O Arnould

K Bytebier

P Cabrolier

R Arinero

NANOMECHANICAL CHARACTERISATION OF THE WOOD CELL WALL USING ATOMIC FORCE MICROSCOPY

Keywords: wood, cell wall layers, (visco)elastic properties, Resonant Contact-AFM

INTRODUCTION

Wood is produced in successive cylindrical layers during the radial secondary growth of a tree by a very thin layer of living cells that divide, called cambium, and located under the bark. Wood is composed of different kinds of cells, with a honeycomb-like cellular organisation, and each plays a particular role for the tree. From a mechanical point of view, fibres are the cells that compose the structure (skeleton) of the tree [START_REF] Thibaut | Mechanics of wood and trees: some new highlights for an old story[END_REF]. Figure 1 shows the idealized multi-layered structure of a typical wood fibre (typically around 1 mm long and around 20 µm in diameter). Each wood cell wall layer plays a particular role in the mechanical behaviour of wood and the elastic properties of wood originate mainly in those of its secondary cell wall layers. Each layer, particularly in the secondary wall, can be seen as a unidirectional long fibre composite whose fibres are cristalline (at around 70%) cellulosic microfibrils (as long as the cell and with some nm in diameter) and the matrix is made up of amorphous polymers: hemicelluloses, lignin and extractives [START_REF] Salmén | Micromechanical understanding of the cell-wall structure[END_REF]. The microfibrils are inclined to the cell axis by the so-called microfibril angle (MFA).

Figure 1. Idealized scheme of a typical fibre wall structure (adapted from Koch, 1985). The cell wall consists of: P-primary wall; S 1 , S 2 , S 3 -layers of the secondary wall; W-warty layer; ML-middle lamella that binds cells together. Definition of the MicroFibrils Angle (MFA) for the S 2 -layer. The empty part inside the fibre is called lumen.

Secondary walls are formed during cell differentiation by addition of constitutive material extruded from the plasma membrane and progressively incorporated into the wall. The mechanical properties of the wall depend on the amount of constitutive polymers, their spatial organisation, and also on the way they are bound to each other during cell development. To date, very little is known about how the mechanical properties of a wall layer progressively change during the early stages of its formation. Improved knowledge of the timing of wall stiffening may be useful to understand its assembly process. More specifically, it is necessary for understanding and modelling the apparition of maturation stress in wood [START_REF] Archer | Growth stresses and strains in trees[END_REF][START_REF] Thibaut | Mechanics of wood and trees: some new highlights for an old story[END_REF][START_REF] Yamamoto | Origin of the biomechanical properties of wood related to the fine structure of the multi-layered cell wall[END_REF][START_REF] Alméras | Modeling anisotropic maturation strains in wood in relation to fibre boundary conditions, microstructure and maturation kinetics[END_REF][START_REF] Coutand | The gravitropic response of poplar trunks: Key roles of prestressed wood Regulation and the relative kinetics of cambial growth versus wood maturation[END_REF], because wall stiffness determines the MFA amount of stress generated by an impeded dimensional change of its constituents [START_REF] Boyd | Tree growth stresses. Evidence of an origin in differenciation and lignification[END_REF]. These maturation stresses allow the tree to improve its mechanical strength against bending loading (e.g., wind or fruit weight) and to modify the shape of its trunk or branches by bending [START_REF] Moulia | Posture control and skeletal mechanical acclimation in terrestrial plants: implications for mechanical modeling of plant architecture[END_REF]. In this case, fibres act like a muscle for the tree and their (ultra)structure can be different from a classical one (i.e., normal wood) in the case of strong reorientation where reaction wood is produced [START_REF] Timell | Compression wood in gymnosperms[END_REF][START_REF] Ruelle | Tension wood and opposite wood in 21 tropical rain forest species. 1. Occurrence and efficiency of G-layer[END_REF]. Hardwood trees, for example, produce the so-called tension wood fibres that have a supplementary layer, generally in addition and inside the S 2 -one, with a close to 0° MFA [START_REF] Ruelle | Tension wood and opposite wood in 21 tropical rain forest species. 1. Occurrence and efficiency of G-layer[END_REF]. This layer is usually called G-layer because its matrix is gelatinous [START_REF] Gril | Characterization of a gel in the cell wall to elucidate the paradoxical shrinkage of tension wood[END_REF].

Variability of wood cells distribution, thickness or properties lead to difficulties in the mechanical studies of wood at the macroscopic scale (e.g., tree ring). Indeed, every tree has its own cellular organisation and structure that have a strong effect on the behaviour at upper (i.e., macro) scales. Thus, nowadays, multi-scale modelling of wood is used to predict, for example, long-term behavior of wood in structural applications but it strongly needs measurements of its properties at the lowest level. Our goal is to measure mechanical properties within the different cell wall layers of mature fibres and, in a second time, their evolution during wall formation. Mechanical property measurements at the cell wall level can be estimated using numerical computations of the properties of its constituents or are more usually carried out experimentally on chemical compounds extracted from cell walls [START_REF] Cousins | Elastic Modulus of Lignin as Related to Moisture Content[END_REF]Cousins;[START_REF] Cousins | Young's modulus of hemicellulose as related to moisture content[END_REF][START_REF] Salmén | Micromechanical understanding of the cell-wall structure[END_REF] and on mechanically or chemically isolated fibres [START_REF] Perez | Fiber behaviour under tensile force, experimentation and modelling[END_REF][START_REF] Mott | Mechanical properties of individual southern pine fibers, Part I: comparison of early wood and late wood fibers with respect to tree height and juvenility[END_REF][START_REF] Eder | The fracture behaviour of single wood fibres is governed by geometrical constraints: in situ ESEM studies on three fibre types[END_REF]. Other measurements consisted in "classical" tensile tests on the scale of the tree rings or tissue using back-calculations [START_REF] Cave | The Longitudinal Young's Modulus of Pinus Radiata[END_REF][START_REF] Navi | Micromechanics of wood subjected to axial tension[END_REF][START_REF] Rüggeberg | Stiffness gradients in vascular bundles of the palm Washingtonia robusta[END_REF] and/or specific strain fields measurements (Fosberg et al, 2008;[START_REF] Réthoré | Multiscale digital image identification of heterogeneous elastic properties of softwoods[END_REF]. Technique based on FIB machining of the cell wall and micro-compression test has first been used recently [START_REF] Zhang | Characterizing strength and fracture of wood cell wall through uniaxial micro-compression test[END_REF]. In our case, it is necessary to have access to the in situ mechanical properties within cell walls with as few modifications as possible. Thus, one of the most promising and used techniques nowadays is nanoindentation. It has already been applied to estimate average elastic modulus of some wall layers of mature cells [START_REF] Wimmer | Longitudinal hardness and Young's modulus of spruce tracheid secondary walls using nanoindentation technique[END_REF]Gindl et al, 2004;[START_REF] Tze | Nanoindentation of wood cell walls: Continuous stiffness and hardness measurements[END_REF][START_REF] Konnerth | Actual versus apparent within cell wall variability of nanoindentation results from wood cell walls related to cellulose microfibril angle[END_REF] or to compare elastic properties of S 2 layers during the lignification process with those of mature cells [START_REF] Gindl | Lignification of spruce tracheid secondary cell walls related to longitudinal hardness and modulus of elasticity using nano-indentation[END_REF]. However, this technique requires the layer thickness to be greater than the indent size [START_REF] Gindl | The significance of the elastic modulus of wood cell walls obtained from nanoindentation measurements[END_REF], i.e., typically greater than some micrometres. As the width of the cell wall layers varies from about 0.1 µm (primary wall) to less than 10 µm (mature S 2 and/or G layer), interpretation of measurements obtained by nanoindentation in the presence of a properties gradient or within a thin layer is not straightforward due to boundary effects [START_REF] Jakes | Nanoindentation near the edges[END_REF]. Atomic Force Microscopy (AFM) allows one to do not only topography images at the nanometre scale but also to measure some (averaged) mechanical properties (elasticity, viscosity, etc) at this scale. Mechanical measurements done by Atomic Force Microscopy (AFM), using force-distance curves, force modulation microscopy, etc., require similar approaches as in nanoindentation but with a spatial resolution of the order of some tens of nanometre or less [START_REF] Nysten | Nanomechanics with the Atomic Force Microscope: Polymer surfaces, interfaces and nanomaterials[END_REF]. In our case, we used a specific mode of an AFM, sometimes called Resonant Contact-AFM [START_REF] Arinero | Vibration of the cantilever in Force Modulation Microscopy analysis by a finite element model[END_REF][START_REF] Rabe | Atomic force acoustic microscopy[END_REF][START_REF] Nysten | Nanomechanics with the Atomic Force Microscope: Polymer surfaces, interfaces and nanomaterials[END_REF], that has already been applied on wood [START_REF] Arinero | Imaging the mechanical properties of wood cell wall layers by atomic force modulation microscopy[END_REF]. It has been more recently improved with a mathematical processing that allows us to perform a quite fast mapping of mean viscoelastic properties [START_REF] Arinero | Image processing for resonance frequency mapping in atomic force microscopy[END_REF]. The present article is restricted to the case of mature cells of chestnut tension wood and mainly focused on demonstrating the ability of this technique to obtain local semi-quantitative measurement and qualitative mapping of the viscoelastic properties at the ultrastructural level.

MATERIAL AND METHODS

Figure 2. Schematic view of the basic principle of an AFM and its modification for doing Resonant Contact measurements

with the use of a sinusoidal electrostatic excitation of the cantilever and a "lock-in" amplifier.

The basic principle of an AFM relies on measuring the interaction(s) of a physical probe, i.e., a tip, with a sample surface (Figure 2). This interaction induces the bending of a very soft cantilever (i.e., stiffness usually between 0.01 and 100 N/m) at the end of which the tip is. The angular deflection of this cantilever is measured through the reflection of a laser on its back onto a position-sensitive photodetector. Relative in-plane (x, y) and out of plane (z) displacement of the sample vs. the probe is achieved through piezoelectric material actuators with a resolution better than 0.1 nm. There is a large variety of utilisation of AFM and way to measure the sample surface viscoelastic properties [START_REF] Nysten | Nanomechanics with the Atomic Force Microscope: Polymer surfaces, interfaces and nanomaterials[END_REF]. In the so-called contact mode, the tip remains in contact with the sample and the cantilever deflection is proportional to the applied contact force. As the tip scans the surface, a feedback loop keeps the contact force constant by adjusting the z-displacement of the actuator that is recorded and corresponds mainly to the surface topography. In that mode, since the tip touches the sample, it is sensitive to the sample viscoelastic properties. In this work, a specific operating contact mode, sometime called RC-AFM, was used [START_REF] Arinero | Vibration of the cantilever in Force Modulation Microscopy analysis by a finite element model[END_REF][START_REF] Rabe | Atomic force acoustic microscopy[END_REF][START_REF] Nysten | Nanomechanics with the Atomic Force Microscope: Polymer surfaces, interfaces and nanomaterials[END_REF].

It consists in applying a small periodic force to the cantilever by means of an electrostatic potential between the tip and the sample holder (Figure 2). When the excitation frequency is close to the natural frequency of the cantilever, in contact with the sample surface through its tip, a resonance occurs. Basically, the measurement is based on performing a frequency sweep in a given point on the surface and recording the cantilever vibrations through the photodetector. According to several authors [START_REF] Arinero | Vibration of the cantilever in Force Modulation Microscopy analysis by a finite element model[END_REF][START_REF] Rabe | Atomic force acoustic microscopy[END_REF][START_REF] Nysten | Nanomechanics with the Atomic Force Microscope: Polymer surfaces, interfaces and nanomaterials[END_REF], the resonance frequency, f 0 , and the quality factor, Q, of the obtained frequency spectrum can be related respectively to the real, k', and imaginary, k", parts of the normal contact stiffness at the resonance frequency. It is then necessary to use the appropriated contact model to derive the elastic contact modulus M of the tested volume of material. The tangent of the loss angle, tan δ = k"/k', which characterizes the viscous dissipation of the material in the tested volume is, in our case, close to Q -1 (if all other dissipations like tip sliding are negligible) for value of the quality factor higher than unity and is not dependant on the contact model [START_REF] Arinero | Image processing for resonance frequency mapping in atomic force microscopy[END_REF]. The last step, as in all nanoindentation measurements, is to identify the material viscoelastic parameter(s). This is not so obvious in the case of an anisotropic and fibrous material such as the wood cell wall layers [START_REF] Gindl | The significance of the elastic modulus of wood cell walls obtained from nanoindentation measurements[END_REF] even if anisotropic indentation model [START_REF] Vlassak | The indentation modulus of elastically anisotropic materials for indenters of arbitrary shape[END_REF][START_REF] Delafargue | Explicit approximations of the indentation modulus of elastically orthotropic solids for conical indenters[END_REF] have been recently applied to a typical S 2 layer [START_REF] Jäger | The relation between indentation modulus, microfibril angle, and elastic properties of wood cell wall[END_REF] with reverse identification of some elastic properties [START_REF] Konnerth | Full set of elastic constants of spruce wood cell walls determined by nanoindentation[END_REF]. This aspect will not be presented in this paper. Finally, without any significant modification in the AFM device, this method theoretically offers submicrometre spatial resolution, as the mean and vibrating applied forces can be tuned as low as possible, and reduced lateral force effect due to the cantilever tilt angle. Moreover, by scanning the surface at a constant mean force and excitation frequency, close to the resonance of the different materials composing the area of interest, it is possible to do a reasonably fast mapping of the resonance frequency and quality factor whilst acquiring the sample topography without doing a frequency sweep at each point. This imaging technique is based on the cantilever vibration parameters (i.e., the real and imaginary parts) that are directly linked to the parameters of the resonant spectrum of Lorentzian shape [START_REF] Arinero | Image processing for resonance frequency mapping in atomic force microscopy[END_REF].

In our case, a commercial AFM (Veeco Enviroscope) is used and its photodetector signal analysed by a lock-in amplifier (EG & G model 5302) to extract the real and the imaginary part of the cantilever vibration generated by the electrostatic excitation through an external generator (FLUKE PM5138A). In order to achieve the frequency sweep and resonance spectra acquisitions, an automated measurement was realized using Labview software and GPIB National Instruments interface. Our experiments show that the use of a theoretical model of cantilever vibration is not so obvious. This is why we decided here to use a series of "reference" materials like more or less stiff polymers (Polyurethane PU, Polyester PE, PMMA) and stiffer and less viscous materials like glass. The macroscopic viscoelastic properties of these materials have been measured at a frequency close to the one used during RC-AFM experiments [START_REF] Camara | Enhanced multiple ultrasonic shear reflection method for the determination of high frequency viscoelastic properties[END_REF]. Frequency spectra are carried out on them and compared to the theoretical contact stiffness. The strongest assumption here is that these reference samples are assumed to be homogeneous even at the submicrometre scale and that properties at this scale are equal to those at the macroscopic level. In order to obtain as semi-quantitative as possible viscoelastic properties, it is moreover necessary to check the shape (e.g., mean radius of curvature) of the AFM cantilever tip apex during calibration and experiments on wood. The main problem arising during the experiment is that, as the tip is always in contact with the surface during imaging, more or less wear occurs and can lead to a drastic change in the tip apex shape. It is then necessary to have a fast way to characterise the shape between two measurements. We compared different calibration gratings and SEM images and have finally chosen a calibration grating (NT-MDT TGT-01) that consists in an array of very sharp spikes with a radius lower than about 8 nm. It allows for some kind of (fast) reverse imaging of the actual apex shape with enough accuracy in the present case. The (average) technical specifications of the cantilever used for the experiments (Nanoworld Arrow FMR) are: thickness 3 µm, length 240 µm, width 35 µm, stiffness 2.8 N/m, free natural frequency 75 kHz. The average tip radius is estimated to be around 55 nm during the measurements. The mean applied force is estimated to be around 180 nN and the sinusoidal electrostatic excitation is applied with an amplitude of 10 V.

In order to investigate the RC-AFM imaging technique in the case of wood, chestnut (Castanea sativa) mature wood containing normal as well as tension wood was used. Tension wood is characterized, in the case of chestnut, by the presence of a G layer and a thin S 2 -layer. All mechanical measurement based on indentation requires samples with a surface as flat as possible compared to the contact radius in order to be able to estimate accurately the contact area. Moreover, in the case of AFM, the tip is very brittle and surface roughness (or holes) must be as low as possible to reduce breakage risks. Wood samples were then embedded in a resin in order to fill the lumen and to decrease the surface roughness by reducing deformation during the cutting process. Sticks (1 cm in longitudinal direction, 1 × 1 mm² in transverse section) were obtained by splitting to guarantee a good axial direction. They were then cut manually with a razor blade to produce a clear transverse surface and to obtain cubes of about 1 mm 3 in size. Samples were dehydrated with an ethanol series (50%, 75%, 90% and 100%) under vacuum and embedded in increasing ratio of LR White medium resin. The whole resin block with the sample was then machined to reduce its cross section. A rotary microtome (Leica RM2235) was then used first with a glass knife to remove the first 100 µm of material containing the border effects that occurs during initial sample preparation [START_REF] Gril | Precautions for the structural analysis of the gelatinous layer in tension wood[END_REF]. Then a diamond knife (Diatom Histo) was used to cut a series of very thin section (about 500 nm in thickness) at the lowest cutting speed to minimize compression during the cutting process. The resulting topography of the remaining wood block sample surface is obtained during the mechanical measurement in RC-AFM mode and shown in Figure 3. Some steps in the topography due to difference in the stiffness of the different layers are observed. However, the typical Root-Mean-Square (RMS) roughness in the thicker, G and S 2 , layers is usually around 10 nm. Finally, a confocal Raman microspectrometer system (WiTec Alpha 300 R) have been used in order to describe chemical distribution at the sub-cell wall level, and more particularly to evaluate resin penetration in the cell wall. Raman microscopy is a nondestructive in situ tool for chemical mapping with a high resolution [START_REF] Agarwal | Raman imaging to investigate ultrastructure and composition of plant cell walls: distribution of lignin and cellulose in black spruce wood (Picea mariana)[END_REF][START_REF] Gierlinger | Chemical imaging of poplar wood cell walls by confocal Raman microscopy[END_REF]). An oil objective, with a numerical aperture of 1.4 (Nikon 60X), combined with a green laser excitation (532 nm wavelength) provide the best results in term of lateral resolution, approximately 230 nm. Thin cross section (3 µm) have been cut with a diamond knife mounted on a rotary ultramicrotome (Leica EM UC6), and placed between a glass slide with a drop of water and a coverslip surrounded by viscous grease to prevent evaporation due to laser heat. Raman scan has been realized by overlapping (pixel size of 0.13 µm). The diffraction spot size of 100 µm has been chosen to keep maximum Raman light to the detriment of the depth resolution in order to decrease the integration time per pixel at 0.06 s. For all pixels corresponds a single spectrum that has been analyzed with the software WiTec Control. Raman Spectrometer (UHTS 300) provides a spectral resolution of 4 cm -1 . By integrating with a sum filter over identified wavenumber areas in the spectrum, chemicals imaging have been realized. Raman band from 2819 to 2914 cm -1 (Figure 4a top) knows as CH and CH2 stretching vibration correspond to carbohydrates, and more particularly cellulose. Higher intensity highlights the gelatinous layer (G), the secondary cell wall (Sec. Wall) and by contrast, darker regions reveals middle lamella (ML) and cell corner (CC). The band between 1218 and 1276 cm -1 unidentified here, highlights lumens and in this case resin of the impregnated sample (Figure 4a bottom). It appears that resin is only concentrated in the lumen. After a selection of zones, by marking distinct regions (CC and ML, G, Sec. Wall and lumen) average spectrum have been calculated using the software Witec Project (Figure 3b). Comparing with cell walls average spectrums of a chestnut sample not impregnated (results not presented in this paper), it appears that resin spectrum have a small contribution in the cell walls spectrums (red ellipses in Figure 4b). With regard to the small contribution in term of resin band intensity in the cell walls average spectrums, it seems possible to assume a weak penetration of the resin in the cell wall. The RC-AFM experiments are done in two steps. The first step is to engage the tip in contact with the sample and to carry out frequency spectra at different points. In Figure 5, the amplitude of the output signal of the photodetector is plotted as a function of the electrostatic excitation frequency. The resonance frequency f 0 and the quality factor Q of the frequency spectrum in each layer are then deduced. The indentation modulus in the longitudinal direction M L is then computed using the different calibrations done (as depicted in the previous chapter). The results are given in Table 1. They correspond to the mean values obtained from at least 3 spectra done in 3 different positions within the same layer. The uncertainty in this table only represents the variation in the value computed from one point to another. It doesn't take into account all the uncertainty coming from the different calibration steps and measurements accuracy that can be much higher and must be estimated. These results are consistent with those obtain previously on oak [START_REF] Arinero | Imaging the mechanical properties of wood cell wall layers by atomic force modulation microscopy[END_REF] and other S 2 cell wall layer [START_REF] Wimmer | Longitudinal hardness and Young's modulus of spruce tracheid secondary walls using nanoindentation technique[END_REF]Gindl et al, 2004;[START_REF] Tze | Nanoindentation of wood cell walls: Continuous stiffness and hardness measurements[END_REF][START_REF] Konnerth | Actual versus apparent within cell wall variability of nanoindentation results from wood cell walls related to cellulose microfibril angle[END_REF]. Moreover, using an elastic anisotropic indentation model [START_REF] Delafargue | Explicit approximations of the indentation modulus of elastically orthotropic solids for conical indenters[END_REF]) and a multi-scale cell wall model [START_REF] Alméras | Modeling anisotropic maturation strains in wood in relation to fibre boundary conditions, microstructure and maturation kinetics[END_REF] with the estimated elastic properties of the cell wall constituents given in [START_REF] Salmén | Micromechanical understanding of the cell-wall structure[END_REF]) and a given composition of the S 2 or G layer (i.e., 30% crystalline cellulose and 70% amorphous cellulose and matrix material), leads to an indentation modulus around 16 GPa for an MFA of 0°. The results obtained by RC-AFM seem quite good in average given all the assumption made on the composition of the layer, the properties of its constituent and the fact that the MFA of the S 2 layer is not known. The fact that they are lower may be explained by the fibrous nature of the material that could lead to different contact behaviour even when anisotropy is taken into account. Moreover, this fibrous structure leads to nanometre topography during the cutting process [START_REF] Falhén | Ultrastructural changes in a holocellulose pulp revealed by enzymes, thermoporosimetry and atomic force microscopy[END_REF]. This nano-roughness can lead to an underestimation of the real contact area using a classical contact model that assumes a perfectly flat surface, and yields an estimated indentation modulus lower than the real one. Moreover, the indentation model used is developed for pyramidal (deep) indentation and not for a sphere-plane contact. Finally, measurements in progress show that the accuracy and sensitivity of the RC-AFM to the elastic modulus can be improved by using a stiffer cantilever.

RESULTS AND DISCUSSION

f im f 0 f 0 /Q Table 1
. Indentation modulus ML and reverse of the quality factor Q -1 ( ~ tan δ at the resonance frequency) in the longitudinal direction for the different layers of the cell wall computed from the spectra of Figure 5. Specified uncertainties only correspond to the variations between 3 measurement locations.

M L (GPa) Q -1 Resin 6±1.5 0.013±0.002 CML 6.5±0.5 0.009±0.003 S 2 12±0.5 0.006±0.003 G 14±1.5 0.009±0.003

The last step of the measurement is to do a mapping at a given excitation frequency f im . To be able to compute the resonance frequency and quality factor from the real and imaginary parts of the cantilever vibration, f im must be chosen as close as possible to the resonance frequency on each layer. In the present case, as we want to demonstrate the ability of this technique to sense differences in mechanical properties mainly in the S 2 and G layers, the imaging frequency is chosen close to that obtained on these layers (Figure 5). As a result, the mechanical properties of the embedding resin and, to a less extent, that of the CML will be poorly estimated. The resulting indentation modulus and reverse of the quality factor maps are given in Figure 6 for an imaging frequency of 350 kHz. In Figure 6a, the S 2 and G layers clearly appear to be the stiffest ones in average whereas the S 1 and CML layers are the softest as in Table 1. Layers appear far more clearly than in the topography image of Figure 3. Variations in the indentation modulus of the S 2 layer are observed. These variations could be due to natural gradient properties within the layer (e.g., tangential vs. radial wall) or to local variation in the MFA [START_REF] Sedighi-Gilani | Within-fiber non-uniformities of microfibril angle[END_REF]. But it appears that theyr are mainly due to a slightly oblique cross section combined with the MFA that induce a different type of loading with respect to the microfibrils axis [START_REF] Konnerth | Actual versus apparent within cell wall variability of nanoindentation results from wood cell walls related to cellulose microfibril angle[END_REF]: the highest frequencies would then mean a loading closer to the microfibril axis than the lowest values. In the latter case, contribution of the matrix in the measured frequency is higher. Furthermore, G layers sometime appear to be composed of two slightly different stiffness parts (see the two arrows in Figure 6). We don't know if it's a real property variation in the layer or if it's due to the embedding protocol as resin penetration within the cell wall may change the measured viscoelastic properties. However, it can be inferred that resin presence in the gel of the G layer should increase the elastic modulus. Lastly, it can be seen that topography (e.g., scratches due to the cutting and step height to a less extent, see Figure 3) has an effect on the measurement such as roughness. Whatever the real origin of all these observations, it demonstrates the ability of the RC-AFM to highlight elastic properties variations within a single cell wall layer. For the viscous parameter, tan δ in Figure 6b, results are not so clear as the CML seems to be surprisingly less viscous than the S 2 layer whereas the S 1 is more. This contradicts the values of Q -1 obtained in Table 1 and it seems to be mostly due to the choice in the imaging frequency that is too far from the resonance of the CML (e.g., see the noise in the resin part). It is interesting to note that, on average, the G layer is more viscous than the S 2 as in Table 1. The assumption we made above on the origin of the elastic variations in the S 2 layer due to a slightly oblique cross section is not really confirmed here. If the indentation modulus increased because the microfibril axis is closer to the contact normal, the mechanical contribution of the matrix is lower and then the dissipation too. Again, the effect of the fibrous nature of the layers, and the resulting cutting nanoroughness, on the contact properties are questioned. Note that topography has a stronger effect in that case. Lastly, one can wonder what is the physical meaning (in the frame of tree biomechanics or usual use of wood as a material) of a viscous parameter obtained at a so high frequency. More work has to be done on this aspect of the measurements.

CONCLUSION

This study shows that RC-AFM allows for semi-quantitative estimation of stiffness in a given point and qualitative estimation of its variations at a submicrometre scale. Studies are in progress on improving its calibration and the experimental conditions to make it more quantitative for the estimation of viscoelastic properties. This technique should be able to provide data on the stiffness gradient within the cell wall and its evolution during the maturation process. Moroever, closer views of the G layer topography, indentation modulus and dissipation were made and structures with typical size around 50 to 100 nm were highlight. They could be ascribed to microfibrils bundles, whose size is typically around 20 nm in softwoods (Fahlén and [START_REF] Falhén | Ultrastructural changes in a holocellulose pulp revealed by enzymes, thermoporosimetry and atomic force microscopy[END_REF] and hardwoods [START_REF] Ruelle | Peculiar tension wood structure in Laetia procera (Poepp.) Eichl. (Flacourtiaceae)[END_REF], with a classical tip dilation effect. This shows again the ability of AFM to study the mechanical properties of the cell wall at the ultrastructural scale. However, concerning the estimates of viscous properties of the material, some questions remain on their significance during these kinds of measurements especially at the lowest scale. An other AFM technique, called UFM [START_REF] Cuberes | Ultrasonic force microscopy on strained antimony nanoparticles[END_REF], has been recently used on a similar sample and gives first encouraging results at the microfibrils scale. In the case of developing cells, the sample preparation is not so obvious as for mature cells. Resin penetration can be stronger in that case and have a higher effect on the measurement as the cell wall is softer. First tests on samples of developing cells taken along a differentiation sequence, from the cambium to the mature wood, are currently done using the above embedding technique and an other kind of embbeding resin, known to not penetrate the cell wall of mature cell [START_REF] Konnerth | Actual versus apparent within cell wall variability of nanoindentation results from wood cell walls related to cellulose microfibril angle[END_REF], will be tried soon.

Figure 3 .

 3 Figure 3. AFM topography (256 × 256 points) in contact mode of the chestnut tension wood cross section. Identification of the different cell wall layers and of the embedding LR White resin in the cell lumina. CML stands for compound middle lamella and corresponds to the middle lamella and the primary wall (Figure 1). The scale bar corresponds to the height in nm.

Figure 5 .

 5 Figure 5. Amplitude frequency spectrum for the different layers. Definition of the resonance frequency f 0 and quality factor Q in the case of the embedding resin. Choice of the imaging frequency f im for Figure 6.

  Semi-quantitative mapping at 350 kHz in the same area as in Figure3: a) longitudinal indentation modulus M L -scale bar in GPa; b) reverse of the quality factor Q -1 (~ tan δ at the resonance frequency).

ACKNOWLEDGEMENTS

Financial support by the CNRS, the University of Montpellier 2 and the COST action FP0802 is gratefully acknowledged.


Cyril Cassagnes

Damien Magoni

Hyunseok Chang

Wenjie Wang

Sugih Jamin

Scalability and Efficiency of Push-Driven P2PTV Systems

Keywords: P2PTV, overlay network, peer churn, peer selection

Television transmitted over IP (IPTV) presents numerous opportunities for users as well as service providers, and has attracted significant interest from industry as well as research communities in recent years. Among the emerging IPTV delivery architectures, the peer-to-peer based delivery mechanism is considered attractive due to the relative ease of service deployment and potential bandwidth savings. However, the question of how well P2PTV networks would support a growing number of users has not been fully investigated so far. In this paper, we try to address this question by studying scalability and efficiency factors in a typical P2P based live streaming network. Through the use of the data provided by a production P2PTV network, we carry out simulations whose results show that there are still hurdles to overcome before P2P based live streaming could become widely deployed.

I. INTRODUCTION

W ITH the increasing broadband speed and contin- ued improvement in video compression technologies, Internet-based television (IPTV) services have been experiencing sustained growth lately. When it comes to realizing IPTV services in today's Internet, peer-to-peer (P2P) based delivery mechanism is considered an attractive option because of the ease of deployment and potential bandwidth savings.

In a typical P2P based IPTV network, clients retrieve video streams by connecting to the broadcast server or any other existing clients that are already connected to the network. The broadcast server generates packetized video streams by encoding live TV signals captured from satellite. After joining the network, clients can contribute their uplink bandwidth by forwarding the incoming video streams to other clients needing those streams. To allow more efficient utilization of client's uplink bandwidth, the video streams are typically distributed via the P2P network in the unit of chunks (e.g., [START_REF] Bracciale | A Push-based Scheduling Algorithm for Large Scale P2P Live Streaming[END_REF]) or substreams (e.g., [START_REF] Xie | CoolStreaming: Design, Theory, and Practice[END_REF], [START_REF] Chang | Live Streaming with Receiver-based Peer-division Multiplexing[END_REF]). Chunks are time-divided segments of packetized streams, while sub-streams are space-divided subsets of the original streams (e.g., layers in H.264 SVC). The chunks or sub-streams are either pushed by forwarding clients, or pulled by receiving clients, depending on the P2P sharing protocol used. In the pull-driven delivery, clients search and pull individual stream units in an opportunistic way, while Manuscript received August 25, 2011; revised September 20, 2011. C. Cassagnes and D. Magoni are with the University of Bordeaux, France (e-mail: {cassagne,magoni}@labri.fr).

H. Chang is with Bell Labs, USA (e-mail: hyunseok@ieee.org). W. Wang is with PPLive, China (e-mail: wenjiew@gmail.com). S. Jamin is with the University of Michigan, Ann Arbor, USA (e-mail: jamin@eecs.umich.edu).

in the push-driven approach, a client establishes a virtual connection to a forwarding client, and continues to receive data pushed from the forwarder until either end terminates the connection. Push-driven delivery design was shown to be more efficient than pull-based counterpart in recent work [START_REF] Zhang | Understanding the Power of Pullbased Streaming Protocol: Can We Do Better?[END_REF].

Compared to traditional P2P data sharing or progressive streaming of video on demand, optimizing end-user experience in the P2P based live streaming environment is a non-trivial task because of its more stringent delay constraint and limited shared buffer space. In addition, upload capacity constraints and inherent churning behavior of participating clients can add to the difficulty in realizing a fully scalable delivery system. Motivated by our earlier studies on the operational scalability of P2P based live streaming [START_REF] Shami | Impacts of Peer Characteristics on P2PTV Networks Scalability[END_REF], [START_REF] Cassagnes | On the scalability of p2p-based push-driven live streaming systems[END_REF], we explore the impact of various peer selection algorithms as well as various overlay configuration parameters on the system performance. Configuration parameters includes the number of sub-streams, the buffer capacity, and the number of search attempts. In our study, we focus on the push-driven, sub-stream based streaming architecture, and perform detailed simulations instantiated with the data contributed by a production system employing such an architecture. Upload capacity and session length are important parameters for the P2P network as they determine its scalability and churn.

The remainder of this paper is organized as follows. Section II outlines the previous work done on P2P based live streaming systems. Scalability of such P2PTV networks relies on many characteristics whose impacts on the networks have not been analyzed in depth, to the best of our knowledge. To provide a realistic and fined-grained study of P2P live streaming, Section III presents realistic parameters derived from the analysis of 9.8M sessions collected by the professional-grade Zattoo P2PTV network. Section IV presents evaluation results obtained by simulating the architecture of the Zattoo P2PTV which is one of the largest production P2PTV providers in Europe and identifies the parameters with the most effect on the scalability and efficiency of P2PTV networks. Finally, we conclude the paper by summarizing our contributions and presenting future research directions in Section V.

II. RELATED WORK

With the P2PTV's growing popularity, new P2PTV systems have been proposed, which include ZigZag [START_REF] Tran | ZIGZAG: An Efficient Peer-to-Peer Scheme for Media Streaming[END_REF], PRO [START_REF] Rejaie | A Framework for Architecting Peer-to-Peer Receiver-Driven Overlays[END_REF], Anysee [START_REF] Liao | Anysee: Peer-to-Peer Live Streaming[END_REF], and PULSE [START_REF] Pianese | PULSE: A Flexible P2P Live Streaming System[END_REF], [START_REF] Pianese | PULSE: An Adaptive, Incentive-Based, Unstructured P2P Live Streaming System[END_REF]. Besides such proposals, a large number of measurement papers on existing P2P live streaming systems have been published as well, characterizing workloads [START_REF] Sripanidkulchai | An Analysis of Live Streaming Workloads on the Internet[END_REF] or specific systems such as Telefonica IPTV service [START_REF] Cha | On Next-Generation Telco-Managed P2P TV Architectures[END_REF] and CoolStreaming [START_REF] Xie | A Measurement of a Large-Scale Peer-to-Peer Live Video Streaming System[END_REF], [START_REF] Zhang | CoolStreaming/DONet: A Datadriven Overlay Network for Live Media Streaming[END_REF].

Being one of the most popular operational P2PTV systems, PPLive has been extensively studied by researchers [START_REF] Hei | A Measurement Study of a Large-Scale P2P IPTV System[END_REF], [START_REF] Vu | Measurement and Modeling of a Large-scale Overlay for Multimedia Streaming[END_REF], [START_REF] Ali | Measurement of Commercial Peerto-Peer Live Video Streaming[END_REF]. Silverston et al. [START_REF] Thomas | Traffic Analysis of Peer-to-Peer IPTV Communities[END_REF] characterized various P2P IPTV traffic generated by PPLive, PPStream, Sopcast and TVants, in terms of the transport-level protocols used and session behaviors.

In addition, numerous research proposals for improving existing P2P-based live streaming systems have been presented, ranging from feasibility study [START_REF] Sripanidkulchai | The Feasibility of Supporting Large-Scale Live Streaming Applications with Dynamic Application End-points[END_REF] and upload capacity analysis [START_REF] Douceur | Maximizing Total Upload in Latency-Sensitive P2P Applications[END_REF], to locality awareness algorithm proposal [START_REF] Pianese | Resource and Locality Awareness in an Incentive-based P2P Live Streaming System[END_REF] and stochastic fluid theory for P2P streaming systems [START_REF] Kumar | Stochastic Fluid Theory for P2P Streaming Systems[END_REF]. Many proposals based on robust incentives [START_REF] Feldman | Robust Incentive Techniques for Peer-to-Peer Networks[END_REF], altruism [START_REF] Chu | Considering Altruism in Peer-to-Peer Internet Streaming Broadcast[END_REF], contribution awareness [START_REF] Sung | Enabling Contribution Awareness in an Overlay Broadcasting System[END_REF] and sub-stream trading [START_REF] Liu | Substream Trading: Towards an Open P2P Live Streaming System[END_REF] aim at avoiding free-riders in large scale systems that have appeared. Most recent works explore topological properties of practical P2P streaming [START_REF] Wu | Magellan: Charting Large-Scale Peer-to-Peer Live Streaming Topologies[END_REF]. Small et al. [START_REF] Small | Scaling Laws and Tradeoffs in Peerto-Peer Live Multimedia Streaming[END_REF] address the subject from a theoretical perspective and propose a heuristic called Affinity which considers in its neighbor selection process multiple parameters such as upload capacity, playback delay and bandwidth cost, in order to build optimal P2P topology for live multimedia streaming.

III. PEER CHARACTERISTICS MEASURED IN A REAL P2PTV NETWORK

In order to carry out realistic simulations and to achieve a fine-grained analysis of the scalability and efficiency of a P2PTV network, we must take into account many peer characteristics. To this end, we collected data from the Zattoo's P2PTV network which is a push-based P2P streaming network. In Zattoo, peer selection is based on delay measurements between peers, as well as their topology and geographic information (e.g., IP address, AS number, country, etc.). The network covers eight European countries, serving over 3 million registered users. The data used in our analysis originate from a Zattoo's session database collected during a two-week period from March 10th to 24th, 2008. Each session in the database records user's stream watching behavior including start/end timestamps, number of bytes uploaded/downloaded, etc. The number of sessions recorded amounts to 9.8 million sessions covering 198 channels and 8 countries. From the collected data, we identify four main peer characteristics that may impact a P2PTV network:

1) Session length (Section III-A).

2) Inter-arrival time (Section III-B).

3) Upload capacity (i.e., redistribution factor, Section III-C). 4) NAT compatibility (Section III-D).

A. Session length

Figure 1 shows the distribution of session lengths with the xaxis using a log scale. As already observed in several previous works [START_REF] Cha | On Next-Generation Telco-Managed P2P TV Architectures[END_REF] [16] [START_REF] Vu | Measurement and Modeling of a Large-scale Overlay for Multimedia Streaming[END_REF], its Cumulative Distribution Function (CDF) fits a log curve. On this figure, we can observe that 80% of the peers have sessions shorter than 10 minutes. This is a typical value also observed in prior works, but it can vary depending on both channel contents (e.g., news-only, movieonly channels, etc.) and users' channel surfing behavior. It is important to note that the shorter the session length is, the higher the rates of churn is. High churn rate could have an adverse effect on the stability of the overlay.

B. Inter-arrival time

Figure 2 shows the distribution of the inter-arrival times measured for one popular channel. We have used a log scale for the x axis. We can observe that the CDF distribution roughly fits a log curve for inter-arrival times between 1 and 6 seconds. On this figure, we can locate the knee of the distribution at roughly 10 seconds for the vast majority of the peers (i.e., 96%). This means that the start times of the sessions are often very close to each others suggesting flash crowd patterns. It is not common that two following starting sessions are separated by a long time interval. For this popular channel the maximum inter-arrival time recorded was 300 seconds but this value can vary depending on both channel content and user behavior.

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FFF Fig. 2. Distribution of the inter-arrival time.

C. Upload capacity

We define the ratio of one incoming stream that can be redistributed to other peers as a redistribution factor, and label it with k. The redistribution factor k may take a value from 0 to infinity depending on the peer's uplink capacity. For instance, if k = 1, it means that the peer can redistribute a full stream, whereas if k = 2, it means that the peer redistributes two copies of the stream. Fractional values are also possible as a full stream can be divided into multiple sub-streams. Subdividing a stream allows a peer to redistribute only a subset of the stream to other peers; for instance, if k = 0.5, it means that the peer redistributes only half of the stream due to its uplink bandwidth constraint or buffer availability. The maximum number of peers able to connect to the system will depend on the average value of k: if it is below 1, the system can not scale and the overlay will reach a maximum size.

Figure 3 shows the distribution of the ratio k, where k is the upload rate divided by the download rate. Upload rate is measured between the peer and a specific server located in Europe. As bandwidth measurement depends on many factors and is very difficult to do, the values reported here may not be accurate. The CDF distribution looks like a log plot although it does not fit a log curve. The distribution is therefore highly heavy-tailed.The average value of k computed from all the distribution values is equal to 0.89, thus still below 1 (and its value is not significant since the distribution is not normal). We found that 50% of the peers can redistribute less than 50% of the full stream (i.e., k < 0.5), while 82% of the peers can redistribute less than the full stream (i.e., k < 1). A P2PTV network relying solely on these redistribution values cannot scale.

D. NAT compatibility

In today's Internet, the majority of peers are behind some type of NAT gateways which can in some cases block the communication between two peers [START_REF] Guha | Characterization and Measurement of TCP Traversal through NATs and Firewalls[END_REF]. Therefore a typical P2P sharing software implements a NAT traversal method [START_REF] Rosenberg | RFC 5389: Session Traversal Utilities for NAT (STUN)[END_REF] in order to facilitate communication between peers behind NAT gateways. Zattoo's NAT traversal process can detect six different NAT configurations: open host, full cone, IPrestricted, port-restricted, symmetric, and UDP-disabled. Each NAT configuration is assigned a distinct NAT type number, from 1 (open; the least restrictive type) to 6 (UDP-disabled; the most restrictive type). Figure 4 shows the reachability among the various NAT types. Consider a pair of peers whose NAT types are represented on the row and column of the matrix. Notice that the matrix is symmetric; it does not matter whether the parent peer or the child peer is represented in the row or column. At the intersection lies the reachability. If the cell is white, the peers can connect to each other. If the cell is black, the peers cannot connect to each other.

Figure 5 shows the distribution of the NAT types of the peers. Most peers have a NAT type of 4 or 5. Some peers have a NAT type of 1, 2, or 6. There is a negligible number of peers with NAT type 3. Given the previous distribution and the matrix, the first chance connectivity probability for a peer to connect at a given layer of depth n > 1 is around 56% (total area minus black area divided by total area, p 1 = (10000 -(1800 + 2000 + 625))/10000 = 0.5575). On the other hand, if the peers try to optimally connect to each other in order to maximize redistribution, the average connectivity probability for the peers to connect to a layer of depth n is around 90%. In this optimal configuration, all type 6 peers connect to type 1 peers, 60% of type 5 peers connect to type 2 peers, all type 4 peers connect to type 4 peers, and all type 2 peers connect to type 5 peers. The remaining 40% of type 5 peers cannot connect to anyone, thus giving 10% chance of connection failures.

IV. SIMULATION OF A P2P LIVE STREAMING OVERLAY

In this section, we propose several enhancements in constructing a P2P overlay and we evaluate them by carrying out detailed simulations.

A. Simulation parameters and metrics

Our simulation code faithfully implements Zattoo's peerdivision multiplexing protocol for P2P based streaming [START_REF] Chang | Live Streaming with Receiver-based Peer-division Multiplexing[END_REF]. The simulation is then performed using the network manipulator software called nem [START_REF] Magoni | Network Topology Analysis and Internet Modelling with Nem[END_REF] which is driven by a packet level discrete event engine. An Internet map consisting of 4,200 nodes is used as the underlying topology [START_REF] Magoni | Internet Core Topology Mapping and Analysis[END_REF]. Each simulation experiment lasts for 12 hours, and analysis is done only for the last 6 hour period when the system is in a steady state regime. We repeat each experiment 30 times, and we report the average taken from those 30 runs. We draw from the peer characteristics described in Section III to set the following input parameters in our simulation: (i) session length, (ii) NAT type, and (iii) upload capacity (k factor). We randomly instantiate these parameters so that the resulting distributions match those reported in Section III. Table I shows the remaining input parameters. Our simulation models Zattoo's peer-division multiplexing based P2P streaming network, except that peer selection is purely random. We consider alternative peer selection algorithms to investigate their impact in Section IV-C. In order to assess the performance of the P2P live streaming system, we study the following output metrics.

1) View time ratio: This metric is calculated by peer's view time divided by the peer's life time. From this metric, one can infer how much time is devoted to joining the P2P overlay and searching for available streams before starting to watch a given channel. 2) Ratio of kicked out peers: This metric is calculated by the number of peers that could not connect to the P2P overlay during a given period, divided by the total number of new peers joining during the period. 3) Average number of interruptions per peer: This metric is calculated by the number of video viewing interruptions for all peers in a given period, divided by the total number of new peers joining during the period.

B. Influence of peer characteristics on simulation results

We analyze the above output metrics by varying the number of newly joining peers per hour, which is defined as the traffic load on the P2P network. We assume that a stream consists of 16 substreams, and that each peer's buffer can store 6 seconds' worth of streaming data. Furthermore, each peer is assumed to attempt two rounds of searches when the peer detects any missing substream in its buffer.

1) Influence of the session length: Figure 6 shows the average view time ratio of peers with different traffic load (i.e., number of newly added peers per hour). To observe the influence of the session length on view time ratio, we set the redistribution factor k to 1. Different NAT configurations are not taken into account in this experiment. Three sets of simulations are performed, one with a constant session length of 12 minutes, another with 24-minutes, and finally with variable session lengths following the distribution shown in Figure 1. Twelve minutes is the average value of the distribution shown in Figure 1. The small difference in the session length curve is due to the necessary startup join time to connect to the network. When sessions are shorter, this startup join time increases, and is no longer negligible, as is the case of the real session length distribution (i.e., around 4%). It turns out that regardless of the session length distribution, the view time ratio is close to 100%. So the number of interruptions is minimal and the short session length allows the overlay not to saturate. We do not show the amount of kicked out peers as it is equal to 0 for all these simulations with k = 1.

2) Influence of the upload capacity: Figure 7 shows the average view time ratio of peers with different traffic load. To highlight the influence of the redistribution factor k on view time ratio, we use a constant session length of 12 minutes. As in the previous case, different NAT configurations are not taken into account in this scenario. We run 3 sets of simulations, with fixed redistribution factors k = 1 and k = 2, as well as variable k following the distribution shown in Figure 3. The figure shows that when realistic redistribution factors k are used, the overlay does not scale. That is, the view time ratio falls rapidly as the traffic load increases. Note that the traffic load is a loose underestimate of the network capacity (as it is computed with the average session length). We can see in Figure 7 that the network starts to get saturated with a traffic load around 500, but not 250, because most of the sessions are much shorter than the average 12 minute length, and thus more sessions are needed to overload the network. We observe that at a traffic load of 1,000, only 50% view time ratio is achieved. At a load of 2,000, view time ratio is as low as 5%. At this load, most peers cannot connect to the network as it is completely saturated. The view time ratio is close to 100% for k = 1 and k = 2 (as already seen above for k = 1). This result illustrates the importance of having peers with k > 1 for the P2P overlay to scale.

In order to see if the view time ratio decrease is due to a higher startup join delay or because peers cannot connect to the overlay, we look at the number of peers that are kicked out of the network. When peer's view time ratio is very low (e.g. below 1%), it may be because the peer could not get the stream and left prematurely). Figure 8 shows the average number of peers kicked out as a function of the traffic load. To observe the influence of the redistribution factor k on the number of kicked out peers, we use the same parameters as above. The ratio of kicked out peers is equal to 0% for k = 1 and k = 2. However, when we use the real distribution of k, the number of kicked out peers increases rapidly as the traffic load increases. Figures 7 and8 together show that the decrease of view time ratio is mainly due to the increase in the number of kicked out peers. These results confirm that the real k distribution is a limiting factor that prevents the overlay from being scalable in itself.

3) Influence of the NAT compatibility: Next, we examine the average view time ratio when we use realistic redistribution factors k and session lengths taken from Figures 3 and6 respectively. Figure 1 shows the average peer view time ratio as a function of the traffic load. We run two sets of simulations, capturing two different scenarios. In the first scenario, every peer has a NAT type 1 configuration, while in the second scenario, each peer is assigned a NAT type taken from the realistic NAT type distribution shown in Figure 5. When the number of peers is small, everybody can connect directly to the source, and the view time percentage is close to 100%. When the number of peers increases, peers have to connect to each other to create a P2P network. Due to the NAT compatibility issues and the limitations caused by the k factor, the view time ratio gradually decreases to 75% and 60% for the first and second scenarios respectively. The relative gap between the first and second scenarios depends on the traffic load. It starts at close to 0% when the load is 250 or less, and then increases up to roughly 15% when the load is 4,000 peers per hour. In the simulations, peers perform only two rounds of searches for available peers before quitting, which explains why the relative difference between the two scenarios is much more than the theoretical 10% defined at the end of Subsection III-D. The latter figure can be reached only after a sufficient amount of tries. With only one try, there is a relative difference of 43% on average between the two. Also, due to the upload capacity limitation, each peer redistributes only a part of the full stream, resulting in the view time ratio decreasing to 75% at traffic load 4,000 in the first scenario. Results in this plot and the next one are different from the ones presented in Figure 7 and Figure 8 because here the session length of the peers is not fixed but instantiated realistically by following the probability distribution shown in Figure 1. The values of the randomly set lifetimes are on average much shorter than the fixed 12 minutes used in the previous subsection. That explains why the percentage of viewing time is much higher in Figure 9 than in Figure 7 and why the percentage of kicked-out peers is much lower in Figure 8 than in Figure 10. As the peers remain on average less time in the overlay, the traffic load must be much higher to saturate the overlay in order to prevents new peers to join and view the stream.

As before, we consider the average number of kicked out peers that account for the decrease of the view time ratio. Figure 10 plots the average percentage of peers that could not connect to the P2P network as a function of the traffic load. We use the same parameters as in the previous figure. When the load is equal to or less than 250, every peer can connect directly to the source, and there is no kicked out peer. When the number of peers increases, the number of kicked out peers with realistic NAT type distribution gradually increases to around 26% for a load of 2,000 and 31% for a load of 4,000. As the view time ratio is equal to 61% at a traffic load of 4,000, we can conclude that the decrease in view time ratio is mainly accounted for by the kicked out peers. Only a small part is due to the startup join time. When all peers have NAT type 1 configuration, they can connect to each other. Therefore, although the number of kicked out peers does increase due to the k factor, it is always relatively 15% or more below the kicked out peers compared to the realistic NAT type case. Based on all these results, we conclude that in a P2PTV overlay network, the NAT compatibility issue can create a non negligible loss of peers.

C. Influence of peer selection algorithms on simulation results

Next, we present the results that highlight the impact of peer selection algorithms on the performance of a typical P2P live streaming system. When a new peer joins an overlay, it performs its own peer selection algorithm to choose the target peer(s) to connect to. If the peer selection is done randomly, the resulting overlay could become quite inefficient in two perspectives. First, the overlay could become too deep and not wide enough, thus incurring large playback lags. Secondly, the overlay could experience a lot of churns, thus incurring frequent playback interruptions for users. Intuitively, P2PTV overlays could be made more efficient by placing more stable and high bandwidth peers closer to the source. The peer selection algorithm is a good place to influence the evolution of the overlay as we can more or less control where the peers will place themselves in the overlay. If a peer selection algorithm manages to put stable peers close to the source, this should reduce the overall churn in the overlay. Also, if this algorithm manages to put high bandwidth peers close to the source, this should increase the capacity of the overlay while keeping a reasonable depth in the overlay.

A carefully designed peer selection algorithm should improve the efficiency of a streaming overlay by incorporating dynamic parameters such as upload capacities, session lengths, distances among peers and overlay depth positions. Such modifications may impact both P2PTV overlays and peers.

According to the session data collected by Zattoo, the CDF of the redistribution factor k follows an exponential distribution, where 50% of the peers can redistribute less than 50% of the full stream (i.e., k < 0.5), and 82% of the peers can redistribute less than the full stream (i.e., k < 1). Following this observation, we assign uplink capacity to individual peers so that the resulting uplink distribution becomes identical to the empirical distribution. The NAT type of a peer, which determines the peer's reachability in the overlay, is also taken from the empirical distribution of NAT types. Finally, session's inter-arrival time and session length are all instantiated from the corresponding exponential distributions.

A peer trying to connect to other peers to get all necessary substreams is called an orphan peer. It sends search messages to discover other peers, sends join messages to connect to available peers, and finally constructs the full stream from them. A peer who is able and willing to offer a part of or all requested substreams for an orphan peer is called an adoptive peer. An adoptive peer positively answers to the search message of an orphan. Once having multiple positive answers from potential adoptive peers, an orphan has to choose to which peer it should send a join message. We evaluate the following four peer selection algorithms all relying on available information: • Random: an orphan peer tries to connect to a randomly selected adoptive peer.

• Local: an orphan peer tries to connect to its closest adoptive peer (in terms of the hop distance).

• Upload: an orphan peer tries to connect to the adoptive peer proposing the highest upload amount (measured in terms of the number of substreams).

• Uptime: an orphan peer tries to connect to the adoptive peer which joined the overlay the earliest as it has the highest probability of remaining in the overlay. Figure 11 shows the average peer view time ratio as a function of the traffic load. We can see that the effects of the various algorithms on the view time do not make much difference compared to random peer selection. Although there is 7% difference between the worst (uptime) and the best (random) algorithms at a traffic load of 2,000, and 5% difference at a load of 4,000, the differences are not significant. This somewhat unexpected result implies the relative importance of the user level characteristics such as upload capacity and session length, over the system level configurations such as the peer selection algorithms.

Figure 12 shows the average percentage of peers kicked out as a function of the traffic load. Compared to the previous results, the decrease in view time ratio, as illustrated in Figure 11, is mainly due to peers being kicked out of the network. Only a small percentage is caused by the interruptions resulting from peer disconnections and reconnections.

Figure 13 shows the average number of interruptions per peer as a function of the traffic load. We observe that the average number of interruptions per peer gradually increases when the number of peers increases until reaching traffic load 2,000. When the number of new peers increases, the overlay grows and the average churn rate becomes higher, and thus leading to more frequent connections and reconnections. However, when the overlay is getting saturated by new peers, those new peers cannot manage to join the overlay and are kicked out. The number of connections and reconnections does not grow as much in this case because those kicked out peers do not significantly contribute to this number. However, the total number of peers still increases, and thus the ratio does not increase anymore.

Two remarks can explain the marginal improvements made by the alternative algorithms compared to the simple random selection algorithm. First, the sessions are typically short-lived. Roughly 50% of the sessions are shorter than 1.5 minutes. This creates a lot of churns that render the evolution of the overlay hard to control over time. Second, the redistribution factor distribution is heavily lopsided towards small values; 50% of the peers have an upload capacity lower than 50%. Thus, peers with long sessions may have a low upload capacity and not be so useful. It turns out that these two factors impact the view time ratio much more than the various selection algorithms. When traffic load is high, the algorithm that performs better than random selection is the local algorithm.

D. Influence of overlay parameters on simulation results

We now study the influence of three important parameters used in the overlay which are the number of substreams per stream, the buffer capacity and the number of search attempts. 1) Influence of the number of substreams: In P2PTV systems such as Zattoo, a full stream is subdivided into multiple substreams. Here we study the impact of the number of substreams that constitute a full stream. In this experiment, we change the peer buffer size so that it can store 12 seconds of streaming data. we keep the other parameters the same as previously, such as realistic inter-arrival time, random peer selection algorithm, and two search attempts. Figure 14 shows that the view time ratio is increasing when the main stream is divided into multiple substreams. The redistribution is easier as peers can allocate their uplink bandwidth on a finer granularity. As a result, substreams improve system scalability.

Figure 15 shows that the number of interruptions increases with the number of substreams, due to the difficulty in finding multiple different substreams that are roughly in sync. In fact, the substreams increase the control traffic overhead. However, this is not an issue while the view time ratio remains high.

2) Influence of the buffer capacity: We now use the same number of search attempts as above with the random peer selection algorithm. To observe the influence of the buffer capacity, we increase it from 3 to 12 seconds. We show in Figure 16 the impact of the buffer capacity on view time ratio and the number of interruptions per peer. Under the heaviest load of 4,000 new peers per hour, the view time ratio is roughly 60% for 16 substreams and 45% for 1 full stream. This shows that splitting the stream does significantly improve the viewing time. The buffer time however, has no real impact on the viewing time. When observing the number of interruptions shown in Figure 17, we see that it grows with the traffic load and is higher when the stream is divided into 16 substreams. When the stream is not divided, a longer buffer duration reduces the number of interruptions. When the traffic load increases, the number of interruptions for a small or medium buffer tend towards the same values whether the stream is split or not. From the previous simulation results, it appears that the division of the full stream into several substreams increases the number of interruptions (especially under low traffic load) but improves the amount of viewing time. Moreover, a large buffer capacity can reduce the number of interruptions but does not affect the view time ratio. Thus, the best solution is to divide the full stream in many substreams and use a buffer with a large storage capacity (i.e., 12 seconds in our simulations). 3) Influence of the number of search attempts: We now study the impact of the number of search attempts. We set a buffer capacity of 12 seconds and use the random peer selection algorithm.Regardless of the number of search attempts, Figure 18 shows that the number of interruptions does not change and remains low. A high number of attempts with several substreams improve the overlay scalability. Figure 19 shows the benefit of using multiple substreams. With substreams the view time ratio reaches 70%. When a peer attempts two rounds of searches, the view time ratio curve reaches 60%, and finally with four rounds of search attempts the view time ratio falls below 50%. Figure 20 shows the network saturation point. When this point is reached, new peers start to get kicked out. This number is minimal when the stream is divided into multiple substreams, and the number of search attempts is equal to 1. If peers increase the search attempts at the saturation point, the saturation phenomenon is only amplified. Dividing the stream is necessary to ease the redistribution while the number of search attempts helps peers find adoptive peers. Without using substreams, the overlay becomes less resilient and increasing the number of search attempts does not help find available adoptive peers. V. CONCLUSION P2PTV network is a content delivery architecture that is particularly attractive due to the relative ease of deployment and its potential bandwidth savings. However, as it gains in popularity, we need to evaluate the behavior of large scale P2PTV network under heavily loaded conditions. Such heavyload scenarios have not been fully investigated in the literature due to the lack of measurement data. In this paper, we studied several factors that can affect the scalability and efficiency of typical P2PTV network by performing detailed simulations. In order to instantiate realistic simulation settings, we analyzed 9.8 million sessions collected from the professional-grade Zattoo's P2PTV network. In this paper, we demonstrated that both the redistribution factor and peers' available upload capacity have a strong impact on the P2PTV network's scalability. Contrary to the intuition, we found that the peer selection process plays a relatively marginal role in improving the P2PTV network scalability. Instead, we observed that the redistribution factor and session lengths have far more significant effect on the maximum capacity of the P2P overlay. Finally, we demonstrated the influence of the buffer size and peer search parameters on the overall efficiency of the overlay. Building a scalable and efficient P2P overlay thus requires a careful consideration of the parameters we have studied in this paper, including peer characteristics as well as overlay configuration parameters. Our contribution is therefore multifold and can be summarized as follows:

• We have analyzed 9 million P2PTV sessions from a real production network and we have derived the probability distributions of the most important parameters such as session length, redistribution factor, inter-arrival time, NAT type. These distributions can be useful to other researchers for realistically simulating P2PTV networks.

• We have simulated a P2PTV network and have shown that the redistribution factor is the parameter that has the highest impact on the viewing time and the amount of kicked out peers.

• We have also shown that peer selection strategies have nearly no influence upon these values.

• We have finally shown that configuration parameters such as the number of substreams, the buffer duration and the number of search attempts do have an impact but only when the traffic load is high. Our future work will be aimed at studying new methods to limit peer churn and relieve the limitations imposed by low upload capacity peers. For example, the positioning of long lived peers at the top of the distribution tree could help to reduce churn. Moreover, the filtering of low upload capacity clients could also help to achieve a redistribution factor close to one thus making the overlay scalable. We plan to carry out further experiments to study these important issues.

FFFFig. 1 .

 1 Fig. 1. Distribution of the peers' session length.

Fig. 3 .

 3 Fig. 3. Achievable redistribution factor.

Fig. 4 .

 4 Fig. 4. NAT type compatibility matrix.

Fig. 5 .

 5 Fig. 5. Distribution of the peers' NAT type.

Fig. 6 .

 6 Fig. 6. Average peer view time vs. traffic load.

Fig. 7 .

 7 Fig. 7. Average peer view time vs. traffic load.

Fig. 8 .

 8 Fig. 8. Number of peers kicked out vs. traffic load.

Fig. 9 .

 9 Fig. 9. Average peer view time vs. traffic load.

Fig. 10 .

 10 Fig. 10. Number of peers kicked out vs. traffic load.

Fig. 11 .

 11 Fig. 11. Average view time vs. traffic load.

Fig. 12 .Fig. 13 .

 1213 Fig. 12. Average percentage of peers kicked out vs. traffic load.

Fig. 14 .Fig. 15 .

 1415 Fig. 14. Impact of the number of substreams on the peers' view time.

Fig. 16 .

 16 Fig.[START_REF] Hei | A Measurement Study of a Large-Scale P2P IPTV System[END_REF]. Impact of the buffer size on the peers' view time.

Fig. 17 .

 17 Fig. 17. Impact of the buffer size on the interruptions.

Fig. 18 .

 18 Fig. 18. Impact of the number of search attempts on the interruptions.

Fig. 19 .

 19 Fig. 19. Impact of the number of search attempts on the peers' view time.

Fig. 20 .

 20 Fig. 20. Impact of the number of search attempts on the kicked out peers.