C and 850 0 C respectively. This suggests that there is a connection between the higher temperatures at which the crystallization process began and the higher temperatures which are reached before the FBG was annealed out. The differences between the values of Tc and Ts for these two kinds of fibers were all consistently in the range of 150 to 200 0 C. Thus, it is reasonable to consider from the spectral data observed, that there is a close relation between the crystallization process of the UV-exposed fiber material and the highest temperature the FBG could sustain and still operate as an effective reflective device.

Further analysis of the experimental arrangement used has found that the inhomogeneous temperature distribution that naturally occurs within the tube oven could only be responsible for a small part of the difference between Tc and Ts. For example, the results of the measurements of the temperature within the commercial tube oven used indicated that the temperature distributions are quite similar, when the oven center temperature varied from 700 0 C to 1050 0 C. The temperature gradients from the center to the end (8 cm from the center) were all close to 40 0 C, even with the range of different center temperatures used. The average temperature that the photosensitive fibers experienced should be within the same bounds, giving essentially the same value of temperature difference at the end, for the same nominal oven temperatures.

By applying the model of cation hopping to the decay of the FBG as presented in [START_REF] Shen | High temperature sustainability of the strong FBGs written into Sb/Ge co-doped photosensitive fiber and its decaying mechanism involved during annealing[END_REF] and comparing with the results shown above, a possible explanation for the experimental observation arises. The connection of the process of spectral narrowing in a specific fiber material and the highest sustainable temperature of the FBG written into this fiber relates to the similarity of the activation energy needed for cation hopping and the nucleation energy needed for crystallization, these all being closely related to the matrix structure of the silica fiber.

The process of crystallization occurring during high temperature annealing was observed by checking the fiber material after annealing with an X-ray analysis approachit can even be observed directly by eye. However, due to the existence of surface crystallization of the fiber during high temperature annealing, it is difficult to distinguish the surface transformation from the change that has occurred in the fiber core. Thus, the initial temperature at which the crystallization process began still remains an issue to be confirmed by other experimental measurements, and thus is the subject of on-going work.

Discussion

An investigation of the highest sustainable temperatures of several FBGs has been carried out by undertaking thermal annealing tests in a tube oven. The fluorescence spectra from a series of Er 3+ doped photosensitive fibers were recorded and cross compared after annealing at various temperatures, and before and after UV exposure. Analysis of the results indicates that the spectral shifting of the Er doped photosensitive fibers correlates with the crystallization temperatures of the fibers studied. The work shows the benefit of introducing Sn into Ge/Er fibers, even at low concentrations, to improve the thermal stability of the FBGs. In the fibers used from the University of Nice, the Sn concentration is < 1 mol%.

Experimental results from the annealing of FBGs at high temperatures have shown that the Sn/Er fiber had a very high sustainable temperature, of around 800 0 C. Results from the fluorescence spectral analysis have also indicated that the UV-exposure had little effect on the crystallization process observed. Taking close account of the analysis of the fluorescence characteristic may be useful in determining the most suitable doping compositions of the fiber to achieve a highly stable photosensitive fiber for the simultaneous measurement of temperature and strain, and may lead to better understanding of the way to design for high temperature and FBG-based sensors.

The work carried out suggests that it may be valuable to investigate further the effects of different levels of UV exposure on photosensitive fiber by means of fluorescence spectral analysis.

As the UV fluences used play an important role in the writing of the FBG, the monitoring of the change in the fluorescence spectra with the accumulated UV dose may led to a better understanding of the mechanisms involved in FBG creation, and thus their important high temperature sustainability. At the current stage, it is still not fully clear how the nucleation process affects the decay of the FBGs, since the writing mechanisms of FBGs are still not fully understood, although several kinds of models, including the color center model and the compaction model, have been presented previously [START_REF] Othonos | Fiber Bragg Gratings: Fundamentals and Applications[END_REF]. Obviously, the cation hopping model recently presented by the authors in [START_REF] Shen | High temperature sustainability of the strong FBGs written into Sb/Ge co-doped photosensitive fiber and its decaying mechanism involved during annealing[END_REF] still needs further experimental research and verification.

Acknowledgement

This work was supported through several schemes and was partly supported by the Science & Technology Project of Zhejiang Province, China (Project No.011106205). Funding from the Engineering and Physical Science Research Council (EPSRC) through a number of schemes and for the collaborative research work between City University and China is also appreciated.

List of Figures

Figure 1 Figure 2 .

 12 Figure 1 Typical transmission characteristics of an FBG written at 248 nm in B/Ge codoped silica

Figure 3 Figure 4 Figure 5 Figure 6 FFFigure 3 FFigure 4 FFigure 4 FFFigure 5 F

 34563445 Figure 3 Fluorescence spectra shifting of the non-UV exposed fibers after high temperature


Serge Defrance

Anne-Marie Kermarrec

Erwan Le Merrer

Nicolas Le Scouarnec

Gilles Straub

Alexandre Van Kempen

Efficient peer-to-peer backup services through buffering at the edge

The availability of end devices of peer-to-peer storage and backup systems has been shown critical for usability and for system reliability in practice. This has led to the adoption of hybrid architectures composed of both peers and servers. Such architectures mask the instability of peers thus approaching the performances of client-server systems while providing scalability at a low cost. In this paper, we advocate the replacement of such servers by a cloud of residential gateways, as they are already present in users' homes, thus pushing the required stable components at the edge of the network. In our gateway-assisted system, gateways act as buffers between peers, compensating for their intrinsic instability. This enables to offload backup tasks quickly from the user's machine to the gateway, while significantly lowering the retrieval time of backed up data. We evaluate our proposal using real world traces including existing traces from Skype and Jabber as well as a trace of residential gateways for availability, and a residential broadband trace for bandwidth. Results show that the time required to backup data in the network is comparable to a server-assisted approach, while substantially improving the time to restore data, which drops from a few days to a few hours. As gateways are becoming increasingly powerful in order to enable new services, we expect such a proposal to be leveraged on a short term basis.

I. INTRODUCTION

While digital data clearly dominates, backup is of the utmost importance. More specifically, online (i.e. off-site) backup is often preferred over simple backup on external devices as it ensures data persistence regardless of the damage cause (e.g. failures, burglars or even fires). To enable their deployment, online backup systems should run in the background and provide reasonable performances so that archives can be stored safely in reasonable times. While cloud backup systems are increasingly adopted by users (e.g. Amazon S3 or DropBox), their peer-to-peer alternatives, potentially offering virtually unlimited storage for backup [START_REF] Bolosky | Feasibility of a Serverless Distributed File System Deployed on an Existing Set of Desktop PCs[END_REF], [START_REF] Huang | FS2: dynamic data replication in free disk space for improving disk performance and energy consumption[END_REF], are still not appealing enough performance-wise, as e.g. retrieval times for saved data can be an order of magnitude higher that the time required for direct download [START_REF] Pamies-Juarez | Availability and Redundancy in Harmony: Measuring Retrieval Times in P2P Storage Systems[END_REF].

Indeed, peer-to-peer backup systems are limited by the low to medium availabilities of participating peers and by the slow up-links of peers' network connections. This limits the amount of data that peers can transfer and places peer-to-peer systems way behind datacenter-based systems [START_REF] Toka | Online Data Backup: A Peer-Assisted Approach[END_REF]. Not only this may impact the reliability of the stored content but also this does not provide a convenient system for users. We focus on this problem and investigate a new way of performing efficient backup on commodity hardware in a fully peer-to-peer way.

In this paper, we propose a new architecture for peer-to-peer backup, where residential gateways are turned into a stable buffering layer in between the peers and the Internet. The residential gateways are ideal to act as stable buffers: they lay at the edge of the network between the home network and the Internet, and are highly available since they remain powered-on most of the time [START_REF] Valancius | Greening the Internet with Nano Data Centers[END_REF]. Our approach relies on the high availability of gateways to compensate for the end peers instability. Our approach enhances the backup system's performance along two lines:

• The network connection can be used more efficiently (i.e. the available bandwidth can be exploited typically 21h/day instead of only 6 to 12h/day on average). This leads to significant enhancements. For example, we observe that the time to backup a 1GB archive is reduced from around one week in a pure peer-to-peer system to around one day in our system. • Additionally, the gateways, offering a high availability (86% on average, according to our measurements), can act as rendezvous to allow any two peers to communicate efficiently, even if they are not up at the same time. In our application, this enhancement mainly has an impact on the time to restore, which is reduced from a few days to a few hours.

Our proposal differs from existing approaches [START_REF] Toka | Online Data Backup: A Peer-Assisted Approach[END_REF], [START_REF] Kubiatowicz | OceanStore: an architecture for global-scale persistent storage[END_REF]- [START_REF] Landers | PeerStore: Better Performance by Relaxing in Peer-to-Peer Backup[END_REF] by taking into account the low-level structure of the network. Indeed, most peer-to-peer applications ignore the presence of a gateway in between each peer and the Internet. As a result they do not leverage the presence of the gateway while it can greatly improve the overall performance of the system. We believe that leveraging the gateway storage space may render peer-to-peer systems viable alternatives for backup. This should provide a reasonable solution even when peers experience a low availability as long as they connect frequently enough to the system. Using those gateways as buffers between peers participating in a backup or restore operation, enables to implement a stable rendezvous point between transient peers.

The remainder of this paper is structured as follows. In Section II, we briefly review some pieces of work that motivated our proposal. In Section III, we detail our architecture and sketch the storage system. Section IV introduces a framework for comparison of our proposal to that of competitors, and Section V presents our evaluation study. We discuss respec- tively some specific points and related work in Section VI and Section VII. Finally, we conclude the paper in Section VIII.

II. BACKGROUND Peer-to-peer storage systems initially relied on the set of all participating peers, typically constituted of users' desktop PCs, without any further infrastructure [START_REF] Kubiatowicz | OceanStore: an architecture for global-scale persistent storage[END_REF], [START_REF] Rowstron | Storage management and caching in PAST, a large-scale, persistent peer-to-peer storage utility[END_REF]. However, it has been acknowledged since then [START_REF] Blake | High availability, scalable storage, dynamic peer networks: pick two[END_REF], [START_REF] Tati | On Object Maintenance in Peer-to-Peer Systems[END_REF] that those pure peer-to-peer architectures may fail to deliver reliable storage by exploiting the resources of peers, mainly due to the low availability of peers and the slow up-link of their network connections. One straightforward solution is to exclude peers with a low availability or a slow network connection to access the service [START_REF] Maille | Managing a Peer-to-Peer Data Storage System in a Selfish Society[END_REF]; this nevertheless excludes many participants and significant amounts of exploitable resources [START_REF] Bolosky | Feasibility of a Serverless Distributed File System Deployed on an Existing Set of Desktop PCs[END_REF], [START_REF] Huang | FS2: dynamic data replication in free disk space for improving disk performance and energy consumption[END_REF].

In order to move towards practical system deployment while still leveraging users' resources, hybrid architectures, where both servers and peers coexist, have been very recently proposed in various contexts [START_REF] Gharaibeh | Exploring data reliability tradeoffs in replicated storage systems[END_REF]. The problem of sharing files while mitigating the load of central servers is addressed in [START_REF] Liu | FS2You: Peer-Assisted Semipersistent Online Hosting at a Large Scale[END_REF], which proposes a BitTorrent like server-assisted architecture where central servers act as permanently available seeders. Lastly, a server assisted peer-to-peer backup system is described in [START_REF] Toka | Online Data Backup: A Peer-Assisted Approach[END_REF]. In their system, which can be referred to as CDN-assisted, the CDN enables to reduce the time needed to backup data, while the use of peers guarantees that the burden of storage and communication on the data center remains low. In this last approach, a peer uploads data to a set of other peers if they are available, and falls back on the datacenter otherwise, thus using the datacenter as a stable storage provider.

Residential gateways connect home local area networks (LAN) to the Internet. They act as routers between their WAN interface (Cable or DSL) and their LAN interfaces (Ethernet and WiFi). They started to be deployed in homes to share Internet access among different devices and got additional functions as services (VoIP, IPTV) were delivered over the Internet. It is now fairly common to have home gateways embedding a hard drive, acting as Network Attached Storage to provide storage services to other home devices and offering some other ones to the outside world [START_REF] Valancius | Greening the Internet with Nano Data Centers[END_REF], [START_REF] Fedak | DSL-Lab: A Low-Power Lightweight Platform to Experiment on Domestic Broadband Internet[END_REF].

III. A GATEWAY ASSISTED SYSTEM

A. Stability of residential gateways

As residential gateways provide not only Internet connectivity, but also often VoIP, IPTV and other services to the home, the intuition tells us that they remain permanently powered on. To confirm this assumption, we extracted a trace of residential gateways of the French ISP Free, using active measurements 1 . We periodically ping-ed a set of IP addresses randomly chosen in the address range of this ISP, which has a static IP addressing scheme. We obtained the uptime patterns of 25, 000 gateways for 7.5 months, covering weekpatterns [START_REF] Douceur | Is remote host availability governed by a universal law?[END_REF], [START_REF] Bhagwan | Understanding Availability[END_REF], and holidays. We plot the availability of those devices against time, in the classical representation of availability, on Figure 1a. Some clear acquisition artifacts appear due to both the unreliability of the ICMP monitoring and temporary failures on the path between our platform and the targeted network. Yet, the trace confirms the common intuition about the stability of those devices, in spite of a few users having power-off habits (on a daily or a holiday basis, see Figure 1c), thus slightly reducing the average availability. The average availability of gateways in this trace is 86%, which confirms the results observed in [START_REF] Valancius | Greening the Internet with Nano Data Centers[END_REF], where the authors used traces from a biased sample (only BitTorrent users) [START_REF] Dischinger | Characterizing Residential Broadband Networks[END_REF]. This has to be contrasted with the low to medium availabilities of peers generally recorded in the literature, as e.g. 27% in [START_REF] Toka | Online Data Backup: A Peer-Assisted Approach[END_REF], or 50% in [START_REF] Guha | An Experimental Study of the Skype Peer-to-Peer VoIP System[END_REF].

This increased stability makes gateways appealing candidates for backing peer-to-peer services. The intuition is that data is temporarily stored on gateways to compensate for peers transient availability. In this paper, we advocate the use of gateways as buffers and not storage. This choice is motivated by the increasing number of devices embedding storage, within the home and attached to a gateway. Dimensioning the storage of the gateway accordingly would be costly and would break the peer-to-peer paradigm by creating a central point in charge of hosting resources of attached devices durably: the contributed resources would no longer scale with the number of clients. In our buffer model, each device is required to provide a portion of its available space [START_REF] Bolosky | Feasibility of a Serverless Distributed File System Deployed on an Existing Set of Desktop PCs[END_REF], [START_REF] Huang | FS2: dynamic data replication in free disk space for improving disk performance and energy consumption[END_REF], to participate to the global backup system.

B. System rationale

In this paper, we propose to decentralize the buffer logic implemented in [START_REF] Toka | Online Data Backup: A Peer-Assisted Approach[END_REF] by a CDN, in order to provide a reliable backup system despite the dynamic nature of peers composing 2. A global picture of the network connecting the peers to the service. Those end-devices are available 6 -12h/day. If we allow the gateway, which is available 21h/day, to perform buffering, we can benefit from the speed difference between local links (7MB/s) and ADSL links (66KB/s). the network. Our system is specifically tailored for the current architecture of residential Internet access. Indeed, most previous works assume that peers are directly connected to the network (see Figure 2a) while, in most deployments, a residential gateway is inserted in between the peers in the home network and the Internet. Hence, a realistic low-level network structure is composed of (i) peers, connected to the gateway through Ethernet or Wifi, (ii) residential gateways, providing the connection to the Internet, and (iii) the Internet, which we assume to be over provisioned (architecture depicted on Figure 2b). In our approach, we propose to use storage resources of residential gateways, thus creating a highly available and distributed buffer to be be coupled with peers.

Such an architecture is appealing as it takes into account (i) the availability that differs between peers and gateways, and (ii) the bandwidth that differs between the LAN and the Internet connection. Firstly, the peers tend to have a low to medium availability (i.e. from 25% or 6 hours/day on average on a Jabber trace, to 50% on a Skype trace we introduce later on) while gateways have a high availability (i.e., 86% or 21 hours/day on average). Secondly, peers are connected to the gateways through a fast network (at least 7MB/s) while the Internet connection (between gateways and the Internet) is fairly slow (i.e. 66 kB/s on average for ADSL or Cable). Our architecture exploits the major difference of throughput between the LAN and the Internet connection (WAN) by offloading tasks from the peer to the corresponding gateway quickly, thus using the Internet connection more efficiently (i.e. 21h/day instead of only 6 -12h/day on average). This enables the large-scale deployment of online storage applications by fixing the issues provoked by the combination of slow up-links and short connection periods (as in the case of pure peer-to-peer). These issues are becoming increasingly important as the size of the content to backup increases while ADSL bandwidth has not evolved significantly over the past years. For example, uploading 1GB (a 300 photo album) to online storage requires at least 4h30 of continuous uptime. Hence, these applications require users to change their behavior (e.g let their computers powered for the whole night to be able to upload large archives); this limits their deployment and makes automated and seamless backup close to impossible. Our approach precisely aims at combining peers' fast but transient connections with gateways' slow but permanent connections. Following this logic, if peers upload directly to the Internet, they can upload on average 1.4-2.8GB/day (Fig. 2a); if we consider that the gateway is an active equipment that can perform buffering, a peer can upload 148-296GB/day to the gateway and the gateway can upload on average 4.8GB/day (Fig. 2b). We then advocate that turning the gateway into an active device can significantly enhance online storage services, be they peer-to-peer or cloud systems.

In the last part of this section, we propose the design of a gateway-assisted peer-to-peer storage system (GWA) based on these observations, and relying on two entities: (i) users' gateways, present in homes and providing Internet connectivity, and (ii) peers, being users' devices connected to the Internet (through a gateway) and having some spare resources to contribute to the storage system.

C. Gateway-assisted storage system

We consider a general setting to backup data to third parties on the Internet, generic enough for us to compare approaches from related work in the same framework.

The content to be backed up is assumed to be ciphered prior to its introduction in the system, for privacy concerns. The content can be located in the distributed storage system through an index, which can be maintained, for example by a distributed hash table connecting each piece of content stored to the set of peers hosting it. We consider that users upload data from one peer, under the form of archives. In order to achieve a sufficient reliability, the system adds redundancy to the content stored. To this end, it splits the archive into k blocks, and adds redundancy by expanding this set of k blocks into a bigger set of n blocks using erasure correcting codes [START_REF] Lin | Erasure Code Replication Revisited[END_REF] so that any subset of k out of n blocks allows recovering the original archive. This enables to increase the file availability as the resulting system-wide availability is

A = n i=k n i pi (1 -p) n-i (1)
where p is the average availability of peers, which is smaller than A. In the rest of this paper, we set a target A t for the system-wide availability so that n must be the smallest n ensuring that A > A t . Intuitively, the availability targeted by the application is the portion of time a backed up data is online for restore. High availability rates have been shown cumbersome to reach in dynamic systems [START_REF] Blake | High availability, scalable storage, dynamic peer networks: pick two[END_REF], so a reasonable trade-off should be considered [START_REF] Pamies-Juarez | Availability and Redundancy in Harmony: Measuring Retrieval Times in P2P Storage Systems[END_REF]. For a backup operation, the client peer uploads the file and the redundancy blocks to other peers as follows:

1. Prepare. As soon as it gets connected, the client peer starts pushing the archive at LAN speed to its gateway, which buffers the data. At this point, the data has been partially backed up but the final level of reliability is not yet guaranteed.

2. Backup. In our system, the gateway is in charge of adding the redundancy; this allows faster transfer from the peer to the gateway as a lower volume of data is concerned. Once done, it starts uploading data to other gateways, at WAN speed (left-hand side of Figure 3). Gateways are active devices that can serve peer requests thus ensuring data availability and durability even if data is not fully pushed to remote peers. Therefore, data can be considered totally backed up when all blocks have reached the selected set of independent remote gateways.

3. Offload. Finally, remote gateways offload, at LAN speed, the content to their attached peers (right-hand side on Figure 3) as soon as the attached peer becomes available.

A user can request access to its data at anytime; the success of immediate data transfer from the storage system to the requesting peer depends on the targeted availability of the backup, that has been set by the system administrator. To reclaim backed up data, the role of all elements in the systems are reversed and the restore is performed as follows:

1. Fetch. To access a data, the requesting client peer informs its gateway of the blocks it is interested in. The client gateway carries on the download on behalf of the client peer by contacting the remote gateways handling peers where the data was uploaded. If the data was offloaded to some peer, it is fetched as soon as possible by the corresponding remote gateway.

2. Restore. Then the remote gateway sends the data to the requesting client gateway.

3. Retrieve When the client gateway has succeeded in getting the whole content (the data has been restored), it informs the client peer that its retrieval request has been completed, as soon as it connects back.

IV. A COMPARISON FRAMEWORK FOR BACKUP SCHEMES

We extensively evaluate our approach through simulations, taking as inputs execution traces of large-scale deployed systems. This section first presents the experimental setup, the competing approaches, namely pure peer-to-peer (noted P2P hereafter) and CDN-assisted (noted CDNA), and the performance metrics.

A. Parameters and data sets

The setting we described in previous section comes with the following set of parameters:

Network Bandwidth: On the WAN side (Internet connection), the bandwidth is heterogeneous and set according to the traces from a study of residential broadband networks [START_REF] Dischinger | Characterizing Residential Broadband Networks[END_REF]; it exhibits an average of 66 kB/s2 . On the LAN side, we assume a constant bandwidth of 7 MB/s, capturing both wired and WiFi connections in home environments. The LAN bandwidth only impacts our gateway-assisted approach, as other approaches suffer from the bottleneck at the WAN interface since they upload data directly to devices in the WAN (peers or CDN).

Backup and Restore requests: The backup and restore user requests are modeled with Poisson processes, which are known to match user requests [START_REF] Guha | An Experimental Study of the Skype Peer-to-Peer VoIP System[END_REF], of parameters λ backup and λ restore that represent the rate of backup and restore requests in the system. Each request is related to one archive. We assume that all archives have the same fixed size for all peers, typically representative of some large multimedia content (we make this size vary). As a result, the behavior of peers is assumed to be homogeneous: we are not aware of any trace giving hints about the real behavior of users within peer-to-peer storage/backup systems.

Peer availability: In order to model the up-time of personal computing devices (i.e. peers), we rely on two instant messaging traces. We only remove from the traces the peers with an availability lower than 1%, since these have a behavior not compatible with a backup application running in the background (e.g. people that have tried Skype only once but never use it again).

• Skype In this trace [START_REF] Guha | An Experimental Study of the Skype Peer-to-Peer VoIP System[END_REF] of about 1269 peers over 28 days, the average availability of peers is 50%, which represents a medium availability when considering peerto-peer systems. • Jabber In this trace, provided by the authors of [START_REF] Toka | Online Data Backup: A Peer-Assisted Approach[END_REF], the average availability is 27%. We used a slice of 28 days containing 465 peers.

All peers strictly follow the behavior of the trace. In particular, since our backup application runs in the background, client peers are not assumed to remain connected during the whole backup (their presence follows the IM/Skype trace), as opposed to the assumptions made in [START_REF] Toka | Online Data Backup: A Peer-Assisted Approach[END_REF]. Note that these traces may however over-estimate uptime period since people using Skype are likely to be online more often than the average user.

Gateway availability: To model the up-time of residential gateways, we rely on our gateway trace presented in Section III. Since the gateway and peer traces have been obtained independently, they do not capture the correlation between the behavior of a peer and of the associated gateway. Hence, we randomly assign a gateway to each peer. In order to avoid unrealistic scenarios where the peer is up while the gateway is down, we assume a gateway to be available when one of its attached peers is up, to allow communication between them: we rely on the gateway trace only for gateway to gateway communication.

Redundancy Policy: As explained previously, the redundancy policy is based on erasure correcting codes and is entirely determined by the number of blocks k each archive is split into and by the targeted availability A t , which is set by the administrator. The backup is thus considered as complete when there are enough redundancy blocks n backed up in the network to guarantee a system-wide availability of at least A t . The relation between the availability of peers and the values k and A t has been studied in papers studying in details redundancy policies [START_REF] Blake | High availability, scalable storage, dynamic peer networks: pick two[END_REF], [START_REF] Lin | Erasure Code Replication Revisited[END_REF], [START_REF] Weatherspoon | Erasure Coding Vs. Replication: A Quantitative Comparison[END_REF].

B. Competitors

We compare the performance of our GWA scheme against the two main classes of related backup systems, namely P2P and CDN Assisted, within the same simulation framework.

P2P The vast majority of peer-to-peer storage protocols historically presents a purely decentralized system with one-toone uploads/downloads, without servers [START_REF] Kubiatowicz | OceanStore: an architecture for global-scale persistent storage[END_REF], [START_REF] Rowstron | Storage management and caching in PAST, a large-scale, persistent peer-to-peer storage utility[END_REF]. They assume that gateways are passive devices that cannot store and forward but only route packets. This protocol is similar to the protocol we described in the previous section but does not have active gateways acting as buffers.

CDNA A possible enhancement consists in introducing a CDN to mitigate the low availability of peers [START_REF] Toka | Online Data Backup: A Peer-Assisted Approach[END_REF]. The CDN is a central service in the core network, having unbounded capacity. We consider the most peer-to-peer variant of the protocol in [START_REF] Toka | Online Data Backup: A Peer-Assisted Approach[END_REF] (i.e. the opportunistic one). In this protocol, the peers upload content to other peers in priority and upload to the CDN only when the whole bandwidth is not used (i.e., not enough remote peers are available). This enables to lower time to backup by avoiding waiting times. However, the CDN does not upload the content to remote peers, but client peers eventually upload again to remote peers thus uploading twice in some cases. Indeed, pricing schemes at CDN implies that uploading from the CDN should be avoided so as to reduce costs. A schematical view is given in Figure 4. The CDN never fails, hence, a single copy of the content on CDN is enough to ensure an availability of 100%. As a result, a data backup is successful as soon as s fragments have been uploaded to the storage server and t fragments have been uploaded to the peers so that the targeted availability is guaranteed, as stated in [START_REF] Huang | FS2: dynamic data replication in free disk space for improving disk performance and energy consumption[END_REF].

t i=k-s t i pi (1 -p) t-i > A t (2)
p is the average availability of a peer and A t is the targeted availability.

C. Simulation setup & Performance Metrics

We implement a cycle-based simulator to compare our GWA architecture with the two aforementioned alternatives. Depending on the simulated architecture namely P2P, GWA or CDNA, the system is respectively composed of only peers, peers and gateways, or peers and a CDN. Devices transfer [START_REF] Toka | Online Data Backup: A Peer-Assisted Approach[END_REF]. Note that the CDN (Server) has an infinite capacity and 100% availability. However, since the bandwidth used at the CDN is billed, the CDN is not used as a relay but as another kind of end-storage (i.e. it does not upload content to other peers but only stores content temporarily until the backing up peers have uploaded content to enough peers.) their data depending on their upload bandwidth and on their behavior, which are trace-driven for peers and gateways while CDN is always up. We evaluate the time for each backup or restore request to be completed, while measuring the storage needs of the system.

In our simulations, the redundancy policy relies on the following values k skype = 16, k jabber = 8, A t = 0.7, pskype = 0.5 and pjabber = 0.27 leading to n skype = 35 and n jabber = 33. We assign to each peer a set of n distinct remote peers in a uniform random way, for example using the hashing scheme of a distributed hash table. When a given peer requests a data backup operation, the n encoded blocks are placed on its set of n remote peers.

At each cycle, backup and restore requests are generated among peers according to the previously defined Poisson processes. Note that a backup request is uniformly distributed among the set of online peers, while a restore request is uniformly distributed among the set of peers whose data has already been fully backed-up (i.e. all blocks have been offloaded on remote peers). The rate of backup requests is set so that each peer requests to store about three archives of 1GB per month on average (i.e. λ backup = 0.4 and λ restore = 0.05 for the Skype trace).

Once all backup and restore requests have been distributed among the peers, each device (i.e. peer or gateway) transfers as much data as its upload bandwidth allows for the duration of the cycle (i.e. since residential connections are asymmetric, we assume that the system is bounded by the upload bandwidth of devices). If the remote device is offline, the client device has to wait until its reconnection.

Our simulations were conducted with a cycle time-step set to 5 minutes. Figures report the average behavior over 50 simulations. We evaluate the three systems according to the following four metrics: Time to backup, noted TTB. A backup request is considered successful when the data is stored safely. Safe storage is achieved when n blocks have been uploaded to the CDN and the remote peers for CDNA, to the remote gateways for GWA, and to the remote peers for the P2P thus satisfying the targeted availability described earlier. The time to backup is evaluated as the difference between the time the n th block has been downloaded and the time of the backup request. Time to offload, shown on the same plots as TTB. A variant measure for both CDNA and GWA is the time to fully offload an archive to the remote peers. This means that no data is left on the CDN or on gateways, accordingly. We note this variant CDNA p and GWA p respectively.

Time to restore, noted TTR. A restore request is considered successful as soon as the data is restored safely at the user's place, that is to say when at least k blocks have been retrieved on the client peer, or on the gateway of the client peer for GWA. The time to restore is evaluated as the difference between the time the k th block has been downloaded and the time of the restore request. We measure this time for random files after a long enough period, so that the selected files have been offloaded to peers. This represents the worst case for TTR, and this assumption reflects the fact that restore requests are more likely to happen long after backups.

Data buffered. It describes the size of the buffer that is required on gateways, for dimensioning purposes. We measured the maximum and the average amount of data stored on those buffers.

V. RESULTS

A. Time to backup & restore results

We first evaluate the performance of our approach to backup and restore data w.r.t. time. We plot the experimental cumulative distribution function (CDF) for TTB and TTR arguably the most critical metrics from the users' standpoint. CDF(t) represents the cumulative number of requests that have been completed after t hours.

Figure 5a depicts the TTB for the Skype trace. Results show that our gateway assisted approach improves the TTB over the CDNA approach 3 . Both considerably improve the performance over the P2P approach. Our GWA completes 90% of backup in 30 hours, the CDNA completes 90% of backups in 60 hours and the P2P completes 90% of backups in 140 hours. A consequence of this improvement is that data is backed up faster, reducing the window of potential losses.

Along the performances of P2P, CDNA and GWA, we also indicate those of CDNA p and GWA p . In GWA and CDNA, once the data is backed up (i.e. it is stored safely at some place being the remote gateways or the CDN), the backup process continues by offloading the data hosted on the remote gateways or on the CDN to the remote peers (i.e. until no data is left on the remote gateways or on the CDN). This process takes some time and its total duration is shown as GWA p and CDNA p . It is interesting to observe that while the CDNA does not enhance this time when compared to P2P (P2P curves and CDNA p curves are superimposed on all plots), our GWA approach improves this time significantly, reducing it from 140 hours to 90 hours (for 90% of backups to be offloaded).

We plot the time to restore for the Skype trace on Figure 5b. Results show that the TTR of our GWA approach is significantly reduced when compared to GWA and P2P approaches. Our GWA allows 90% of restores to be completed in less than 3 hours while both CDNA and P2P require 40 hours to complete 90% of restores. This makes the system much more user-friendly, when it comes to retrieving lost files.

In order to show that these results are not trace-dependent, we run the same set of experiments on a trace exhibiting a lower peer availability, namely the Jabber trace. We observe similar results. Previous observations hold as the time to backup (Figure 5c) for our GWA is reduced when compared to both CDNA and P2P. Similarly, the time to restore is also reduced (Figure 5d). Overall, the absolute times are increased when compared to results observed over the Skype trace because of the lower average availability of peers in this trace (25% instead of 50%).

Note that the absence of full convergence in some cases is due to some peers leaving the network for good before the backup is complete and because the trace duration is limited.

In the remaining part of this section, we evaluate the impact of other parameters, namely the targeted availability A t , the number of blocks k, the number of peers involved in the system and the amount of data to backup and restore (i.e. the archive sizes) on both the TTB and TTR. We vary parameters one by one, keeping the other parameters to the values previously defined. Previous results have shown that some small part of backups may take significantly more time to complete than average; this somehow introduces a bias in observation of the system. In the following results, we will then consider the 90 th percentile for all approaches, in order to gain clear insights from systems' trends (i.e. the times displayed are the time so that 90% of the operations have been completed). The behavior, for one set of parameters, of the remaining 10% can be seen on the previously described CDF.

B. Influence of targeted availability

On Figure 6a, we plot the opposed variations of TTB and TTR when the targeted availability changes. We observe that the TTB increases when the targeted availability increases. This is due to the fact that achieving a higher availability for the file requires uploading more data, to introduce more redundancy. However, as shown on Figure 6b, increasing the targeted availability (i.e., the amount of redundancy introduced) helps to reduce the TTR. As a result the targeted availability is a tradeoff between having a low TTR and keeping the TTB reasonable. We observe that the improvement of our GWA approach is very significant over CDNA or P2P approaches. This is due to the fact that our approach represents a paradigm shift: the data is now considered as restored when stored in the home of the requester (on its gateway). Indeed, this prevents exterior factors such as block losses in the system from having any impact. When the requesting peer comes back online, it can seamlessly fetch data in order of minutes from its gateway, making this step nearly transparent when compared to operations at WAN speed.

Another aspect is impacted by the availability setting of the storage system: increasing the targeted availability requires to store more redundancy blocks thus increasing the storage costs I. Hence, keeping the targeted availability reasonably low helps to keep storage costs per peer low thus increasing the total amount of data that can be backed up. In the remaining simulations, we choose to use a medium value of 0.7 for that targeted availability.

C. Influence of code length k

Increasing the code length k (i.e. the number of blocks required to decode) slightly improves both TTB and TTR, as shown on Figures 7a and7b. However, increasing k also increases some side costs such as coding and decoding costs. As a consequence, we choose to set k = 16 to leverage the code properties while retaining low coding and decoding costs.

D. Influence of the size of the network

Next, we evaluate the influence of the number of peers participating in the system by varying the number of peers from 200 to 1269 (all the peers of our trace). We also set the parameters for the restore and backup events so that on average each peer performs around 3 backup requests per month and 3 restore requests per year, similarly to what was done for all other simulations. Our results are shown on Figures 8a and8b. Both TTB and TTR remain constant. Our simulations are limited by the total number of peers present in the trace; yet, we observe on this moderate scale that our system is likely to be scalable in the number of participating peers, as no bottleneck occurs at some gateways, which could have increased the TTR. Note that these constant TTB and TTR are consistent with the fact that the load (backup and restore requests) per peer is constant.

E. Influence of the amounts of data to backup and restore

In order to assess the gains with respect to the usability of GWA, we plot the evolution of the TTB (Figure 9a) and the TTR (Figure 9b) as the amount of data to backup increases. Our architecture enables to leverage the difference of bandwidth between the local network and the Internet connection in order to use the uplink more efficiently (21h/24h instead of only 12h/24h); clearly, in this case, it enables users to backup larger amounts of data (here by a factor of 2). Note that our simulations are limited by the trace length (28 days).

F. Resulting needs for storage dimensioning on buffers

For dimensioning purposes, we evaluate how much disk space should be provisioned on the gateways in order to implement our backup service. Figure 10 shows the CDF of maximal storage at gateways resulting from 1GB archive backups, at any time, on the Skype trace (i.e. the worst case space occupied on any gateway at any simulation step). Storage needs remain within reasonable bounds: 99% of gateways have stored at most 2.5GB of data at anytime. In a deployment scenario, if we limit the provisioned storage to 2.5GB at each gateway, the remaining 1% of gateways could ask peers pushing blocks to delay their query until their buffers have emptied, without impacting performance since it would impact less than 1% of peers and would occur only exceptionally. Buffers are used in burst mode for relatively short periods of time, as shown on Figure 11, which plots the average of the same storage functionalities for the whole trace period: the average is negligible compared to the maximum presented on the previous figure. Furthermore, we observe that data is effectively offloaded since nothing remains on buffers when no new backups are requested (on the simulations, we performed backups only for the 13 first days) thus confirming results shown on previous curves for GWA p . These results are related to our model where each gateway hosts one peer. The storage requirements would increase if multiple peers are behind each gateway. However, we study residential gateways, which are shared among a very small number of users. The storage requirements increase at most linearly with the number of users and hence would remain rather low as only a few peers are behind each gateway.

VI. DISCUSSION

Our results clearly indicate that our proposal efficiently distributes the centralized buffer scheme of [START_REF] Toka | Online Data Backup: A Peer-Assisted Approach[END_REF], while increasing general backup performances and represents a significant improvement over previous approaches.

The Web architecture, in particular when considering CDN, relies on cache servers close to clients [START_REF] Leighton | Improving Performance on the Internet[END_REF]. However, these servers are located within the Internet and cannot benefit from the difference of throughput between the local home network and the Internet: our system relies on the specific place of the gateway in between the home network and the Internet to leverage this difference. Moreover, cache servers are generally passive (e.g., HTTP proxy) while in our system, the gateway is not only a cache but also an active participant that can serve directly other peers when data is requested.

Additionally, from the user's standpoint, our storage system could enable the bandwidth usage to be smoothed to provide users with a more transparent service (i.e. using the upload for backup when users are not using their computer/Internet connection). Indeed, using an important part of the upload bandwidth to quickly complete the backup operation, may severely affect the user's experience of Internet browsing or activity. A user's gateway is able to upload, as long as there is some available bandwidth and even if the user's computer is turned off (typically nightly). A similar advantage, appealing for Internet and service providers [START_REF] Laoutaris | Delay Tolerant Bulk Data Transfers on the Internet[END_REF], is that such an architecture enables the implementation of scheduling policies for delaying transfers from gateways to the Internet so as to smooth the usage of the core network.

Lastly, this method also solves another issue that might appear when the distributed application operates worldwide. It has been shown that peers' availability patterns can vary according to local time (depending on geographical location) [START_REF] Douceur | Is remote host availability governed by a universal law?[END_REF], [START_REF] Bhagwan | Understanding Availability[END_REF]; in systems where some resources are insufficiently replicated, this could lead to an asynchrony of presence between a requesting peer and another peer hosting the resource. At best, the overlap of presence of both peers is sufficient to download the file, while it may also require a few sessions to complete, due to insufficient time overlap. As our GWA proposal relies on the hosting peer to upload the requested file to a more stable component (its gateway), asynchrony is no longer an issue as gateways provide stable rendezvous point between requesters and providers. This is of interest for delay tolerant applications such as backup, allowing the service to be operated with much lower costs on storage. Beyond the practical problem of using gateways in home environments, our solution then makes the case for leveraging clouds of stable components inserted in the network, to make them act as buffers in order to mask availability issues introduced in dynamic systems.

VII. RELATED WORK

We compared our approach to the peer-assisted one presented in [START_REF] Toka | Online Data Backup: A Peer-Assisted Approach[END_REF] that leverages a central server and offloads backed up data to peers when they become available. Such a servercentric approach is also to be found in [START_REF] Gharaibeh | Exploring data reliability tradeoffs in replicated storage systems[END_REF], where authors propose an hybrid architecture coupling low I/O bandwidth but high durability storage units (being an Automated Tape Library or a storage utility such as Amazon S3 [START_REF]Amazon Web Services[END_REF]) with a P2P storage system offering high I/O throughput by aggregating the I/O channels of the participating nodes but low durability due to the device churn. This study provides a dimensional and system provisioning analysis via an analytical model that captures the main system characteristics and a simulator for detailed performance predictions. The simulator does not use real traces but synthetic ones, mainly to be able to increase the failure density and to reveal the key system trends. This work explores the trade-offs of this hybrid approach arguing it is providing real benefits compared to pure P2P systems [START_REF] Kubiatowicz | OceanStore: an architecture for global-scale persistent storage[END_REF]- [START_REF] Landers | PeerStore: Better Performance by Relaxing in Peer-to-Peer Backup[END_REF]. Durability of the low I/O bandwidth unit is considered as perfect, but it always comes at a certain cost. In our approach, we do not assume we have such nodes and show that our approach is sustainable under real availability traces. Finally, FS2You [START_REF] Liu | FS2You: Peer-Assisted Semipersistent Online Hosting at a Large Scale[END_REF] proposes a BitTorrent-like file hosting, aiming to mitigate server bandwidth costs; this protocol is not designed to provide persistent data storage.

The increasing power of residential gateways has enabled numerous applications to be deployed on them. This may allow savings in terms of power. One widely deployed system is the implementation of BitTorrent clients in those boxes (see e.g. FON [START_REF]FON[END_REF]), which avoids the user to let her computer powered on [START_REF] Fedak | DSL-Lab: A Low-Power Lightweight Platform to Experiment on Domestic Broadband Internet[END_REF]. Another example is the concept of Nano Data Centers [START_REF] Valancius | Greening the Internet with Nano Data Centers[END_REF], where gateways are used to form a P2P system to offload data centers. Similarly, some approaches were proposed to move tasks from computers to static devices as set-top boxes, for VoD [START_REF] Janardhan | Peer assisted VoD for set-top box based IP network[END_REF] and IPTV [START_REF] Cha | On next-generation telco-managed P2P TV architectures[END_REF]. Yet, those applications fully run on gateways while, in our approach, the gateway only acts as buffering stage.

VIII. CONCLUSION

This paper addresses the problem of efficient data backup on commodity hardware. It has been widely acknowledged that availability of transient peers is a key parameter, that can by itself forbid a realistic service deployment if too low. We propose to address this inherently transient behavior of end peers by masking it through the use of more stable hardware, already present in home environments, namely gateways. Our experiments, based on real availability traces, show that this architectural paradigm shift, significantly improves the user experience of backup systems over previous approaches, while remaining scalable.

We also provide a new trace of gateway availabilities, which is of interest for trace-based simulation of systems built upon gateways. As future works, it would be interesting to acquire a trace of user behaviors with respect to storage demand in peer-to-peer systems.

Figure 1 .

 1 Figure 1. Availability of residential gateways mesured on a French ISP. The dataset has been acquired sending pings to a random sample of gateway IPs.

Figure

  Figure2. A global picture of the network connecting the peers to the service. Those end-devices are available 6 -12h/day. If we allow the gateway, which is available 21h/day, to perform buffering, we can benefit from the speed difference between local links (7MB/s) and ADSL links (66KB/s).

Figure 4 .

 4 Figure 4. A global picture of the network connecting peers and CDN, as used in[START_REF] Toka | Online Data Backup: A Peer-Assisted Approach[END_REF]. Note that the CDN (Server) has an infinite capacity and 100% availability. However, since the bandwidth used at the CDN is billed, the CDN is not used as a relay but as another kind of end-storage (i.e. it does not upload content to other peers but only stores content temporarily until the backing up peers have uploaded content to enough peers.)

Figure 5 .

 5 Figure 5. CDF of Time to Restore and Time to Backup for two traces of Instant Messaging.

Figure 6 .Figure 7 .

 67 Figure 6. Results (Skype trace), as a function of availability target, 90th percentile. Labels follow the order of the curves.

Figure 8 .Figure 9 .

 89 Figure 8. Results (Skype trace), with a varying network size, 90th percentile

Figure 10 .

 10 Figure 10. Maximal storage measured on gateways at any time (Skype trace)

Figure 11 .

 11 Figure 11. Average storage measured on gateways (Skype trace)

This trace and additional information can be found at the following URL http://www.thlab.net/ ∼ lemerrere/trace gateways/ . To the best of our knowledge, this is the first trace tracking availability of gateways.

Note that all amounts of data and bandwidth are given in bytes.

Note that results for CDNA are consistent with simulations made in[START_REF] Toka | Online Data Backup: A Peer-Assisted Approach[END_REF], with an improvement factor between 2 and 3 over P2P storage