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...imize the vector {s(0),...,s(K −1)} (for a node), or the vector {ru(0),...,ru(K − 1), rv(0),...,rv(K − 1)} (for a link). Similar approaches have been used to achieve fairness in data generation [13], =-=[26]-=- and in session rate allocations [12]. The network utility maximization framework is also well-developed [29], [33], but mostly for fairness among nodes, not across the different time slots. To apply ...

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...non-decreasing functions parameterized by α ≥ 0: Uα(·) = (·) 1−α /1 − α, for α ≥ 0, α = 1 and log(·) for α = 1. Under our objective function, we use them to achieve max−min and proportional fairness =-=[31]-=-. We apply the utility maximization framework to find both the optimal spending rates s(i) and the optimal communication rates ru(i) and rv(i). IV. CHARACTERIZING LIGHT ENERGY One of the important dim...

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...rvesting, ultra-low-power networking, indoor radiant energy, measurements, energy-aware algorithms. I. INTRODUCTION Recent advances in the areas of solar, piezoelectric, and thermal energy harvesting =-=[34]-=-, and in ultra-low-power wireless communications [41] will soon enable the realization of perpetual energy harvesting wireless devices. When networked together, they can compose rechargeable sensor ne...

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..., it is time-dependent and periodic, but harder to predict. Time-dependent and somewhat periodic behaviors (along with inputs such as weather forecasts) would allow to develop an energy profile [13], =-=[24]-=-. We will refer to ideal energy profiles that accurately represent the future as predictable profiles, and to those that are not accurate as partially-predictable profiles. Energy behavior that does n...

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...n ultra-low-power wireless communications [41] will soon enable the realization of perpetual energy harvesting wireless devices. When networked together, they can compose rechargeable sensor networks =-=[23]-=-, [35], [45], networks of computational RFIDs [19], and Energy Harvesting Active Networked Tags (EnHANTs) [15]–[17]. Such networks will find applications in various areas, and therefore, the wireless ...

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...ink). Similar approaches have been used to achieve fairness in data generation [13], [26] and in session rate allocations [12]. The network utility maximization framework is also well-developed [29], =-=[33]-=-, but mostly for fairness among nodes, not across the different time slots. To apply it, α−fair functions are used under certain objective functions that will be described in Sections V and VI. α−fair...

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...a-low-power wireless communications [41] will soon enable the realization of perpetual energy harvesting wireless devices. When networked together, they can compose rechargeable sensor networks [23], =-=[35]-=-, [45], networks of computational RFIDs [19], and Energy Harvesting Active Networked Tags (EnHANTs) [15]–[17]. Such networks will find applications in various areas, and therefore, the wireless indust...

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...s in cases in which the predictions are not accurate. Stochastic process: Dynamic activation of energy-harvesting sensors is described in [25]. Admission and power allocation control are developed in =-=[14]-=-. Model-free approach: Duty cycle adjustments for a single node (and under the linear storage model) are examined in [40]. A capacitor-based system is presented and the capacitor leakage is studied in...

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... is described in [25]. Admission and power allocation control are developed in [14]. Model-free approach: Duty cycle adjustments for a single node (and under the linear storage model) are examined in =-=[40]-=-. A capacitor-based system is presented and the capacitor leakage is studied in [45]. Additional related work includes a study of the effect of duty cycle adaptations on network-wide parameters [18] a...

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...power wireless communications [41] will soon enable the realization of perpetual energy harvesting wireless devices. When networked together, they can compose rechargeable sensor networks [23], [35], =-=[45]-=-, networks of computational RFIDs [19], and Energy Harvesting Active Networked Tags (EnHANTs) [15]–[17]. Such networks will find applications in various areas, and therefore, the wireless industry is ...

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...y predictable, [24], [29], [32] have provisions for adjustments in cases in which the predictions are not accurate. Stochastic process: Dynamic activation of energy-harvesting sensors is described in =-=[25]-=-. Admission and power allocation control are developed in [14]. Model-free approach: Duty cycle adjustments for a single node (and under the linear storage model) are examined in [40]. A capacitor-bas...

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...matic diagram of the relationships between energy parameters: irradiance (I), irradiation (H), energy available to a device (D), and energy collected in storage (Q). rate [43], and routing efficiency =-=[28]-=-, [44]. Per-slot short-term predictions are assumed in [29]. Partially-predictable energy profile: While considering energy predictable, [24], [29], [32] have provisions for adjustments in cases in wh...

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...onment, it is time-dependent and periodic, but harder to predict. Time-dependent and somewhat periodic behaviors (along with inputs such as weather forecasts) would allow to develop an energy profile =-=[13]-=-, [24]. We will refer to ideal energy profiles that accurately represent the future as predictable profiles, and to those that are not accurate as partially-predictable profiles. Energy behavior that ...

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...ical results. We summarize and discuss future work in Section VIII. II. RELATED WORK In this section we briefly review related work using the outlined general settings. Predictable energy profile: In =-=[22]-=-, [24], duty cycle adaptations (mostly for single nodes) are considered. For a network, various metrics are considered including data collection rates [13], end-to-end packet delivery probability [42]...

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...over 0.5Hd. For the outdoor datasets the average prediction errors are approximately 0.3Hd. Improving the energy predictions (for outdoor conditions) using weather forecasts has been studied in [27], =-=[39]-=-. We examined whether the Hd values in the indoor settings are correlated with the weather data [10]. We determined substantial correlations for some locations. For example, for setup L-1 the correlat...

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...(t)dt H A, η D Fig. 3. A schematic diagram of the relationships between energy parameters: irradiance (I), irradiation (H), energy available to a device (D), and energy collected in storage (Q). rate =-=[43]-=-, and routing efficiency [28], [44]. Per-slot short-term predictions are assumed in [29]. Partially-predictable energy profile: While considering energy predictable, [24], [29], [32] have provisions f...

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... by an ideal linear model, where the changes in the energy stored are linearly related to the amounts of energy harvested or spent, or more realistically by considering their chemical characteristics =-=[37]-=-. Use of capacitors for storing harvested energy recently started gaining attention [17], [19], [23], [45]. Specifically, capacitor self-discharge (leakage) is considered in [45]. We consider another ...

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...diagram of the relationships between energy parameters: irradiance (I), irradiation (H), energy available to a device (D), and energy collected in storage (Q). rate [43], and routing efficiency [28], =-=[44]-=-. Per-slot short-term predictions are assumed in [29]. Partially-predictable energy profile: While considering energy predictable, [24], [29], [32] have provisions for adjustments in cases in which th...

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...less devices. When networked together, they can compose rechargeable sensor networks [23], [35], [45], networks of computational RFIDs [19], and Energy Harvesting Active Networked Tags (EnHANTs) [15]–=-=[17]-=-. Such networks will find applications in various areas, and therefore, the wireless industry is already engaged in the design of various devices (e.g., [9]). In this report we focus on devices that h...

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...n [40]. A capacitor-based system is presented and the capacitor leakage is studied in [45]. Additional related work includes a study of the effect of duty cycle adaptations on network-wide parameters =-=[18]-=- and specific considerations for indoor radiant energy harvesting [15], [17], [19], [36]. Q III. MODEL AND PRELIMINARIES In this work we focus both on light measurements and on resource allocation pro...

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... wireless devices. When networked together, they can compose rechargeable sensor networks [23], [35], [45], networks of computational RFIDs [19], and Energy Harvesting Active Networked Tags (EnHANTs) =-=[15]-=-–[17]. Such networks will find applications in various areas, and therefore, the wireless industry is already engaged in the design of various devices (e.g., [9]). In this report we focus on devices t...

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...l soon enable the realization of perpetual energy harvesting wireless devices. When networked together, they can compose rechargeable sensor networks [23], [35], [45], networks of computational RFIDs =-=[19]-=-, and Energy Harvesting Active Networked Tags (EnHANTs) [15]–[17]. Such networks will find applications in various areas, and therefore, the wireless industry is already engaged in the design of vario...

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...s: irradiance (I), irradiation (H), energy available to a device (D), and energy collected in storage (Q). rate [43], and routing efficiency [28], [44]. Per-slot short-term predictions are assumed in =-=[29]-=-. Partially-predictable energy profile: While considering energy predictable, [24], [29], [32] have provisions for adjustments in cases in which the predictions are not accurate. Stochastic process: D...

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...-harvesting-aware algorithms for networks of nodes considering the various other problem dimensions. Moreover, we plan to evaluate these algorithm in an EnHANTs testbed that we are currently building =-=[16]-=-. IX. ACKNOWLEDGEMENTS This work was supported in part by the Vodafone Americas Foundation Wireless Innovation Project, NSF grants CNS0916263, CCF-0964497, and CNS-10-54856, DHS Task Order #HSHQDC-10-...

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...]. Performing this iterative procedure for a large number of slots K, we obtain, for each energy storage level B(i), a corresponding stationary (same for all i) s(i) value that approaches the optimal =-=[21]-=-. Although policy calculations are computationally expensive (the running time of the algorithm is O([C/∆] 2 ·M · K)), such a policy needs to be computed only once for a particular distribution of D. ...

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... the case. The demonstrated σ(HT) values suggest that these energy inputs generally fall under the partially predictable profile energy models. We have studied whether, similarly to outdoor scenarios =-=[11]-=-, [27], in the indoor datasets the profile characterization for a given day can be improved when a device has observed some of the incoming energy. We examined the correlations between the amount of e...

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...energy, measurements, energy-aware algorithms. I. INTRODUCTION Recent advances in the areas of solar, piezoelectric, and thermal energy harvesting [34], and in ultra-low-power wireless communications =-=[41]-=- will soon enable the realization of perpetual energy harvesting wireless devices. When networked together, they can compose rechargeable sensor networks [23], [35], [45], networks of computational RF...

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...[22], [24], duty cycle adaptations (mostly for single nodes) are considered. For a network, various metrics are considered including data collection rates [13], end-to-end packet delivery probability =-=[42]-=-, data retrieval3 TABLE I NOMENCLATURE. I Irradiance (W/cm2) H Irradiation (J/cm2) D Energy harvested given device physical parameters (J) K Number of slots C Energy storage capacity (J) B,B0,BK Ener...

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...storage (Q). rate [43], and routing efficiency [28], [44]. Per-slot short-term predictions are assumed in [29]. Partially-predictable energy profile: While considering energy predictable, [24], [29], =-=[32]-=- have provisions for adjustments in cases in which the predictions are not accurate. Stochastic process: Dynamic activation of energy-harvesting sensors is described in [25]. Admission and power alloc...

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... (e.g., [9]). In this report we focus on devices that harvest environmental light energy. Since there is a 3 orders of magnitude difference between the light energy available indoor and outdoor [17], =-=[36]-=-, significantly different algorithms are required for different environments. However, there is lack of data and analysis regarding the energy availability in such environments. Hence, over the past 1...

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...g the energy predictions (for outdoor conditions) using weather forecasts has been studied in [27], [39]. We examined whether the Hd values in the indoor settings are correlated with the weather data =-=[10]-=-. We determined substantial correlations for some locations. For example, for setup L-1 the correlation coefficient of the Hd values with the weather data is rc = 0.35 (p < .001), and for setup L-6 it...

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...eristics, in a simple system, the amount of power harvested depends both on the amount of energy provided (irradiance in the case of light energy harvesting), and on the amount of energy stored [19], =-=[30]-=-. The non-linear relations are demonstrated in Fig. 2. C. Storage Capacity, Decision Timescale, and Problem Size Storage capacity vs. amount of energy harvested – Energy storage capacity can vary from...

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...cm 2 ) I (µW/cm 2 ) I (µW/cm 2 ) x 104 10 5 0 200 0 100 50 0 1 2 3 4 Days 1 2 3 4 Days 15 30 45 60 Minutes Fig. 1. Examples of different light energy sources: (top) predictable profile (Las Vegas, NV =-=[5]-=-, outdoors), (middle) partially-predictable profile (New York, NY, a static indoor device), and (bottom) stochastic behavior (New York, NY, a mobile device in Times Square at nighttime). renewable ene...

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...door mobile device measurements. Table II provides a summary of the indoor measurement locations. Schematically, they are show in Fig. 4. For the measurements we use TAOS TSL230rd photometric sensors =-=[8]-=- installed on LabJack U3 DAQ devices [4]. These photometric sensors have a high dynamic range, allowing capturing of widely varying irradiance conditions. We verified the accuracy of the sensors with ...

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...portant dimensions of the problem space is environmental energy modeling. Since large-scale outdoor solar panels have been used for decades, properties of the Sun’s energy were examined in depth [5], =-=[27]-=-, [36]. Until recently4 TABLE II LIGHT ENERGY MEASUREMENT SETUPS, AVERAGE DAILY IRRADIATION, AND ACHIEVABLE BIT RATES. Location Location description Experiment timeline Hd σ(Hd) r index (J/cm 2 /day)...

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...e indoor irradiance measurement locations. using indoor radiant energy for networking applications was considered impractical, and indoor light was studied mostly in architecture and ergonomics [20], =-=[38]-=-. However, in these domains the important factor is how humans perceive the given light (photometric characterization – i.e., measurements in Lux) rather than the energy of the light (radiometric char...

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...otometric sensors have a high dynamic range, allowing capturing of widely varying irradiance conditions. We verified the accuracy of the sensors with a NIST-traceable [6] Newport 818-UV photodetector =-=[7]-=-. In addition to the indoor measurements, we also analyze a set of outdoor irradiance traces provided by the National Renewable Energy Laboratory (NREL) [5]. The provided measurements and irradiance t...