Maxime Lanoy

Fabrice Lemoult

Geoffroy Lerosey

Arnaud Tourin

Valentin Leroy

John H Page

Three-dimensional acoustic lensing with a bubbly diamond metamaterial

A sound wave travelling in water is scattered by a periodic assembly of air bubbles. The local structure matters even in the low frequency regime. If the bubbles are arranged in a face-centered cubic (fcc) lattice, a total band gap opens near the Minnaert resonance frequency. If they are arranged in the diamond structure, which one obtains by simply adding a second bubble to the unit cell, one finds an additional branch with a negative slope (optical branch). For a single specific frequency, the medium behaves as if its refractive index (relative to water) is exactly n = -1. We show that a slab of this material can be used to design a three three-dimensional flat lens. We also report super-resolution focusing in the near field of the slab and illustrate its potential for imaging in three dimensions.

I. INTRODUCTION

All classical wave phenomena are influenced by a single quantity: the refractive index. In the late 1960s, the Russian researcher Veselago wondered how an electromagnetic wave would propagate if this index became negative [START_REF] Veselago | Electrodynamics of substances with simultaneously negative and[END_REF] . He predicted that, at the interface between a negative index material (NIM) and a regular medium, negative refraction would occur. Three decades later, the first experimental observation of a negative refractive index was performed for electromagnetic waves in the microwave range [START_REF] Shelby | Experimental verification of a negative index of refraction[END_REF] . In the previous year, Pendry [START_REF] Pendry | Negative refraction makes a perfect lens[END_REF] had claimed that a slab made of a NIM of index n = -1 could be turned into a perfect lens, without being subject to the diffraction limit. A quest for NIMs started in the early 2000s.

The main strategy to obtain these negative indices has involved building artificial materials, namely metamaterials. In the low frequency regime, wave propagation can be fully described in terms of two macroscopically homogeneous effective parameters. For electromagnetic waves, the refractive index is negative when both the effective permittivity [START_REF] Pendry | Low frequency plasmons in thin-wire structures[END_REF] and permeability [START_REF] Pendry | Extremely low frequency plasmons in metallic mesostructures[END_REF][START_REF] Pendry | Magnetism from conductors and enhanced nonlinear phenomena[END_REF] are negative. For acoustic waves, the effective density [START_REF] Liu | Locally resonant sonic materials[END_REF] and compressibility [START_REF] Fang | Ultrasonic metamaterials with negative modulus[END_REF] should be simultaneously negative. Most designs rely on the use of subwavelength resonant scatterers, which may either be arranged in random or ordered configurations. To achieve double negativity, one can tune the effective parameters of the medium by exploiting the nature of these resonances. For instance, in acoustics, a monopolar resonance can lead to a negative compressibility while a dipolar one gives a negative density. Combining these two types of resonances has allowed 9,10 a negative index, or strictly speaking a negative sound velocity, to be reached.

Interestingly, anomalous refraction, and notably a negative one, had actually been observed earlier in another kind of artificial medium, namely the photonic/phononic crystal [START_REF] Kosaka | Superprism phenomena in photonic crystals[END_REF][START_REF] Luo | All-angle negative refraction without negative effective index[END_REF][START_REF] Yang | Focusing of sound in a 3d phononic crystal[END_REF][START_REF] Xu | All-angle negative refraction and active flat lensing of ultraviolet light[END_REF][START_REF] Dubois | Acoustic flat lensing using an indefinite medium[END_REF] . a) Electronic mail: maxime.lanoy@gmail.com. b) Electronic mail: John.Page@UManitoba.ca Note that these media can be either two- [START_REF] Kosaka | Superprism phenomena in photonic crystals[END_REF][START_REF] Luo | All-angle negative refraction without negative effective index[END_REF] or three- [START_REF] Yang | Focusing of sound in a 3d phononic crystal[END_REF][START_REF] Xu | All-angle negative refraction and active flat lensing of ultraviolet light[END_REF][START_REF] Dubois | Acoustic flat lensing using an indefinite medium[END_REF] dimensional. The refraction in this case is actually due to the intrinsic periodic nature of these media, and can be seen as a generalization of the diffraction orders of periodic gratings. Indeed, due to the periodicity, the propagating eigensolutions inside these media are Bloch waves, which are the superposition of many plane waves. They all share the same orientation of the group velocity, which completely governs the refraction of beams. The implementation of this concept in a twodimensional phononic crystal [START_REF] Sukhovich | Negative refraction and focusing of ultrasound in two-dimensional phononic crystals[END_REF] has even reached the ultimate case of all angles being refracted similarly, thus resembling the case of an effective medium of index n = -1 . Focusing below the diffraction limit was also demonstrated in this case as a consequence of trapped slab modes [START_REF] Sukhovich | Experimental and theoretical evidence for subwavelength imaging in phononic crystals[END_REF][START_REF] Robillard | Resolution limit of a phononic crystal superlens[END_REF] .

In between metamaterials with randomly arranged scatterers and phononic crystals resides a category of media that we could call crystalline metamaterials [START_REF] Kaina | Negative refractive index and acoustic superlens from multiple scattering in single negative metamaterials[END_REF][START_REF] Lemoult | Soda cans metamaterial: A subwavelength-scaled phononic crystal[END_REF][START_REF] Yves | Left-handed band in an electromagnetic metamaterial induced by sub-wavelength multiple scattering[END_REF] . Indeed, close to the resonance frequency of the scatterers introduced inside a metamaterial, the effective wavelength can become as small as the average separation distance between scatterers. Then, the long wavelength approximation no longer applies and the propagation is sensitive to the spatial structure of the medium. This sensitivity to structure was a crucial aspect of the observation of negative refraction in two dimensional materials in acoustics consisting of a honeycomb arrangement of soda cans [START_REF] Kaina | Negative refractive index and acoustic superlens from multiple scattering in single negative metamaterials[END_REF] .

In this article, we exploit a similar strategy to design a threedimensional medium which exhibits all-angle negative refraction. The medium is made of underwater bubbles, which are effective ultrasonic low-frequency resonant scatterers. Interestingly, the appropriate three-dimensional crystalline structure turns out to be that of diamond, one of the natural crystals of the carbon atom (analogous to the honeycomb structure in two dimensions). We verify numerically the negative refraction of a beam as well as the focusing of a point source by a flat lens. We also demonstrate its capabilities in terms of subwavelength focusing. Note that the recent advances in 3D printed frames for the design of stable air bubble assemblies [START_REF] Choi | Large-scale generation of patterned bubble arrays on printed bifunctional boiling surfaces[END_REF][START_REF] Cai | Bubble architectures for locally resonant acoustic metamaterials[END_REF][START_REF] Combriat | Acoustic interaction between 3d-fabricated cubic bubbles[END_REF] make our proposal achievable in practice. Also, as only monopolar scatterers and the specific periodicity are relevant here, it makes the design adaptable to airborne acoustics (with spherical Helmholtz resonators for instance) or even to other kind of waves (e.g. elastic waves).

II. METAMATERIAL DESIGN

As indicated in the previous paragraph, the design of our acoustic metamaterial is based on the acoustic resonance of air bubbles. Indeed, the significant contrast in density and in compressibility between the inclusion (air) and the host medium (water) results in a monopolar resonance that occurs at very low frequency: the so-called Minnaert resonance [START_REF] Minnaert | On musical air-bubbles and the sounds of running water[END_REF] . For instance, the resonance of an air bubble of radius r = 1 mm is expected at f m = 2890 Hz 26 , which corresponds to a wavelength in water of 52 cm (520 times the bubble radius). In this regime, the pressure field at resonance is roughly homogeneous over the whole bubble surface and the acoustic response can be considered as isotropic. When a plane wave of unity amplitude impinges on such an air bubble, it gives rise to a scattered spherical wave whose amplitude s(ω) can therefore be modelled by a complex Lorentzian function:

s(ω) = - r 1 -ω 2 m /ω 2 + ik 0 r . (1)
Here, k 0 stands for the wavenumber of the initial incident plane wave in bulk water and ω m corresponds to the Min- naert frequency. Note that this expression does not account for viscous and thermal damping mechanisms, which will be discussed later on.

When several bubbles coexist, multiple scattering effects must be taken into account [START_REF] Kafesaki | Air bubbles in water: a strongly multiple scattering medium for acoustic waves[END_REF] . Although there is no analytical solution for this self-consistent problem, the calculation can be computed thanks to the formalism introduced by Lax [START_REF] Lax | Multiple scattering of waves. ii. the effective field in dense systems[END_REF] . Technical details are available in a previous publication dealing with multiple scattering of sound in a disordered bubbly medium [START_REF] Lanoy | Subwavelength focusing in bubbly media using broadband time reversal[END_REF] . At low frequency, the propagation in such a multiple scattering medium of bubbles is similar to the propagation in a homogeneous medium described by effective parameters which are essentially ruled by the scattering function s(ω) and the concentration of scatterers. In this article, instead of a random cloud, we propose to position the bubbles (radius r = 1 mm) in a periodic fashion. We start off by arranging them on the lattice sites of a face-centered cubic (fcc) lattice [Fig. 1(a)], with a lattice constant of a = 11.8 cm (Note that this means the sample is highly diluted since the corresponding air volume fraction is φ = 0.001%). This crystal is expected to behave roughly isotropically since its Brillouin zone is a fairly regular octahedron [see Fig. 1(c)], a characteristic that facilitated the first observation of a complete band gap in three-dimensional phononic crystals [START_REF] Yang | Ultrasound tunneling through 3d phononic crystals[END_REF] . The eigenvalue problem is numerically solved in COMSOL considering the unit cell drawn in Fig. 1(b) and applying periodic boundary conditions on its edges. Following this procedure along the main directions of the crystal, one obtains the band structure displayed in Fig. 1(d) (blue solid line). One can notice two propagative bands (branches) separated by a complete band gap that opens near the Minnaert frequency. As for the random distribution of scatterers [START_REF] Lanoy | Subwavelength focusing in bubbly media using broadband time reversal[END_REF] , the propagation could be described in terms of an effective compressibility which is influenced by the resonance of the bubbles. The band gap corresponds to a negative compressibility while the flattening of the dispersion relation for the lower branch corresponds to a high compressibility.

One interesting feature can be seen for the branch just below the bandgap, near the Minnaert frequency: it exhibits solutions for wavenumbers at the edges of the first Brillouin zone. This might seem surprising since, as pointed out earlier, the wavelength in water is 52 cm (i.e., nearly 5 times the lattice constant a). This indicates that, near this frequency, the sound wave travels inside the crystal with a much smaller "effective" wavelength, suggesting that both the local and long range spatial structure of the medium can influence the propagation even in the very low frequency regime. Thus, judicious modification of the crystal structure could be expected to have a significant impact. We illustrate this effect by introducing a second bubble into the primitive unit cell so that it contains two identical scatterers with x, y, z coordinates 0,0,0 and 1 4 , 1 4 , 1 4 in units of the cubic cell parameter a. We hereby obtain the diamond structure, for which the corresponding band structure is displayed in Fig. 1(d). One consequence of adding the second bubble is that the nearest-neighbour spacing of the bubbles is reduced, with each pair of bubbles in the unit cell being separated by only 0.433a, compared with a separation of 0.707a in the original fcc structure. While this increase in the bubble concentration is responsible for small changes in the band structure at low frequencies (e.g., the slope near zero frequency is slightly smaller, due to a rather modest increase in the effective compressibility of the diamond crystal), by far the most significant change in the band structure is the emergence of a new branch within the original fcc bandgap. Interestingly, this branch features a negative slope and can be regarded as a metamaterial equivalent of the optical branch observed in the phonon dispersion relations of diatomic crystals.

In addition to having a low-frequency negative branch, which is associated with the existence of two bubbles in the primitive unit cell, the metamaterial with the diamond structure has another notable feature, namely that propagation is expected to be isotropic, or nearly so. Figure 2 indicates how isotropic the behaviour actually is, and compares results for diamond with those of the fcc structure. Starting from the band structures of Fig. 1(d), the normal mode frequencies for all branches and different directions are displayed in a single dispersion graph as a function of the wavevector magnitude. We find that all points for the different directions match up very well, especially for wavevectors in the lower two thirds of the Brillouin zone (k 40 rad•m -1 ). Beyond the L point (vertical red dashed line), which corresponds to the shortest wavevector touching the Brillouin zone boundary, the spread of wavevector values at a given frequency increases and the propagation becomes anisotropic (there is even a gap in certain directions). But returning back to lower wavevectors and focusing on the negative branch of the diamond structure (solid black circles in Fig. 2), we note that the deviations from isotropy become less and less as the frequency increases, with the deviations appearing to be negligible when the dispersion curves cross the water line (solid blue line in Fig. 2). At the crossing frequency (2929 Hz), the variation in the magnitude of the wavevectors is less than 0.3%, so that the equifrequency surface is essentially spherical and the propagation really is for all practical purposes isotropic.

III. RESULTS AND DISCUSSION

A. Negative refraction

For the optical branch, as we increase the frequency, the radius of the isofrequency surface decreases, meaning that this branch is associated with a negative refraction effect: an obliquely incident wavevector is refracted through the crystal interface with a negative angle. Here, we illustrate the negative refraction by shining a Gaussian beam towards the bubbly diamond metamaterial at an incident angle of 45 • with respect to the normal at the interface. Using the method explained in reference 29, we compute the full solution to the multiple scattering problem of the acoustic wave field inside the metamaterial when this beam is incident on a slab of thickness 1.5λ 0 and width 11λ 0 containing 81,000 bubbles. (Here, λ 0 denotes the wavelength in water.) In Fig. 3(a), we display the corresponding acoustic energy map (in dB) at the frequency 2929 Hz. The incident beam is mostly reflected at the first interface but the remaining energy which enters the crystal is negatively refracted at the two slab interfaces. It finally exits the slab with a spatial shift towards negative x values. The real part of the pressure field, shown in Fig. 3(b), provides additional information. First, looking at the wave-fronts' orientation inside the crystal, we find that the refraction angle is exactly opposite to the incident angle, suggesting a phase velocity being the exact opposite of the water one. This is further confirmed by the fact that the wavelengths inside and outside the crystal are equal at this frequency. Nevertheless, we have to stress that the n = -1 condition is not accompanied by good impedance matching, as shown by the significant reflection at the first interface.

B. Focusing of a point source

Since the original predictions of Veselago 1 and Pendry [START_REF] Pendry | Negative refraction makes a perfect lens[END_REF] , n = -1 materials have been attracting much attention for the possibilities they offer in terms of imaging. The seminal configuration consists of a point source placed in front of a slab with a n = -1 refractive index. The expectation is that all wavevectors emitted by the source spontaneously converge back to a single location on the other side of the slab. The only requirement for the formation of an image on the far side of the slab is that the source should not be located further than the slab thickness away from the first slab's interface. Here, the point source is located just outside the slab, in front of a bubble, with the distance from the source to the bubble being approximately λ 0 /17. We numerically investi- gate this configuration and observe the focusing effect through the slab [see Fig. 4(a)] by again solving the multiple scattering problem of wave transport inside the slab, this time resulting from a point source excitation. To estimate the lateral resolution, the transverse profile at the focus is displayed as a solid line in Fig. 4(b). In this case, the distance from the peak to the first minimum, ∆/2, is 0.6λ 0 , and the corresponding Full Width at Half Maximum (FWHM) is 0.7λ 0 . This is close to the optimal value set by the Rayleigh criterion, which considers diffraction-related limitations. It basically states that wavevectors of magnitude higher than ω/c (with c being the acoustic wave velocity) cannot be collected simply because these waves are evanescent and cannot propagate in the uniform medium outside the slab, since they decrease exponentially away from the source.

However, if the image of the point source is located in the near field of the lens, the evanescent waves at these larger wavevectors are not eliminated by the need to propagate out of the slab. As a consequence, the information they carry can be collected at the focal point. In order to shift the focus closer to the slab, one can simply increase the refractive index of the metalens which, it turns out, can be done by slightly lowering the frequency. For instance, at 2917 Hz the refractive index is roughly n = -3.2 which sets the focus at a distance λ 0 /10 from the bottom interface [see Fig. 5(a)]. Again, we display the transverse profile of the focal spot in Fig. 5(b); the FWHM is 0.4λ 0 and ∆/2 = 0.3λ 0 , which beats the lower limit predicted by the Rayleigh criterion.

C. Imaging in three dimensions

The focusing effect for a point source is just a step towards demonstrating that the device is capable of imaging an actual extended object. Our bubbly metalens operates in three dimensions. To highlight this specific attribute, we now use the lens to image an extended source consisting of 92 incoherent individual point sources arranged to form the acronym "3D" [see Fig. 6(a)]. The object is actually two-dimensional and contained in the (x,z) plane. In order to demonstrate the ability of the lens to image an object that extends over a three-dimensional region of space near the lens, we simply tilt the slab around the z-axis (by 18 • ). (This, of course, is equivalent to keeping the lens fixed in position while rotating the object by -18 • .) Tilting the slab (or alternatively tilting the planar object) amounts to breaking rotational invariance with respect to the y-axis, thereby involving all three dimensions in the imaging process. For the image shown in Fig. 6(a), the bubble concentration in the slab was reduced by a factor of 4, thereby extending the lateral width of the lens to enable a larger object to be imaged without excessively impacting the computation time. The frequency is 2910 Hz, which corresponds to n = -1 for this diluted concentration. After propagation through the slab, an image that respects the shape, size and orientation of the original object is created [Fig. 6(a)]. To illustrate the depth of field of the image, two-dimensional cross sections of the acoustic energy in equally spaced planes perpendicular to the y-axis are displayed in Fig. 6(b).

D. The damping issue

So far, damping terms resulting from thermal and viscous mechanisms have not been considered. As a consequence, it is not obvious if similar results would be observed in a realistic bubble slab. More specifically, with the chosen set of parameters, these additional terms actually undermine the lensing effect because the field decays faster. As the characteristic decay length becomes comparable to the slab width, fewer wavevectors are collected at the location of the focus simply because obliquely incident wavevectors cover a longer distance within the slab before reaching the second interface. As a result they undergo more scattering events and are hence more attenuated than their normally incident counterparts. However, there are concrete solutions to this limitation, allowing it to be overcome. In a previous contribution reporting a negative branch in a random set of pair-wise correlated bubbles, we showed that increasing the bubble concentration was a means of reducing attenuation in the frequency range of the negative branch [START_REF] Lanoy | Acoustic double negativity induced by position correlations within a disordered set of monopolar resonators[END_REF] . Although we could not examine higher concentrations here due to practical computation limitations, we expect similar trends considering the strong analogy between the diamond bi-periodic structure and the disordered pair-correlated system.

Another possible way of reducing the overall dissipation is to consider using bigger bubbles. Indeed both the thermal and viscous damping terms weaken as the bubble radius is increased [START_REF] Jr | Survey of thermal, radiation, and viscous damping of pulsating air bubbles in water[END_REF] . In practice, air bubbles in water that are much larger than a millimeter in diameter cannot be considered, as their shapes deviate from spherical. However, the trapping technique recently developed by Harazi et al. [START_REF] Harazi | Acoustics of cubic bubbles: six coupled oscillators[END_REF] allows much bigger ranges of size to be explored, since the shape is then set by a solid frame. Finally, one should keep in mind that the Lorentzian formalism of Eq. ( 1) is quite universal among scattering problems. As a result, our results are transferable to other kinds of metamaterials. The only real requirement concerns the scattering function which should remain isotropic. Three-dimensional spherical Helmholtz resonators could be envisaged as these objects tend to exhibit less loss.

IV. CONCLUSIONS

In this article, we demonstrate numerically that a bubble assembly organized in the diamond structure constitutes an effective three-dimensional acoustic flat metalens. The negative refractive index in the optical branch of this crystalline metamaterial's dispersion relation is a consequence of the bi-periodic structure, and is highlighted by demonstrating the anomalous refraction of an obliquely incident Gaussian beam. The diamond structure consists of a fcc Bravais lattice with a basis of two scatterers per unit cell. Just like the fcc lattice, it is highly isotropic, as shown in Fig. 2: the refractive index is essentially the same in all directions throughout a large part of the Brillouin zone, with deviations from isotropy only becoming clearly noticeable when the equifrequency surfaces approach the zone boundary, which they do first at the L points (where the Brillouin zone edges are closest to the zone center). Isotropic propagation is a key feature to avoid aberration effects, making the choice of the diamond structure for this three-dimensional metalens an ideal one compared with other crystalline structures that might be envisaged. We demonstrate the lensing performances by presenting evidence of the focusing of a single point source. The position of the focus can be tuned by sweeping the frequencies. As the focus moves into the near-field of the slab, the focus gets sharper and eventually beats the Rayleigh criterion. This indicates that the evanescent field then contributes to the image formation so that the imaging resolution is not limited to half the operating wavelength. Finally, imaging of an extended object is demonstrated to illustrate the three-dimensional possibilities.

Beyond the specific properties of this diamond structure, there is an interesting physics point to make here. This study should be regarded as a crystalline counterpart of our previous work on the consequences of introducing a spatial pair correlation within a disordered assembly of monopolar resonators [START_REF] Lanoy | Acoustic double negativity induced by position correlations within a disordered set of monopolar resonators[END_REF] . In this previous paper, we considered pairs of monopolar scatterers, separated by a fixed distance, that were otherwise randomly distributed in the medium; the resulting pair correlation was found to induce a statistically resilient dipolar resonance. At the dipolar resonance frequency, the effective density and the effective refractive index both become negative (the effective bulk modulus being negative is a consequence of the monopolar resonance). In the diamond structure metamaterial, the physics is intrinsically analogous. The biperiodicity due to the presence of two scatterers in the primitive unit cell can be regarded as a way of introducing a dipolar mode. However, since the observations could very well be interpreted with strictly crystallographic arguments, no mention was made previously in this article to such a dipolar mode or to the effective density. This brings forward a fascinating feature of the metamaterial regime. The intensive parameters of the material can be dictated by the properties at the scale of the basic building block of the structure (e.g., unit cell in the crystalline case or nearest-neighbor separation for a random distribution of bubble pairs) and essentially rely on two aspects. The first is the nature of the inclusion (monopole, dipole...) while the second is its spatial patterning (random, pair-correlated, fcc, diamond...). This rather general statement is illustrated here by the mechanism leading to a negative branch in the dispersion relation of two disparate structures built from bubble pairs: on the one hand we can consider that the bubble pair is a single complex scatterer with two resonances that may be positioned randomly in the medium [START_REF] Lanoy | Acoustic double negativity induced by position correlations within a disordered set of monopolar resonators[END_REF] , while on the other hand we have a spatially relevant crystalline combination of two identical monopolar scatterers (the description presented in this article). Thus, under certain circumstances, the macroscopic properties of metamaterials that might normally be considered to be very different (e.g., disordered dispersions of complex scatterers versus perfectly ordered bi-periodic crystals) can end up being two facets of a single phenomenon.

  FIG. 1. (a) Sketch picturing the super-cell of a face-centered cubic (fcc) lattice populated with air bubbles. (b) Corresponding unit-cell in the fcc case (blue bubble) and in the diamond case (blue and brown bubbles). (c) First Brillouin zone for the fcc lattice. (d) Band structure for the fcc lattice (dashed blue line) and diamond structure (black line) computed with COMSOL Multiphysics by finding the eigenvalues for an infinite crystal (periodic boundary conditions). The upper plot corresponds to a zoom in the 2850 to 2950 Hz frequency range, with the solid grey horizontal line intersecting the optical branch of the diamond band structure at the frequency for which the n = -1 condition applies.

FIG. 2 .

 2 FIG. 2. Dispersion relations obtained by plotting all branches fromFig.1(d) in a single graph for which the frequencies are displayed as a function of the magnitude of the wavevector for the different directions in the Brillouin zone. Open symbols correspond to the lower frequency branches (blue for fcc, black for diamond), whereas solid black symbols depict the negative branch (only for diamond). The almost vertical blue line shows the dispersion in pure water and the red dashed line indicates the wavenumber magnitude at the L point.

6 FIG. 3 .

 63 FIG. 3. Refraction of an obliquely incident Gaussian beam on a slab of bubbly diamond. The arrows indicate the propagation directions. (a) Normalized energy in dB. (b) Real part of the pressure field, showing the wavefronts. Here, λ 0 = 51.2 cm.

7 FIG. 4 .

 74 FIG. 4. (a) Map of the pressure field magnitude obtained when the bubbly diamond slab is excited by a point source facing its upper edge. At a frequency (2929 Hz) such that n = -1, the wave-vectors are collected in phase at a conjugate location on the opposite slide of the slab thus forming an image of the source. (b) Transverse profile of the focal spot (solid line) and comparison with an optimal diffraction-limited focus (dashed line). Here, λ 0 = 51.2 cm.

FIG. 5 .

 5 FIG. 5. (a)Map of the pressure field magnitude obtained when the slab is excited by a point source facing its upper edge. At a frequency (2917 Hz) such that n = -3.2, the wave-vectors are collected in phase at a conjugate location on the opposite side of the slab, thus forming an image of the source. Since the image is located in the near field, evanescent wavevectors are involved in the image formation. (b) Transverse profile of the focal spot (solid line) and comparison with an optimal diffraction-limited focus (dashed line). Here, λ 0 = 51.4 cm.

FIG. 6 .

 6 FIG. 6. (a) Imaging in three dimensions of an inclined extended planar object consisting of the letters 3D. Note that the colorbar scale is expressed in dB. (b) Slices of the acoustic energy (in dB) in equally spaced planes perpendicular to the y-axis in (a), illustrating the depth of field of the image.

ACKNOWLEDGMENTS

Some of this research has been supported by LABEX WIFI (Laboratory of Excellence within the French Program "Investments for the Future") under references ANR-10-LABX-24 and ANR-10-IDEX-0001-02 PSL, and by Agence Nationale de la Recherche under reference ANR-16-CE31-0015. JHP would like to acknowledge support from the Natural Sciences and Engineering Research Council of Canada's Discovery Grant Program (RGPIN-2016-06042).

DATA AVAILABILITY

The data that supports the findings of this study are available within the article


Anna Fleitoukh
email: a.fleitoukh@gmail.com

Kentaro Toyama
email: toyama@umich.edu

Are Ride-Sharing Platforms Good for Indian Drivers? An Investigation of Taxi and Auto-Rickshaw Drivers in Delhi

Keywords: ICT, Sharing Economy, Gig Economy, ride-aggregator platforms, auto-rickshaws, India, Delhi

It has been several years since ride-sharing platforms such as Ola and Uber have entered the Indian market. As a type of matching service, mainstream economic theory predicts that they will bring economic efficiencies to hired transportation. In this study, we investigate the impact of ride-sharing on drivers of taxi cabs and auto-rickshaws in New Delhi through a mixed-methods study involving 60 drivers. We find mixed outcomes for drivers with little clear evidence of overall benefit. We saw no statistically significant impact of ride-sharing on drivers' average revenue per day, though the data is suggestive of income gains of 7-18% which seem likely to be due to longer hours driven. In contrast to the corporate marketing where driver autonomy and flexibility are oft-cited perks, our participants tended to report less autonomy and control with ride-sharing. And, we find evidence that drivers face greater uncertainty with respect to their income as ride-sharing companies offer intermittent promotional incentives. Our findings are consistent with technological amplification theory. Through ride-sharing platforms, unequal power dynamics between large corporations and low-wage workers are amplified: ride-sharing companies wrest control from drivers while providing little in return.

Introduction

Ride-sharing -that part of the so-called "sharing economy" [START_REF] Sundararajan | The 'gig economy' is coming. What will it mean for work?[END_REF][START_REF]The People Who Share Blog[END_REF] that matches drivers with riders for personal ground transportation through smartphone apps -is now a worldwide phenomenon. In high-income countries, ride-sharing companies such as Lyft and Uber are widely hailed for providing transport services that are convenient, low-cost, widely available, quick to pick up, and good for drivers [START_REF] De Stefano | The Rise of the 'Just-in-Time Workforce': On-Demand Work, Crowd Work and Labour Protection in the 'Gig-Economy[END_REF][START_REF] Fuchs | Rereading Marx in the Age of Digital Capitalism[END_REF][START_REF] Slee | What's yours is mine, Against the Sharing Economy[END_REF]. On the other hand, critics point out that the platforms bypass local transport regulations, compete with public transportation, and underpay their drivers [START_REF] De Stefano | The Rise of the 'Just-in-Time Workforce': On-Demand Work, Crowd Work and Labour Protection in the 'Gig-Economy[END_REF][START_REF] Morozov | Résister à l'ubérisation du monde[END_REF][START_REF] Slee | What's yours is mine, Against the Sharing Economy[END_REF].

In India, the two major ride-sharing companies are Ola, an Indian company, and Uber, the U.S. multinational company. Personal, hired, ground transportation in urban India is a different phenomenon compared with much of the developed world. There are vehicle classes other than four-wheeled automobiles, whether it is auto-rickshaws, bicycle rickshaws, or even human-pulled rickshaws. The services are extremely inexpensive, and rides are plentiful and easy to hail [19].

In this paper, we report on a study that focuses on the impact of ride-sharing on drivers of hired transport in India in terms of revenue and driver perceptions. We used a mixed-methods study of 60 drivers in New Delhi, split evenly among three groups: taxi (automobile) drivers who used ride-sharing apps, auto-rickshaw drivers who used ride-sharing apps, and auto-rickshaw drivers who did not use ride-sharing apps.

Overall, we find that the impact of ride-sharing on Indian drivers is mixed, with no clear evidence of net benefit. We find no statistically significant impact on drivers' average revenue per day, and even a suggestive (i.e., not statistically significant) 7-18% increase in mean revenue is likely due to drivers working more hours. Qualitatively, we find that many Indian drivers feel pressured into ride-sharing so as not to be "left behind," but there are complaints about a resulting loss of autonomy. Among drivers, ridesharing appears to exacerbate existing inequalities, with a few high-performing drivers benefiting from the rewards offered by ride-sharing companies while relatively older, smartphone-less drivers who do not own their own vehicles struggle either to participate in ride-sharing or to maintain their levels of income. These findings build on the small literature on ride-sharing in the developing world.

We situate our findings in a critique of capitalism, mediated by technology's amplifying effect [START_REF] Toyama | Fair Share? The Sharing Economy Goes Global[END_REF]. Contrary to claims that the sharing economy represents a departure from capitalism's pathologies that elevates workers by providing new opportunities through individual entrepreneurship, what we suggest is that ride-sharing in urban India is an extreme form of capitalism in which the unequal power dynamics between corporations and workers are amplified, with workers likely losing out as tech titans clash overhead. Thus, while our findings differ in the details, they extend some of the existing criticism of the sharing economy [START_REF] De Stefano | The Rise of the 'Just-in-Time Workforce': On-Demand Work, Crowd Work and Labour Protection in the 'Gig-Economy[END_REF][START_REF] Morozov | Résister à l'ubérisation du monde[END_REF][START_REF] Slee | What's yours is mine, Against the Sharing Economy[END_REF].

Related Work

Ride-Sharing and Its Impact on Labor

There is a considerable literature about ride-sharing in developed-world contexts. Some research focuses on the benefit to rider-consumers that includes lower costs compared to local taxi cabs, at least for routine rides [START_REF] Cohen | Using big data to estimate consumer surplus: the case of Uber[END_REF], as well as shorter wait times and ease of use [START_REF] Cramer | Disruptive Change in the Taxi Business: The Case of Uber[END_REF]. Indeed, riders in many cities express delight about ride-sharing, with accompanying complaints about over-priced and outdated taxi services [START_REF] Cramer | Disruptive Change in the Taxi Business: The Case of Uber[END_REF]. Riders are even willing to pay the premium when ride-sharing platforms implement "surge pricing" -raising the price of rides during moments of driver scarcity [START_REF] Cohen | Using big data to estimate consumer surplus: the case of Uber[END_REF].

Other work considers the impact on drivers. One prominent study compared the gross hourly earnings of Uber drivers with those of taxis and chauffeurs across six U.S. cities, and suggested that Uber drivers earn more per hour [START_REF] Fuchs | Rereading Marx in the Age of Digital Capitalism[END_REF]. They found that on average, Uber driver-partners earned $19.19 per hour compared to a $16.90 for their counterparts and the authors conclude, "Unless their after-tax costs are more than $6 per hour, the net hourly earnings of Uber's driver-partners typically exceed the average hourly wage of employed taxi drivers and chauffeurs."

The same study found that, again in the United States, Uber drivers differ as a group from their taxi-driving counterparts [START_REF] Fuchs | Rereading Marx in the Age of Digital Capitalism[END_REF]. Among UberX drivers, 19.1% are between 18 and 29 years old, but only 8.5% of taxi drivers are; 21.8% of UberX drivers are between 50 and 64, while 36.6% of taxi drivers. Moreover, "Nearly half of Uber's driver-partners (48%) have a college degree or higher, considerably higher than the corresponding percentage for taxi drivers and chauffeurs (18%)." Uber drivers also often have another job apart from driving, and use driving as a complement to their wage, compared to their taxi-driving counterparts who tend to be drivers full time. Finally, many Uber drivers appear to engage in driving as a temporary option. After a year of driving for Uber, almost half of the drivers quit.

Scholars have also noted that drivers are lured to the platform with promises of high wages for short hours of driving, but Uber intermittently reduces fare rates unilaterally [START_REF] Rosenblat | Uberland: how algorithms are rewriting the rules of work[END_REF]. Another issue is the myth of flexibility that has gradually faded away as the drivers face constant pressure from the platform to drive longer hours, at particular times, and in specific neighborhoods, or rating systems forcing drivers to bear the burden of customer service. Some scholars argue that the algorithms at the center of Uber's system consolidates power fully in the hands of the platform [START_REF] Rosenblat | Uberland: how algorithms are rewriting the rules of work[END_REF]. Unlike a human manager, Uber's system is relentless and uncompromising in its monitoring of drivers' performance and behavior.

A common criticism of the sharing economy overall is that it leads to "casualization of the workforce, informalisation of the formal economy and the so-called 'demutualisation of risk' in modern labour markets" [START_REF] De Stefano | The Rise of the 'Just-in-Time Workforce': On-Demand Work, Crowd Work and Labour Protection in the 'Gig-Economy[END_REF]. Ride-sharing companies gain all of the benefits of wage work without the responsibilities through "disguised employment relationships." Indeed, drivers are responsible for their own vehicle maintenance, insurance, and other costs and have neither overtime pay nor sick leave [START_REF] Fuchs | Rereading Marx in the Age of Digital Capitalism[END_REF][START_REF] Rosenblat | Uberland: how algorithms are rewriting the rules of work[END_REF]. Critics of ride-sharing tend to agree that the "uberisation of society" exaggerates the problems of capitalism [START_REF] Morozov | Résister à l'ubérisation du monde[END_REF][START_REF] Toyama | Fair Share? The Sharing Economy Goes Global[END_REF]. Moreover, the use of algorithms erodes job quality in the platform economy. The bargaining power of the worker is truncated when operating through a digital tool. The constant monitoring through the process, and rate given when completing the task creates an unfair imbalance [START_REF] Wood | Good Gig, Bad Gig: Autonomy and Algorithmic Control in the Global Gig Economy[END_REF].

Ride-Sharing in India

The two major ride-sharing companies in India are Ola and Uber [START_REF] Bhattacharya | Ola vs Uber: The latest score in the great Indian taxi-app game[END_REF][START_REF]Uber Wants to Rule the World. First It Must Conquer India[END_REF]3130]. Ola was founded by an Indian entrepreneur who began with a ride-sharing service for cabs in 2010 and then expanded to auto-rickshaws in 2014, the ubiquitous, covered, threewheeled vehicles that are common throughout South Asia. Uber, of course, is the U.S.based multinational [START_REF]Uber Wants to Rule the World. First It Must Conquer India[END_REF], entered the market in 2013 and launched the auto-rickshaw option two years later. One scholar, pointing out that ride-sharing is an organization of informal work, suggests that in contexts like India where the informal economy is prevalent, ride-sharing's impact is muted; it is not as disruptive as it is elsewhere [START_REF] Surie | The Emerging Nature of Work in Platform Economy Companies in Bengaluru, India: The Case of Uber and Ola Cab Drivers[END_REF]. Indeed, "92% of these drivers were driving to earn an income before joining a platform economy company. Only 8% shifted to these companies from different professions" [START_REF] Surie | The Emerging Nature of Work in Platform Economy Companies in Bengaluru, India: The Case of Uber and Ola Cab Drivers[END_REF].

Another study of drivers in Bengaluru emphasizes how ride-sharing changes the way that drivers operate, often in undesirable ways [START_REF] Isthiaque | Peer-to-peer in the workplace: A view from the road[END_REF]. "Without Ola, drivers locate passengers by sight, negotiate whether to take them then set off towards their destination… Ola changes the dynamics as drivers must first accept the passenger's request then physically locate them, and do not negotiate with the customer." Customers, however, often cancel, causing drivers to burn fuel without compensation. "Some drivers prefer their regular [i.e., pre-ride-sharing] taxi dispatch systems because they enable seeing and choosing freely between incoming requests," a choice they lose with ride-sharing platforms. Unhappiness with ride-sharing has prompted Indian drivers to strike [START_REF] Uber | Ola drivers strike in India, demanding higher fares[END_REF].

Research also highlights the inequalities among drivers that ride-sharing may aggravate. Generally, the drivers using the application are more literate, for example [START_REF] Isthiaque | Peer-to-peer in the workplace: A view from the road[END_REF]. Such findings are consistent with the literature on the digital divide in developing countries [START_REF] Cecchini | Can Information and Communication Technology Applications Contribute to Poverty Reduction? Lessons from Rural India[END_REF][START_REF]Understanding the Digital Divide[END_REF][START_REF] Toyama | Geek Heresy, Rescuing social change from the cult of technology[END_REF], which finds that digitally mediated activities tend to highlight existing inequalities in economic status, social standing, or education.

The research in this paper builds on the above literature through a preliminary attempt to capture the financial impact of ride-sharing on drivers in India, as well as to tease out some of the key differences that Indian drivers experience compared with their developed-world counterparts.

Methodology

Data Collection

We conducted 60 interviews in New Delhi, India, between January and June 2019, each consisting of a questionnaire with questions related to demographics and business as well as a semi-structured portion with open-ended questions. Interviews were conducted with three types of drivers:

• Auto-rickshaw drivers who used Ola or Uber (Abbreviation: RU; 20 interviews) • Auto-rickshaw drivers who did not use Ola or Uber (Abbreviation: RN; 20 interviews) • Taxi cab drivers who used Ola or Uber (Abbreviation: TU; 20 interviews) All interviews were conducted verbally by the first author during hailed (and paid) rides. Interviews were conducted in Hindi through paid interpreters on all rides.

The questionnaire portion asked about their demographic profile as well as the details of the costs and revenues of their driving-related work. The semi-structured portion asked about their perceptions of their job, ride-sharing platforms, and their economic situation in general.

Rides were hailed from well-known ground-transportation hubs in South Delhi (e.g., Hauz Khas Metro Station, Nehru Place), Central Delhi (e.g., Connaught Place, Central Secretariat) and Old Delhi (e.g., Jama Masjid, Red Fort). Ride-sharing apps were used to recruit participants for the 40 participants on ride-sharing platforms. Regular on-the-spot hailing of rides was used to recruit the other 20 participants. Rides were requested for common destinations, as well, so as to allow a series of interviews to be conducted in a single day.

Rides were requested for destinations typically 4-6 kilometers away. On Delhi's crowded streets, this allowed for recruiting of the participant, obtaining informed consent, and an interview that lasted about 15 minutes. Drivers were generally very open to being interviewed in this way and tended to be succinct and to-the-point. Interviews quickly came to an end when the destination was reached. In addition to the payment for the ride, we paid tips of 30% of the cost of the ride as a token of our gratitude. Audio recordings were not practical due to engine and traffic noise, so notes were taken by hand as the interviews occurred.

Beyond interviews with drivers, we also met with two Ola Mobility Institute employees who conveyed the specifics of Ola's outreach and interaction with drivers. These interviews provided clarification about some of the drivers' claims about their interaction with Ola (e.g., the specific nature of promotional deals), and also provided a view into the ride-sharing companies' perspectives.

Data Analysis

Our research involved mixed methods with both quantitative and qualitative data analysis.

All of the demographic and business data were entered into a spreadsheet and cleaned. Though most drivers responded to all of our questionnaire questions, they sometimes varied in the specifics of their responses. In a few cases, we used averages from other drivers to infer specific figures -for example, some drivers reported renting their vehicles; even where we did not have their rental rates, we used average figures based on other respondents. Throughout this paper, we report ARPD as net revenue for the driver in the local currency, the Indian Rupee (Rs). (At the time of the interviews, Rs. 70 was equal to US$1.) Once cleaned, the data was analyzed to determine summary statistics and correlations. For the latter, several regressions were run, using a subset of the following independent variables: age, education, length of time as a driver, use of a ride-sharing app, length of time using an app, number of hours driven per day, type of vehicle, and vehicle ownership. ARPD was cast as the primary dependent variable, but we also tried regressions with vehicle ownership as the primary dependent variable. Both dependent variables, incidentally, were highlighted by drivers as how they assessed their own performance or success. Vehicle acquisition can have long-term benefits for the drivers, separate from ARPD.

For qualitative findings, participants are referred to throughout by codes: RUx for rickshaw drivers who are ride-sharing app users; RNx for non-user rickshaw drivers; TUx for taxi drivers (all of whom were app users).

Limitations

Though we made an attempt to capture a diverse set of Delhi-area drivers, our sample sizes are not large, and the samples were biased in a number of ways: Geographically, of course, our results do not necessarily hold beyond Delhi. Even within Delhi, there may be selection biases due to where the rides were hailed (generally, in high-traffic areas). All interviews were conducted during the day, and drivers taking early morning or late evening shifts were not represented. However, because our ride-hailing methodology was effectively random, we believe our findings have validity within those times and places. We also acknowledge potential problems with language and culture. Though weboth authors -have lived in large Indian cities, speak some Hindi, and are personally familiar with rickshaws, taxis, and other forms of urban transportation, there are likely nuances of expression that we may have missed.

Findings

Business Basics

Auto-rickshaws have traditionally operated by taking passengers who hail them on the streets. With the advent of ride-sharing platforms, this situation has changed for some drivers in the last few years, but almost all drivers reported a willingness to pick up passengers on the spot. This scenario, however, is somewhat rarer for cab drivers who have over the last 10-15 years, become accustomed to booking rides through private companies and mobile-phone calls.

Next to the type of vehicle driven, ownership of a vehicle is a key differentiator among drivers. When the vehicle is owned, the driver is himself (all of our drivers were male) liable for gasoline, maintenance, and insurance costs. However, for drivers who rent their vehicles, maintenance and insurance are paid by the owner. (Gasoline is typically paid for by the driver, regardless, though there appears to be some variation.) The business relationship that drivers have with vehicle owners is diverse: some pay a rental fee on a daily or weekly basis; others pay their owners a percentage of their daily earnings; still others earn a fixed wage per month (more frequent among ride-sharing drivers). Drivers often aspire to own their own vehicles, and as below, it does appear that ownership leads to greater net income.

4.2

Quantitative findings ). In addition, each additional hour driven per day appears correlated with Rs. 60 more in earnings. (p=0.037). On the other hand, ride-sharing app usage did not have a statistically significant correlation with increased revenue (p=0.5), even though there is a suggestive difference of Rs. 99. If we perform regressions only on ride-sharing app users, driving a cab is positively linked with an increase of Rs. 658.64 (p=0.0007), while every additional hour driven correlates with an increase of Rs. 74 (p=0.08). To conclude, while app usage may be correlated with greater revenue, the difference was not statistically significant with our relatively small sample size, suggesting at the least that the variation among drivers due to other variables outweighs use of the app. If our mean differences hold for larger sample sizes, however, ride-sharing app usage may account for an additional 7-18% in net revenue. However, there does seem to be an advantage to being a cab driver over a being a rickshaw driver, and for rickshaw drivers to be vehicle owners, though we caution that these are correlations, not confirmations of causality. Finally, we confirm, unsurprisingly, that across the board, additional hours driven correlates with greater revenue. Ownership of the vehicle. The ownership rate was the highest among rickshaw drivers ride-sharing app users at 71% compared to 47% for non-user rickshaw drivers, and 55% for cab drivers. Group averages suggest that ownership rates are linked to education owners whole group non-owners level, with higher educational levels correlated with higher ownership rates. Whether ownership causes an increase in revenue, or revenue enables ownership is not clear from the data. When taking all drivers together, both education (p=0.0033) and revenue (p=0.0052) are statistically significant in explaining the likelihood of vehicle ownership. On the whole, our participant cab drivers were less educated than rickshaw drivers using ridesharing apps (who tended to have the higher ownership rate). The same trend is visible whether rickshaw, cab drivers or app users were considered on their own. To conclude, vehicle ownership does not appear to correlate with app usage, though daily revenue and education do. It seems reasonable to conclude that education directly or indirectly influences ownership (not the contrary). What is unclear is the exact mechanism -it is possible that more educated drivers earn more, making it easier for them to acquire vehicles in the long run; or, it may be that more educated drivers see the value of ownership more clearly, or plan for it better; or, it may be something else. The relationship between income and ownership, however is unclear -our data allows for either greater daily income leading to greater chance of ownership or ownership leading to greater income. App Usage. Average time of driving with the app was exactly the same for both autorickshaw drivers and cab drivers at 2.03 years. First quartile, median and third quartiles are also very similar for both categories: respectively 0.54, 2 and 3 years for rickshaw drivers and 0.56, 2.25 and 3 years for cab drivers.

Volatility of app use among cab drivers is slightly higher because 75% of them have tried both apps, while only 54% of rickshaw drivers report this. 2.03 years of app use on average is quite low compared to the number of years the apps are on the market (since 2013 so, or over 5 years at the time of the interviews). That suggests that our drivers joined recently and the ride-sharing phenomenon is intensifying. Drivers may feel the need to join because they would lose customers otherwise, or because they perceive that ride-sharing apps are advantageous. Of our 20 rickshaw drivers who were not using ride-sharing at the time of the interview, only two had previous experience with Ola or Uber.

Percentage of vehicle owners

Ownership rate Average grade completed Age and Education. On average, rickshaw drivers not using apps are 5.38 years older than their peers using the apps. Similarly, cab drivers using the apps are 3.25 younger than rickshaw drivers using the apps, and thus 8.63 years younger than auto drivers not using them.

A single-variable regression of age against app usage for all drivers together suggests that age influences whether the driver is likely to use an app or not: for every 10 years of age, the likelihood of using a ride-sharing app drops by 15% (p=0.04). Rickshaw drivers using the apps are also more educated than drivers not using the apps on average: they completed 8.5 and 10.5 years of formal education, respectively. Cab drivers are not more educated than auto-rickshaw drivers using the app: on average they have completed 9.6 years of education. However, we found no statistically significant link between education and app usage.

Qualitative Findings

Overall views on ride-sharing. All of our participants were familiar with both Ola and Uber, regardless of whether they were app users, or whether they used only one of the two ride-sharing platforms. Many drivers perceived ride-sharing as a new trend that they could not afford to neglect. TU3 said, "Every cab driver came to know about the apps when they entered the market, and I started driving for them because I predicted the market to shift. So, I have used Uber since the beginning." For these cases, it appears that Uber and Ola were not seen as advantages necessarily, but as necessities to begin or to remain in business. Indeed, non-user rickshaw drivers saw themselves to be at a distinct disadvantage: RN4 said, "I am disadvantaged because of Ola and Uber because I get less passengers and thus I earn less". However, it is not clear, especially in light of our quantitative results above, how much these sentiments were based on reality. In fact, some non-user drivers perceived no disadvantage. RN7 said that he did not feel threatened by the apps because "Auto-rickshaws on the apps are not very popular. Indeed, the fares for booking a cab are close to the ones for an auto, so people tend to prefer booking a cab because it is more convenient." With respect to revenue, reports were mixed. For some, there are clear advantages to ride-sharing, though often, these are based on promotional rewards that do not apply to all drivers. TU18 said, "Uber chose the 100 best drivers in Delhi and I was one of them. I was thus invited in Gurugram for a party, and I was offered an incentive of Rs. 5'700." A commonly cited reward was one attached to a bonus for making, e.g., 44 rides over 4 days. Such schemes are common for both apps.

Others, however, questioned the financial value of ride-sharing. RU4 said, "I do not see much difference between using the app or not." RU10 -an app-user -confessed, "The margins are better when I get customers from the street." And, many have noticed that promotional incentives have decreased in monetary amounts and frequency over time. TU3 said, "I am not very happy with the incentives because they are much lower than before." TU5, who has 3 years of experience with Uber, was specific about the decline in his average revenue: "My wage used to be higher when I joined the company, at about Rs. 80,000 to 90,000 per month the first year. Then, it decreased to Rs. 60,000 to 70,000 the second year. And, now I am left with Rs. 30,000 to 40,000 per month." Several drivers began driving based on rumors of high income, and now they felt trapped. TU20 regretted, "I have no real choice if I want to change my job because I only know driving and nothing else." RU9 said, "I am not happy with the app. The oil prices have increased during the past years, but not the number of customers and incentives are decreasing."

Between Ola and Uber, the participants expressed relative pros and cons to each, though Uber appeared to be the favorite overall. Ola was said to care better for drivers and to have better incentives. Uber was said to bring more customers and to lead to greater revenue. TU6 said, "The incentives are better with Ola, but there are more rides and more customers through Uber." RU11 said, "I prefer the way Ola is done, but I would like to switch to Uber because I could get more money. Ola is also easier to use and Uber is very demanding with the everyday selfies that have to be sent to the platform for identity check." Overall, the majority of our participants (75%) used Uber, which is consistent with anecdotal reports of Uber's dominance in Delhi.

Among drivers using the apps, only three of our cab-driver participants were not professional drivers before they began; the availability of the ride-sharing apps likely lowered barriers to entry for driving taxis. All of our rickshaw-driving participants, however, were drivers prior to using the ride-sharing apps.

Obstacles to becoming a ride-sharing driver. Some of our participants mentioned problems with technology access, digital literacy, or general education as obstacles to effective use of the ride-sharing platforms. It also emerged that ride-sharing is spread along social networks.

Several participants, mostly non-users of ride-sharing apps, mentioned smartphone ownership as a hard requirement. RN14 said, "Look, I have a very simple phone! I cannot use the apps." Similarly, RN19 was a previous Ola driver who had lost his smartphone.

Others noted lack of education as a barrier: RN14 suggested that even had he owned a smartphone, "I am not educated enough to use the apps." Taxi drivers also mentioned this. TU20 said, "I have failed 10th grade," suggesting it was difficult for him to use the apps. RU12 said, "I know that the older people are more scared to use the apps because they are not well educated and they prefer driving by themselves.", a sentiment was shared by RU13: "Rickshaw drivers using the apps are only 10 to 15% of the rickshaw drivers in Delhi because most of them are scared." Meanwhile, app users affirm that their own education allowed them to take advantage of ride-sharing. RU10 said, "I did not need a training, because I was educated enough to understand the app." Some mentioned that vehicle ownership was critical. TU13 said, "Using an app is beneficial when the auto is owned." TU4 emphasized, "Owning the auto is what makes the real difference for earnings.", even though ownership was not a hard requirement.

Finally, responses to questions about drivers' colleagues exhibited a trend where ride-sharing habits tended to cluster within drivers' social networks. RU11, an Ola user, said, "My friends are also using Ola over Uber because they had a bad experience in the past." Similarly, non-users of ride-sharing tended to know many other non-users. RN3 said, "I know other drivers, they also do not use the apps.", and some also told us that some of their family members were also drivers. A few interviewees declared they have taken part in protests organized by the auto-rickshaw union, and RN9 also expressed the peer-pressure he felt in the community: "I do observe the strikes because I do not want to be beaten up by other drivers".

The pressures of ride-sharing. Though ride-sharing companies often cite benefits for drivers such as independence and flexible work hours, most of our participants expressed dissatisfaction about longer work hours, inability to choose drivers, inconvenience with pick up (relative to on-street hailing).

Several times, drivers told us that they have to drive longer hours to benefit from ride-sharing. TU12 said, "Before, it was more relaxing to work for my own company because I had only 2 to 3 rides a day." Similarly, in a context of decreasing incentives, TU16 said, "To get the same amount, I used to drive 2 hours less every day." Some drivers do not join the companies because they consider that they do not drive sufficient number of hours per day. RN18 said, "I cannot drive for long hours because of health problems, so I have never tried the apps for this reason."

A number of participants mentioned that arranging and finding pick-up locations through ride-sharing apps was less convenient than picking up people hailing rides on the streets. RN9, who had used Ola in the past, said, "I prefer getting customers from the streets because I do not have to spend time to pick them up. The pick-up locations can be hard to find and some drivers go round and round to find a way to get to the location." But, this feeling was not universally shared. RU13 mentioned the convenience of not having to bargain: "It is easier with the app, because I do not have to bargain, but only wait for customers."

One of the major issues that a few participants raised was ride cancellations, when the customer cancels at the last minute. RU14 said, "It is not always fair, because we sometimes have to go towards the pick-up point and it is costly, especially if the customer cancels the trip while we are on the way."

Depending on the ride-sharing app, drivers also have less freedom to decline passengers. RN11 revealed that he did not like Uber's system because "the driver has to accept all requests, while with Ola, I can just ignore [a ride] because other drivers around will be sent the notice." Ride-sharing or not, licensed drivers are not legally allowed to refuse rides for the most part [START_REF]Kejriwal allows auto drivers to refuse customers while returning home, announces fare revision[END_REF], but regulatory enforcement is weak.

Relationship with ride-sharing companies. While most of our participants felt that both apps were generally good companies, some mentioned that they felt poorly treated. TU1 noted pointedly, "I have the feeling that Uber and Ola want to make the passenger happier than the drivers." RU17 added that "Apps are good for customers, but [the companies] do not always listen to the drivers." A common frustration was having ridesharing accounts suspended because of customer complaints. RN13 said, "My Uber account was blocked a few years back because of a customer complaint.", an experience also shared by RU11. Reactivation typically requires a visit to the corporate office, which can cost drivers a day of work.

Upskilling of the drivers. Many reported being trained by the company representatives on the spot to learn about the different features of the app, and how to use it, "Uber people told me how to use the app, and how to register" told us RU3. It seems that when going online, the drivers have acquired a set of digital skills. Beyond the ride-sharing app itself, drivers become familiar with bank accounts and digital payments, both of which may have other benefits related to financial inclusion, a point that was raised in our interviews with Ola employees.

Discussions

Overall, our findings suggest that the value of ride-sharing for drivers is mixed, with little evidence of clear positive value. We find that much the same phenomenon identified with Uber in North America [START_REF] Rosenblat | Uberland: how algorithms are rewriting the rules of work[END_REF] occurs in India, as well, with minor differences. While ride-sharing may enable a new income opportunity for some taxi drivers, for others, the benefits seem not to outweigh the inconveniences. Ride-sharing apps appear to push Delhi drivers to work harder for less revenue per kilometer, all while distorting a pre-existing market and reducing overall driver autonomy. First, we did not find a statistically significant increase in revenue for drivers who use ride-sharing. Second, ride-sharing introduces a host of controls for app-using drivers, which reduce real and perceived autonomy; for non-user drivers, the ride-sharing increases fears of being left behind. Third, it seems evident that ride-sharing companies are distorting the market for drivers in unpredictable ways, causing some novices to enter a market and experience difficulties as incentives decrease over time.

These findings extend and qualify previous findings about ride-sharing. Compared with developed-world contexts [START_REF] Fuchs | Rereading Marx in the Age of Digital Capitalism[END_REF][START_REF] Slee | What's yours is mine, Against the Sharing Economy[END_REF], both the financial and non-financial benefits (e.g., ability to choose one's working hours) to ride-sharing drivers seem muted.

In developed countries, drivers tend to be from the middle-class, with driving often being a supplementary second job; meanwhile, low-income individuals find it difficult to enter the market as ride-sharing drivers [START_REF] Malone | The Promise of the Sharing Economy among Disadvantaged Communities[END_REF]. While they share some challenges with their developed-world counterparts [START_REF] Malone | The Promise of the Sharing Economy among Disadvantaged Communities[END_REF], they seem better able to engage with the platforms. We suspect this is because the apps have adapted to Indian drivers in the race to recruit them, but also because of the way labour was organized among drivers prior to the existence of the apps. Our findings in Delhi are also similar to many of the qualitative findings from Bangalore [START_REF] Isthiaque | Peer-to-peer in the workplace: A view from the road[END_REF]. Our work adds evidence to the suggestion [START_REF] Isthiaque | Peer-to-peer in the workplace: A view from the road[END_REF] that under ride-sharing, drivers are having to drive more, for little or no increase in revenue.

A key novel contribution of our work is a report on the impact of recruiting promotions and incentives on drivers. Many take up ride-sharing because of the promises of bonuses. However, such promotions temporary and, at least at the time of our research, declining. We predict that reports of drivers going into debt as a result will begin surfacing. Meanwhile, the duopoly structure of the market in the Indian case is likely to lead to more rate-cuts in the future.

All of our findings are ultimately consistent with an amplification theory of digital technology [START_REF] Rosenblat | Uberland: how algorithms are rewriting the rules of work[END_REF][START_REF] Toyama | Fair Share? The Sharing Economy Goes Global[END_REF]. While technology may enable new activities, benefiting some while harming others, overall, its effect is to amplify underlying human forces. In the case of ride-sharing in India, those human forces are the routine, sometimes pathological forces of global capitalism, as other critiques of the sharing economy have noted [START_REF] Morozov | Résister à l'ubérisation du monde[END_REF][START_REF] Slee | What's yours is mine, Against the Sharing Economy[END_REF][START_REF] Sundararajan | The 'gig economy' is coming. What will it mean for work?[END_REF], but further compounded by the inequalities of the developing world. Among drivers, too, ride-sharing amplifies existing inequalities: Vehicle owners benefit more than non-owners. And, more educated drivers who can afford smartphones are better able to take advantage. Ultimately, the technology that manages ride-sharing is owned by corporations setting the rules unilaterally. This disproportionate share of power echoes and amplifies classical Marxist literature, which highlights the exploitation of workers who own little of the "means of production" [START_REF] Marx | Capital. A Critique of Political Economy[END_REF]. Neo-Marxist theories that incorporate modern digital phenomena are particularly relevant in our case [START_REF] Fuchs | Rereading Marx in the Age of Digital Capitalism[END_REF][START_REF] Wood | Good Gig, Bad Gig: Autonomy and Algorithmic Control in the Global Gig Economy[END_REF]. Our findings suggest that while some drivers benefited from new livelihood opportunities from the apps, most drivers -even those who use the platforms -are not benefiting greatly. If anything, ride-sharing drivers feel pressured to drive longer hours for smaller margins, and non-user drivers begin to feel they are at a disadvantage -all of this is enforced by the technology. Moreover, our participants were conscious that they were at the bottom of the totem pole, with the companies concerned more about customers than drivers. Meanwhile, intense competition between Ola and Uber causes market distortions and collateral damage from powerful entities in conflict is amplified.

There might be a different evolution of the market in the future: First, auto-rickshaw drivers may be able to retain their historical working paradigm, as Uber and Ola remain relatively lightly used among rickshaw drivers. Second, Indian drivers seem to have a measure of community (formal and informal) that might allow them to collectively resist the power of ride-sharing companies. They meet at traffic hotspots, and a vast majority of them have a family member also driving, and friends in the sector; in some cities, there are labour organizers coordinating drivers (including strikes). Whether this collective potential is fully actualized remains to be seen. As result, short of significant policy interventions to protect drivers and their interests, we suspect that over time, benefits to drivers will be shaved down to just the bare minimum to keep enough of them within the fold of ride-sharing companies.

Conclusion

This paper presented an exploratory study that sheds light on the effects of ride-sharing on drivers in New Delhi. We find that there are a number of differences in the reported experiences of drivers in India as compared with those in developed countries, with a tendency ride-sharing's problems to be further exacerbated. For one, the financial benefit of participating in ride-sharing is much less clear in India than in, for example, the United States. We found no statistically significant economic benefit for drivers to participate in ride-sharing, and many reported that they feel less autonomy with ridesharing, as they feel they must work longer hours and the apps direct almost all of their activity. Overall, ride-sharing appears to exacerbate the potential for low-wage workers to be exploited by large corporations in the developing world.

Fig. 1 .

 1 Fig. 1. ARPDs by type of vehicle, vehicle ownership, and app usage. Owners and app-user drivers are likely to earn more than non-owners and non-user drivers. Error bars represent standard errors.

Fig. 2 .

 2 Fig. 2. Rates of vehicle ownership by group plotted alongside level of education. Educational level is likely a direct or indirect cause of vehicle ownership.

Fig. 3 .

 3 Fig. 3. Boxplots showing the drivers' age scope in years. The age range is wider for RN drivers. TU drivers are consistently younger that RU or RN drivers.

Table 1 .

 1 Table of the main qualitative findings. ARPD varies significantly by vehicle type, use of ride-sharing apps, and vehicle ownership. Rickshaw drivers not using ride-sharing apps earned the least, at an average of Rs. 588 a day. App-using rickshaw drivers earned an average of Rs. 743 per day, and cab drivers earned Rs. 1406 on average. Thus overall, cab drivers earned Rs. 647 more per day than auto drivers (p<0.01

	Criteria/Groups	RN	RU	TU
	Percentage of vehicle-owners	47%	71%	55%
	Percentage of non-owners	53%	29%	45%
	ARPD (whole group in Rs.)	587.93 737.88 1405.75
	ARPD of vehicle owners (in Rs.)	750.86 798.48 1516.22
	ARPD of non-owners (in Rs.)	425.00 620.00 1231.19
	Average age in years	40.48	35.10	31.85
	Average grade completed	8.50	10.54	9.55
	Average time being a professional driver	15.82	13.05	7.71


Ismael Bouassida Rodriguez

Khalil Drira

Christophe Chassot
email: chassot@laas.fr

Mohamed Jmaiel
email: mohamed.jmaiel@enis.rnu.tn

Context-aware adaptation for group communication support applications with dynamic architecture

Keywords: Software architecture, Producer-Consumer style, Adaptation, Context-aware, Graphs

In this paper, we propose a refinement-based adaptation approach for the architecture of distributed group communication support applications. Unlike most of previous works, our approach reaches implementable, context-aware and dynamically adaptable architectures. To model the context, we manage simultaneously four parameters that influence Qos provided by the application. These parameters are: the available bandwidth, the exchanged data communication priority, the energy level and the available memory for processing. These parameters make it possible to refine the choice between the various architectural configurations when passing from a given abstraction level to the lower level which implements it. Our approach allows the importance degree associated with each parameter to be adapted dynamically. To implement adaptation, we switch between the various configurations of the same level, and we modify the state of the entities of a given configuration when necessary. We adopt the direct and mediated Producer-Consumer architectural styles and graphs for architecture modelling. In order to validate our approach we elaborate a simulation model.

Introduction

Our work aims to makeing context-aware applications selfadaptable. For this kind of applications, it is necessary to be able to dynamically adapt the architecture during execution. Designing and implementing self-adaptive communicating systems is a complex task, which may be addressed via model-based design approaches associated with automated management techniques for dynamic architectural adaptability. In self-adaptable applications components are created, and connected, or removed and disconnected during the execution. The architectural changes respond to constraints in the communication and resources and to energy variation. They may also respond to evolution in the supported activities. The changes can also result from the user mobility. Static architectures are described by instances of components and interconnection links. This approach appears inappropriate when the architecture structure changes need to be described. The dynamic architectures character requires additional description rules. Several works have addressed the dynamic architecture description, using different approaches [START_REF] Allen | A formal basis for architectural connection[END_REF]. In order to guarantee the architecture updates correctness we use formal techniques. In particular, graphs represent a powerful expressive mean to specify respectively static and dynamic architectures aspects. For architecture description we use ACG (Abstract Component Graph) [START_REF] Guennoun | A proved componentoriented approach for managins dynamic software architectures[END_REF] approach. The graph nodes represent the software components, and the edges represent the links between these components. The evolution is implemented by an architecture transformation specified by a rewriting rule. In this context we are interested in group communication support applications. These applications require adaptation ability to their various contexts. We use direct and mediated Producer-Consumer architectural styles [START_REF] Eugster | The many faces of publish/subscribe[END_REF]. To illustrate the proposed models and their transformations, we consider a case study of Emergency Management Activities (EMA) involving several cooperating participants or nodes having different roles and functions dealing with several context changes.

This paper, is organized as follows. In section 2, we present the related work. In section 3 we detail our refinement approach for adaptation illustrated on the considered case study. Then, in section 4, we propose a simulation for the refinement approach where we handle the internal structure of nodes and the communication links between the nodes. Finally, in section 5 we conclude.

Related work

The adaptation solutions suggested in the literature are defined in various ways. Adaptation may be ruled by architecture based transformation laws. In [START_REF] Friday | Developing adaptive applications: The most experience[END_REF] the classification of common adaptation techniques are identified and classified. The adaptation is architectural when the structure of adaptive services can be modified. [START_REF] Friday | Developing adaptive applications: The most experience[END_REF][START_REF] Exposito | FPTP: the XQoS aware and fully programmable transport protocol[END_REF] provides frameworks for designing Transport level protocols whose internal structure can be modified according to the application requirements and network constraints. The replacement of a processing module by another(s) can implement adaptation actions, following a plug and play approach where the new component has the same interfaces as the replaced one. The applications have requirements and constraints provided by entities exchanging high level information. Requirements and constraints may change dynamically depending on the supported cooperative activity and its evolution. Two different adaptability approaches may be distinguished: the design time adaptability and the run time adaptability. For the design time adaptability, we can find commercial tools for application architecture adaptability like AAA of HP [START_REF]The HP AAA presentation[END_REF], a design support tool. The AAA tool handles the application development cycle and optimizes the resource value, by insuring that the infrastructure answering clearly and in a measurable way to activity requirements. For the run time adaptability [START_REF] Friday | Developing adaptive applications: The most experience[END_REF] presents several adaptation techniques among which use proxy services, change model of interaction and reorganize application structure. Adaptability is also implemented by multimedia retrieval systems like the search engine framework CARSA [START_REF] Bade | Carsa -an architecture for the development of context adaptive retrieval systems[END_REF]. Behavioral and architectural adaptability are the two approaches addresses by the proposed solutions. [START_REF] Chang | Automatic configuration and runtime adaptation of distributed applications[END_REF] describes a distributed image visualization application that consists of components that implement different compression methods. On the other side, at the application level, [START_REF] Wu | Streaming video over the internet: Approaches and directions[END_REF] addresses the need for adaptation in video streaming applications distributed over the Best-Effort. In general the application adaptability is implemented as a handling of features provided by lower layers. The adaptation can also be managed at the component-tocomponent communication level, aiming at supporting a given application level architecture and considering resource related constraints. Multiple architectures may be designed by adopting partially or totally centralized and distributed styles [START_REF] Friday | Developing adaptive applications: The most experience[END_REF][START_REF]Net passport technical overview[END_REF]. Different criteria may be used for routing and connecting strategies. Similarly to [START_REF] Carzaniga | Design and evaluation of a wide-area event notification service[END_REF], we can consider typed channel managers where producers and consumers are connected to one or another manager depending on the type of information they produce or consume. The Peer to Peer technology [START_REF] Milojicic | Peer-to-peer computing[END_REF] has initiated publishing and dynamic discovery of components. Service-oriented technologies as Web Services constitute a continuation towards this direction. Service-Oriented Architectures (SOA) are based on dynamically publishing and discovering services. This kind of architectures provides the possibilities to dynamilically compose services for adapting applications to contexts. Service descriptions are published, via the registry, by service providers and dynamically discovered by service requesters. We distinguish also some projects that focus on the middleware-level adaptation like "The Adaptive Application Project" [START_REF]The Adaptive Application Project home page[END_REF].The goal of "The Adaptive Application Project" is to provide a programming framework (a programming model, language, compiler, and runtime environment) that enable programmers to design, develop, and optimize the performance of adaptive distributed applications. Here we can say that the adaptation question is widely addressed in the literature, we distinguish two different approaches: design time adaptability and run time adaptability where we find several adaptation techniques. This diversity is extended here by answering to questions dealing with energy management and computing load balancing.

Adaptation approach

Managing architectural adaptation requires considering abstraction levels dedicated to specific parts of the whole adaptation, and self-adaptation has to be managed in a coordinated manner both within and between these abstraction levels. Distinguishing these abstraction levels allows designers and developers to master specification and implementation of adaptation rules. For a given configuration An,1 at level n, multiple configurations (An-1,1, ,An-1,p) may be implemented at level n-1. Adapting the architecture to constraint and requirement changes at level n-1 by switching among these configurations allows maintaining unchanged the n-level configuration. Likewise, when adaptation requires changes at level n, this may need no change at level n-1 if initial and new configurations of level n (e.g. changes from An,1 to An,2) have common implementations at level n-1 (e.g. An-1,p). We consider distributed component-based applications deployed on mobile communication nodes. The communication has to be maintained adapted to the context change factors. These factors are given according to the application and the node properties. Being aware of these factors, that we call context, provides a certain form of adaptability. The application and the node properties are: The mobile nodes move in a limited perimeter, each node has limited resources in term of energy and memory, priorities are associated with the communications among nodes. Moreover, on the same links it is possible to have several types of data with different priority degrees. We drive the evolutions between levels by considering the context changes.

Case study

Recent advances in computing and networking technologies enabled the deployment of complex group communication activities, such as Emergency Management Activities (EMA) involving mobile users cooperating within a common mission. This section presents the graph-based models of the three abstraction levels through a case study related to EMAlike activities.

General description

We assume an EMA group composed of a fixed controller, say A1, and two investigators, say A2 and A3, moving within the exploration field. For simplifying the model explanation, coordinator and controller are merged into a single role: controller. Functions performed by investigators include Observing the exploration field and Reporting feedbacks to the controller. Two kinds of feedbacks are distinguished: feedbacks D are Descriptive data; they are transmitted by means of audio/video; feedbacks P are Produced data; they express the analysis of the situation by an investigator. They are transmitted by means of audio. Investigators A2 and A3 provide continuous feedbacks D to A1; they also provide periodical feedbacks P; there is no priority difference between communications A2-A1 and A3-A1, but transmission of feedbacks D is more important than those of feedbacks.

Architecture Modelling

The architecture is represented by a directed graph, the vertices represent communication devices hosted by mobile nodes. The edges are labelled by the sent data types from a node to another and the priority of each type. The edge direction indicates the data flow direction. The producer and consumer are respectively at the tail and the head of the arrows. We also specify the factors the architecture has to adapt. This consists in defining the context elements. The elements we consider are: the energy level of the nodes, the memory saturation level of the nodes and the bandwidth available on the link. These three factors and the communications priority degree change during time and trigger the architecture transformations to adapt the application to these changes.

Architectural Refinement

We describe a refinement approach which implements the initial architecture on an event-based architecture, and on which we act for the adaptability. We proceed step by step. Initially we handle the internal structure of each node and then we refine the communications links between the nodes.

The nodes internal structure processing

We also proceed here step by step. Step 1 implements Functional entities decomposition. We consider now, the case of a node (A1). We split the entities inside the node according to their functional role. In our example, we consider that each node has a communication entity C and several processing entities T. At the end of this step, it is possible to proceed in two manners: Mediated Producer-Consumer style and Direct Producer-Consumer style. We detail first, the reasoning for the mediated Producer-Consumer style. Step 2 addresses communication message filtering. The communication entity receives a number of messages addressed to the different processing entities. The event server has the role of an event dispatcher. In one node, we distinguish one communication entity (C) and two processing entities (TD and TP). Each entity manages one flow type (D or P). Step 3 addresses the communications type choice. We consider the communication between the processing entities and the communication entity inside each node. The D data type has a high priority, therefore we choose a push link. A push link makes it possible to transfer the data as soon as it is produced. The P data type has a low priority, therefore we choose a pull link. A pull link makes it possible to transfer the data on demand of the consumers. We consider the internal structure of a refined producer node. The associated processing entity TD pushes the data when it is produced. On the other hand, the associated processing entity TP pulls the data when it is requested. We consider the internal structure of a refined consumer node. The communication entity C pushes the D data type because it has a higher priority. We detail now, the logic reasoning for the direct Producer-Consumer style. Like for step 2 when we consider the mediated Producer-Consumer style, we choose a push link which makes it possible to transfer the D data type as soon as it is produced. We choose a pull link which makes it possible to transfer the data on the consumer demand. In direct Producer-Consumer style, we do not use a filtering entity (event dispatcher). We have direct communication links between the communication entity and the processing entities. The functional differentiation makes it possible to deactivate the least important processing entities when the energy level of the nodes goes down.

Communication links refinement

The communication link refinement is related to the current context. To be able to adapt the system, we associate to each link a "rate". The rate represents the data transfer frequency by a node on a link. Through the rate and the nature of the link we will act to adapt the system. We also define thresholds associated with each parameter the context to define the rates witch trigger the adaptability actions. For instance, we define the scale for the energy level. If the node energy level is between 80% and 100%, the required rate is PR1. If the node energy level is between 40% and 80%, the required rate is PR2. If the node energy level is between 0% and 20%, the required rate is PR3. This rule is defined at the system deployment time and can be modified during the execution automatically or through an administrator intervention. Similar rules are associated with the bandwidth available on the link and the memory saturation level on the node. For each link, we associate a priority degree which is initially set to zero. Each factor can require a specific rate and we define a global link rate. We adopt the following policy. For two nodes A and B, each node calculates the rate required according the threshold rules. We have for each node: ER the rate associated with the energy level of the node; MR the rate associated with the memory saturation level of the node; BR the rate associated with the bandwidth available on the link and LR the rate associated with the link priority degree. Each node calculates his global link rate (GR) as follows:

µ γ β α µ γ β α + + + + + + LR BR MR ER
. Where the values α, β, γ and µ are weights that allow an importance degree to be associated with each factor. For instance, if the administrator knows that for a specific node the memory saturation level is the most important factor, he/she sets β to a value higher than α, γ and µ. The threshold scales for the four factors and the weights constitute the node profile. This profile depends on the technical characteristics of the node in the deployed application. Node A and Node B calculate their global link rates (GRA,GRB). Then the link rate LR is calculated. The new LR corresponds to the minimum between the GRA and the GRB. We obtain newLR= minimum (GRA, GRB). At the end of the operation, we reach a tradeoff which provides the adaptability until the next context change.

Simulation model and results

To validate our approach, we simulate the behaviour of an architecture composed of four mobile nodes. The D data type has a high priority and the P data type has low priority. We apply the three refinement steps and we adopt the direct Producer-Consumer style. Each link is mapped on a push or a pull interaction link. The pulls implement the transfer of data P because this transfer has a low priority. The pushes implement transfer of the data D because this transfer has a high priority. We consider the internal structure of each node, our approach allows to deactivate the component that the node does not use. We have two types of processing components (TD and TP). In each node we represent only the active components. For node A4, we deactivate TD because this node does not process D data type. For the other nodes, we have the communication entity (C) and two processing entities (TD and TP). The links between the two processing entities and the communication entity are of type push or pull. We associate the pull interaction mode with the transfer of data P. And we associate the push interaction mode with the transfer of the data D. Each node has a profile: a rate rule and four factor importance values α, β, γ and µ.

Simulation parameters

To simplify, we focus here, on the energy evolution for each node. We consider two random variables: X that represents a Poisson law of parameter λ, which characterizes the node's message production and Y that represents a Gaussian law with parameters m and σ, which characterizes the bandwidth variation on the links. For the memory state, we use a trace of a mobile node previously logged and we take into account the variable X. We calculate the node energy according to the node state (consuming or producing, inactivity and idle).

Results and interpretations

We give here the curves of node energy evolution during time with and without adaptability. We draw the curves that show the energy evolution on each node with and without adaptability.

Fig 1. Energy evolution on nodes

We estimate how much time the node stays "alive" or has enough energy to work properly. For node A4 (fig 1), we notice that adaptability provides energy 23 minutes (14%) more. This is due mainly to the deactivation of the processing entity TD and the fact that node A4 makes only pulls. For node A2 (fig 1), we notice that adaptability provides energy 19 minutes (11% )more. This is due mainly to the adaptation of the push rate. During simulation, the energy decrease made the node decrease the push rate. For nodes A1 and A3 (fig 1), the improvement was only of 8 minutes (5%) and can be improved by a different tuning of the rate rules and the parameters α, β, γ and µ.

Conclusion and perspective

We presented in this paper an approach of adaptation for group communication support application with context-aware architectures sensitive to the context. We consider different refinement steps that make it possible to decompose the nodes into processing and communication entities. It also allows us to act on the communication links. In particular, we can tune the rate on a link. This adaptation is not static, but it is specific to each node through, the weights α, β, γ and µ and the threshold scales according to the role of the node. To validate our approach, we provided a model to simulate the architectural quantitative attributes. The effectiveness of our approach was shown but we still work on adjusting the importance parameters α, β, γ and µ and the threshold scales. We plan in addition, to develop an ontology that will characterize better the context and its various parameters.

Acknowledgements

This work has been done within the context of the ITEA UseNet Project.