Resource and Task Scheduling for SWIPT IoT Systems with Renewable Energy Sources

Transcription

1 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JIOT , IEEE Internet of 1 Resource and Tas Scheduling for SWIPT IoT Systems with Renewable Energy Sources Hyun-Su Lee and Jang-Won Lee, Senior Member, IEEE Abstract In this paper, we consider IoT systems that can be applied to various applications with low-mobility or static IoT devices such as wireless sensor networs and charging systems for low-power devices with communication. The IoT systems consist of IoT devices and a hybrid access point (H-AP) powered by both on-grid and renewable energy sources. The IoT devices have a capability to harvest energy from the H-AP s RF signal, and they perform their tass by using only their harvested energy. We consider the tass do not have a real-time requirement which can be stored in the tas queues of the IoT devices and performed later. We study resource and tas scheduling for the IoT systems which aims at minimizing the on-grid energy consumption at the H-AP while guaranteeing the minimum average data rate and minimum tas performing rates of IoT devices. To achieve the goal, we first propose a centralized resource and tas scheduling algorithm. However, its computational complexity and signaling overhead are too large due to the tas scheduling for each IoT device. Thus, to resolve these issues, we propose a hybrid resource and tas scheduling algorithm in which each IoT device determines its own tas scheduling in a distributed manner and the H-AP determines the resource scheduling. We then provide performance analyses showing that our proposed algorithms are asymptotically optimal and well satisfy the QoS requirements of IoT devices even with distributed tas scheduling. Through the simulation results, we verify the analyses and show the performance of our algorithms. Index Terms SWIPT, IoT systems, resource allocation, tas scheduling, renewable energy. I. INTRODUCTION As Internet of Things (IoT) is emerging, various renewable energy sources (RESs) such as solar, wind, and piezoelectric energy sources are utilized for powering IoT devices [1], [2], and various management techniques for IoT devices such as tas scheduling [3] [6] and power management [7], [8] are widely studied with the RESs. These wors allow the IoT devices to prolong their battery lifetime or to achieve selfsustainability by efficiently using their resources such as energy stored in the battery and computation power. Recently, radio frequency (RF) energy harvesting has been also studied for the self-sustainability of the IoT devices. Since the energy source of RF energy harvesting, i.e., RF signals, is controllable by the networ, RF energy harvesting can stably provide energy contrary to the conventional RESs which are intermittent and uncontrollable [9], [1]. Such an energy provisioning technique is called wireless power transfer (WPT) [11]. When access The authors are with the Department of Electrical and Electronic Engineering, Yonsei University, Seoul 3722, Korea. This wor was supported by Samsung Research Funding Center of Samsung Electronics under Project Number SRFC-IT171-13, and Midcareer Researcher Program through NRF grant funded by the MSIT, Korea (No. NRF-217R1A2 B4698). points (APs) utilize the WPT technique, they can transfer not only power but also information to the IoT devices at the same time. Such a technique is called a simultaneous wireless information and power transfer (SWIPT) [12] [14]. The SWIPT technique enables an IoT device to harvest energy as well as to receive information from the received signal, and thus, allows APs to efficiently perform both wireless information transfer (WIT) and WPT to IoT devices. Even though WPT techniques can stably provide energy to IoT devices, it is still hard to enable the IoT devices to stably operate using the harvested energy from the RF signals without resorting to external energy, since the energy consumption by each IoT device is determined by its tass, which randomly arrive in general. Thus, to achieve such a stable operation using the harvested energy, the characteristics of the IoT devices tass, such as arrival rate and required energy to be performed, should be appropriately considered in the WPT techniques [15].As a related research, in a wireless powered communication networ (WPCN), IoT devices transmit their data in an uplin (UL) by using the harvested energy by the WPT in a downlin (DL) from a hybrid access point (H-AP) [11]. Recently, various WPCNs have been studied considering various communication technologies such as full-duplex, massive MIMO, user cooperation, and SWIPT techniques [16] [22]. However, most existing researches on the WPCN have a limitation that they consider only UL transmission as a tas of IoT devices and do not consider other various types of tass such as sensing and computing. For greener energy provision to the IoT devices using WPT techniques, the H-APs can be powered not only by the on-grid energy source but also RESs to reduce the carbon footprint due to the on-grid energy consumption. In green communications, there have been a lot of researches to minimize the amount of on-grid energy consumption on networ equipments, such as APs and switches, by effectively utilizing energy harvested from RESs [23]. In these wors, various techniques to manage APs, such as on-off switching [24], CoMP techniques [25], [26], and subcarrier allocation and power control [27], [28], are incorporated with utilizing the harvested energy. As the related wors in green communications, the energy dependency of the H-APs on the on-grid energy source can be effectively reduced by appropriately managing the H-APs with utilizing the harvested energy from RESs [29]. By integrating the above techniques, a typical SWIPT IoT system with RESs can be deployed. In the SWIPT IoT system, an H-AP transmits both information and power to IoT devices by the SWIPT technique, and the IoT devices are powered by the harvested energy from the SWIPT signal and perform their (c) 218 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

2 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JIOT , IEEE Internet of 2 Sensors Headphones Effective range for SWIPT ~ tens of meters Keyboard Wearable devices Mouse Fig. 1. The example of the SWIPT IoT system. (Green lines represent energy paths.) various tass by using the harvested energy. Also, the H-AP is powered by both on-grid energy source and RESs. For RF energy harvesting, the minimum level of RF input power is required to operate the energy harvesting circuit. Thus, the effective range considered in the SWIPT IoT system is given by tens of meters due to the attenuation of the SWIPT signal. This limited effective range maes the SWIPT IoT system hard to be used for the applications with high-mobility. Thus, as shown in Fig. 1, the SWIPT IoT system can be applied to various applications with low-mobility or static IoT devices such as wireless sensor networs and charging systems for a wide variety of low-power devices with communication [3], [31]. In such a SWIPT IoT system in which the IoT devices are powered by the harvested energy, the H-AP should provide the sufficient energy to the IoT devices to ensure their stable operation. This can be easily achieved if the H-AP continuously transmits with a large transmission power. However, such a large transmission power is too inefficient in terms of energy utilization, which incurs high costs and high carbon footprints. To resolve this problem, the SWIPT IoT system should operate to ensure the stable operation of the IoT devices while minimizing the on-grid energy consumption. Such a SWIPT IoT system can be used for variable applications as a general-purpose SWIPT IoT system. However, it is hard to be used for some applications such as public safety and mission-critical infrastructure networs since it is hard to even meet their extreme requirements such as ultra reliable and low latency. Thus, for such applications, a specialized SWIPT system highly focused on such requirements is required. In this paper, we focus on the general-purpose SWIPT IoT that efficiently ensures the stable operation of the IoT devices. To this end, we investigate how the H-AP efficiently transmits both information and power to the IoT devices while enabling the IoT devices to satisfy their QoS requirements on receiving data and performing tass. We also investigate how the IoT devices schedule their tass considering its harvested energy from the SWIPT signal and their QoS requirements on performing tass. In addition, to capture the non-linearity in practical RF energy harvesting circuits, we consider a nonlinear RF energy harvesting model for the RF energy harvesting at the IoT devices. We summarize the distinguishing features of our wor compared with those in the related wors in Table I. Specifically, we focus on the resource and tas scheduling for IoT systems which aims at minimizing the average ongrid energy consumption while guaranteeing QoS requirements of the IoT devices, i.e., the minimum average data rates, the minimum average harvested energy, and the minimum tas performing rates. To achieve the goal, we first develop a centralized resource and tas scheduling algorithm by using the Lyapunov optimization framewor. The centralized algorithm does not require any a priori information about the statistical characteristics of system uncertainties, such as channel gain, tas arrivals, and harvested renewable energy. Instead, we only have to solve a deterministic optimization problem in each time-slot using only current system states. However, the centralized algorithm requires a large computational complexity exponentially increasing according to the number of IoT devices. Moreover, for the centralized algorithm, each IoT device should report its tas arrivals to the H-AP in every timeslot, which incurs a considerable amount of energy consumption for the IoT device. To resolve these issues of the centralized algorithm, we also propose a hybrid resource and tas scheduling algorithm that is a hybrid of centralized resource scheduling and distributed tas scheduling. In the algorithm, the tas scheduling of each IoT device is determined by itself in a distributed manner, and the resource scheduling is determined by the H-AP in a centralized manner. To this end, we first develop a distributed tas scheduling algorithm which aims at enabling each IoT device to satisfy its tas performing rate requirements by efficiently utilizing its harvested energy. However, to allow an IoT device to satisfy its tas requirements, the harvested energy at the IoT device should be sufficiently provided. Thus, we investigate a sufficient condition on the amount of harvested energy at each IoT device for the satisfaction of its tas requirements. We then develop a resource scheduling algorithm for distributed tas scheduling which aims at minimizing the average ongrid energy consumption. Moreover, the resource scheduling algorithm guarantees the minimum average harvested energy requirements using the sufficient condition and the minimum average data rate requirements of IoT devices. We provide the performance analyses of our centralized and hybrid algorithms, which show that they are asymptotically optimal and satisfy the QoS requirements. The rest of this paper is organized as follows. Section II provides the system model studied in this paper. In Section III and Section IV, we propose a centralized resource and tas scheduling algorithm and a hybrid resource and tas scheduling algorithm, respectively. We provide simulation results and discuss them in Section V, and we finally conclude in Section VII. II. SYSTEM MODEL We consider a time-slotted TDMA SWIPT system that consists of one H-AP with a single antenna 1 having a capability of scheduling both information transfer and energy transfer and 1 If the H-AP has multiple antennas, beamforming techniques can be used. Since there are many researches on the beamforming techniques for the SWIPT systems [32], [33], in this paper, we focus on the system operation issues, i.e., resource and tas scheduling, with the H-AP having a single antenna (c) 218 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

3 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JIOT , IEEE Internet of 3 TABLE I COMPARISON WITH RELATED WORKS ( : CONSIDERED, -: NOT CONSIDERED) AP with RESs WPT/SWIPT Tas-awareness Non-linear RF energy harvesting model [12] - SWIPT - - [13], [14] - SWIPT - [11], [16] [2] - WPT Only UL transmissions - [22] - SWIPT Only UL transmissions - [24] [28] Our wor SWIPT General tass On-grid energy source RESs SWIPT WIT WPT AP IoT device Battery Fig. 2. The system model. Downlin SWIPT Tas operation Tas A Tas B Tas C Tas operation Tas operation Tas operation t t+1 Fig. 3. The time-slot structure of the system. Tas queues K IoT devices 2 with a single antenna having a capability of a power splitting SWIPT scheme [13]. In addition, the H-AP is powered by both on-grid energy source and RESs. The set of devices is denoted by K = {1, 2,..., K}. We assume that H-AP and devices have their own batteries to store their surplus energy. The system model in this paper is shown in Fig. 2. As shown in Fig. 3, each time-slot consists of a DL SWIPT phase and a device s tas operation phase. 3 Since we consider the SWIPT system with low-mobility devices as in Fig. 1, we assume a bloc fading channel model, where the channel gains between the H-AP and the devices are time-varying but constant during one time-slot. Note that this assumption is widely used in the literature [11], [12], [17] [2], [22]. In the DL SWIPT phase, the H-AP transmits a SWIPT signal to a device which is scheduled. Then, the scheduled device receives information and harvests energy simultaneously by using the power splitting SWIPT scheme. The other devices which are not scheduled only harvest energy using the transmitted signal from the H-AP. Then, in the tas operation phase, the devices operate their different tass which stochastically arrive in each time-slot, such as sensing and computing, by using the harvested energy and the stored energy in their own batteries. 2 In the rest of this paper, we omit IoT from IoT device for the convenience. 3 In this paper, for the compatibility to time division duplex for DL and UL transmissions, we consider the separate phases for DL SWIPT and tas operation. However, the proposed algorithms in this paper can be easily adopted in the system, where DL SWIPT and tas operation are performed in parallel by incorporating the harvested energy in time-slot t into the available energy in time-slot t + 1, not into that in time-slot t. In each time-slot t, the H-AP schedules one device for SWIPT. The scheduling indicator to device in time-slot t is denoted by q (t) {, 1}, where 1 represents that device is scheduled in time-slot t and not. For each time-slot, at most one device can be scheduled as q (t) 1. (1) K Then, the H-AP determines its transmission power considering both SWIPT to the scheduled device and WPT to the harvesting devices. The transmission power of the H-AP in time-slot t is denoted by p(t) and bounded as p(t) P max, (2) where P max is the maximum transmission power of the H-AP. Note that the pea energy consumption of the H-AP in each time-slot is limited by this constraint. In our system, the H-AP is powered by both on-grid and RESs. The amount of harvested renewable energy of the H-AP in time-slot t is denoted by H(t), which is assumed to be an independent identically distributed (i.i.d.) random variable whose support is bounded as H(t) H max, (3) where H max is the maximum energy capacity of the RESs. The amount of on-grid energy consumed by the H-AP in time-slot t is denoted by G(t) and bounded as G(t) G max, (4) where G max is the maximum amount of on-grid energy consumption during a time-slot due to the capacity limitation of the power line. The H-AP can store its surplus energy in its battery and use the stored energy later. The battery level of the H-AP in time-slot t is denoted by B (t). Then, the total available energy at the H-AP is given by the sum of its battery level, its harvested renewable energy, and its on-grid energy that will be consumed. Since the energy consumption at the H-AP due to its transmission cannot exceed its total available energy in the time-slot, the following condition should be satisfied: B (t) + H(t) + G(t) p(t)t DL, (5) where T DL is the duration of the DL SWIPT phase. The dynamics of the battery level at the H-AP is described as B (t + 1) = B (t) + H(t) + G(t) p(t)t DL. (6) In each time-slot t, device receives the SWIPT signal from the H-AP, and by using the power splitting SWIPT scheme, it (c) 218 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

4 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JIOT , IEEE Internet of 4 can harvest energy and decode information at the same time [13]. To this end, the received signal power is split to its energy harvester and its information receiver according to the given ratio called a power split ratio. Let ρ (t) 1 be the power split ratio of device in time-slot t. Then, a ratio ρ (t) of the received signal power is split to its energy harvester and the remaining is split to its information receiver. Since only the scheduled device receives the information from the signal, the power split ratio of device which is not scheduled in time-slot t is naturally set to be ρ (t) = 1. To ensure this, we consider the following constraint: (1 q (t))(1 ρ (t)) =. (7) Harvested power (mw) Measurement data [34] Linear model Non-linear model [36] Piecewise linear model Input RF power (mw) At the information receiver, the splitted signal is used for the information decoding. The data rate of device in time-slot t is derived by using the Shannon capacity as follows: ( r (t) = q (t)w log (1 ρ ) (t))h (t)p(t), (8) n W where h (t) is the channel gain of device in time-slot t, W is the system bandwidth, and n is the noise spectral density. Then, the average data rate of device, R, is obtained as 1 t 1 R = lim r (τ). (9) t t τ= We consider the average data rate requirement of device as R R, (1) where R is the minimum average data rate of device. At the energy harvester, the split signal is used for RF energy harvesting. In the related wors [12], [17] [2], [22], the harvested energy at the energy harvester is modeled based on a linear energy harvesting model in which the harvested energy eeps increasing as the input RF power increases. However, practical energy harvesting circuits have non-linearity characteristics on the harvested energy [34], [35]. Specifically, the practical circuits have the maximum power that can be harvested. Thus, such a non-linearity in the practical circuits must be considered in order to prevent from over-estimating the amount of harvested power at the IoT devices. To capture such a non-linearity of practical circuits, in [36], the practical non-linear energy harvesting model is proposed. However, the non-linear model in [36] is quite complex, which incurs a large computational complexity to be handled. Thus, instead of using the non-linear model in [36], we propose a simple piecewise linear model. For the harvested energy of device in time-slot t, e (t), the piecewise linear model is given by e (t) = min ( ρ (t)ξ h (t)p(t)t DL, e max ), (11) where ξ is the energy conversion efficiency of device and e max is the maximum possible harvested energy of device in a time-slot. In Fig. 4, we provide the experimental measurement data for a practical circuit in [34], and also provide the linear model, the non-linear model in [36], and the piecewise linear model used in this paper. From the figure, we can see that the proposed piecewise model closely captures the measurement Fig. 4. Comparison of measurement data in [34], the linear model, the non-linear model in [36], and the piecewise linear model. data. We denote the average harvested energy of device by E, which is defined as 1 t 1 E = lim e (τ). (12) t t We then consider the average harvested energy requirement of each device as E Ē. (13) Each device has several types of tass to perform such as sensing, computing, and UL transmission. The set of types of tass in device is denoted by M = {1, 2,..., M }. We assume that for each device, each type of tas stochastically and independently arrives at its corresponding queue in each time-slot. The arrival of tas 4 m of device in time-slot t is modeled as an i.i.d binary random variable, α m (t), where 1 represents that tas m of device arrives in time-slot t and represents that it does not arrive. The arrival rate of tas m of device, a m, is obtained as a m τ= = lim 1 t 1 t t τ= α m (τ). (14) When each device performs its tass, a certain time duration is consumed for each tas. Let T m be the duration to perform tas m of device. Then, for the feasibility of the stable system, we assume T m am T TO, (15) m M where T TO is the duration of the tas operation phase. At the tas operation phase in each time-slot, each device can perform the arrived tass at its tas queues considering its energy condition and QoS requirements. The tas scheduling indicator for tas m of device in time-slot t is defined by 1, if the tas m of device β m (t) = in time-slot t is performed., otherwise For the simple presentation, we assume that each device cannot perform an identical type of tas many times in one tas 4 In the rest of this paper, we denote a tas whose type is m by a tas m for a simple presentation (c) 218 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

5 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JIOT , IEEE Internet of 5 operation phase, i.e., β m (t) can have the value or 1. However, the algorithms that will be developed in this paper can be easily generalized to the algorithms without this assumption by allowing β m (t) to be a non-negative integer and letting it be the number of tas m of device that will be performed in time-slot t. The total duration of device in time-slot t to perform its scheduled tass cannot exceed the duration of the tas operation phase as follows: β m (t)t m T TO. (16) m M In addition to the time, the device consumes energy when performing the tass. The energy consumption for tas m of device is denoted by C m. Then, the total energy consumption to perform the scheduled tass of device in time-slot t is obtained as C (t) = β m (t)cm. (17) m M The available energy of each device at the tas operation phase is given by the sum of its battery level and amount of the harvested energy at the DL SWIPT phase. We denote the battery level of device in time-slot t by B (t). Since the energy consumption of device cannot exceed its available energy, the following condition should be satisfied: B (t) + e (t) C (t). (18) After performing tass, each device can store its surplus energy in its battery, and the dynamics of the battery level in device is obtained as B (t + 1) = B (t) + e (t) C (t). (19) In the above dynamics, the maximum battery level due to the finite battery capacity is not considered. However, it will be shown that the proposed algorithms in this paper can be used even if the battery level is limited by the capacity of practical energy storages in Section V by the simulation results. From the tas scheduling indicator, the performing rate of tas m in device, b m, is obtained as b m = lim 1 t 1 β m t (τ). (2) t τ= We consider the tas performing requirement for tas m of device as b m am. (21) Note that by considering the tas performing requirements, the energy consumption of the devices is implicitly addressed since the devices consume their energy by performing their tass as in (17). We mainly consider the tass that do not have a real-time requirement. Thus, it is reasonable that the arrived tass can be stored in the tas queues and performed later. We denote the tas queue length of tas m in device in time-slot t as Z m (t). Then, we define the dynamics of the tas queue length by Z m (t + 1) = [Z m (t) + αm (t) βm (t)]+, (22) Notation q (t) p(t) H (t) G(t) B (t) ρ (t) r (t) R R e (t) E Ē α m (t) a m β m (t) b m C (t) B (t) Z (t) TABLE II LIST OF NOTATIONS Description Scheduling indicator to device Transmission power of the H-AP Amount of harvested renewable energy of the H-AP Amount of on-grid energy consumed by the H-AP Battery level of the H-AP Power split ratio of device Data rate of device Average data rate of device Average data rate requirement of device Harvested energy of device Average harvested energy of device Average harvested energy requirement of device Arrival of tas m of device Arrival rate of tas m of device Tas scheduling indicator for tas m of device Performing rate of tas m in device Total energy consumption to perform the scheduled tass of device Battery level of device Tas queue length of tas m in device where [ ] + = max [, ]. The vector of the tas queue lengths { of all devices in time-slot t is denoted by Z(t) = Z m (t)}. The satisfaction of tas performing K, m M requirement for tas m of device in (21) is equivalent to the mean rate stability of the tas queue Z m (t) [37], where the mean rate stability is defined as follows: Definition 1: A queue is mean rate stable if its queue length, Q(t), satisfies lim E[ Q(t) ]/t =, (23) t where E[ ] denotes the expectation operator. The mean rate stability will be also used in the following sections for the transformation of time average constraints into queue stability constraints. For the ease of reference, we summarize some notations in Table II. Note that we consider the time-varying system uncertainties for the channel gain, amount of renewable energy, and tas arrivals. The parameters in Table II which do not depend on time are the statistical parameters such as average data rate requirements and tas arrival rate. III. CENTRALIZED RESOURCE AND TASK SCHEDULING A. Problem Formulation In this subsection, we formulate a resource and tas scheduling problem in the SWIPT system powered by RESs and on-grid energy source. The problem aims at minimizing the on-grid energy consumption at the H-AP while guaranteeing the minimum average data rate, minimum average harvested energy, and minimum tas performing rate of each device. The problem is formulated with the constraints in the previous section as follows: 1 t 1 (C) minimize lim E {G(τ)} t t τ= subject to (1), (2), (4), (5), (7), (1), (13), (16), (18), (21). and the control policy is denoted by A(t) = {q(t), p(t), ρ(t), β(t), G(t)}, (c) 218 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

6 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JIOT , IEEE Internet of 6 where q(t) = {q (t)} K, ρ(t) = {ρ (t)} K, and β(t) = { β m (t)} K, m M. Note that the QoS requirements of each device should be satisfied in an energy-efficient way to minimize the on-grid energy consumption at the H-AP. In particular, the tas requirements of each device indirectly address the energy efficiency of the device since the devices consume their energy by performing their tass. In problem (C), we have time average constraints for average data rates, average harvested energy, and tas performing rates, i.e., the constraints in (1), (13), and in (21). To deal with them, we transform such time average constraints into queue stability constraints by defining virtual queues for the constraints. Note that virtual queues are not actual queues in the system but are implemented only for the algorithm. We first introduce a data virtual queue for the minimum average data rate constraint in (1) and an energy virtual queue for the minimum average harvested energy constraint in (13). Let X (t) and Y (t) be the data virtual queue length and energy virtual queue length of device in time-slot t, respectively. We define the dynamics of the data virtual queue length by X (t + 1) = [ X (t) + R r (t) ] +, (24) where r (t) is the data rate in time-slot t in (8), and also define the dynamics of the energy virtual queue length by Y (t + 1) = [Y (t) + Ē e (t)] +, (25) where e (t) is the harvested energy of device in time-slot t in (11). The vectors of the data virtual queue lengths and energy virtual queue lengths of all devices in time-slot t are denoted by X(t) = {X (t)} K and Y(t) = {Y (t)} K, respectively. Then, the following proposition shows that the mean rate stabilities of the rate virtual queues and energy virtual queues imply the satisfaction of the minimum average data rate requirements and minimum average harvested energy requirements, respectively. Proposition 1: For each device, if its data virtual queue X (t) is mean rate stable, then its minimum average data rate requirement is satisfied, i.e., R R. Moreover, if its energy virtual queue Y (t) is mean rate stable, then its minimum average harvested energy requirement is satisfied, i.e., E Ē. We omit the proof of Proposition 1 since it can be proved in a similar way introduced in [37]. By the proposition, we can substitute the constraints for the minimum average data rate and minimum average harvested energy with the mean rate stability constraints for the rate virtual queues and energy virtual queues, respectively. In addition, as mentioned in the previous section, the queue stability of the tas queue for tas m of device, Z m (t), implies the satisfaction of the corresponding tas performing requirement for tas m of device in (21). Thus, we can also substitute the constraints for the tas performing rate requirements with the mean rate stability constraints for the tas queues. Then, the reformulated problem is given by (C 1 t 1 ) minimize lim E {G(τ)} t t τ= subject to (1), (2), (4), (5), (7), (16), (18), Tas queues are stable All virtual queues are stable. B. Lyapunov Optimization Framewor In this subsection, we use the Lyapunov optimization framewor, which allows us to efficiently solve problem (C ) without any a priori information of the system uncertainties. To this end, we first formulate a Lyapunov optimization problem from problem (C ). Let Θ(t) = [X(t), Y(t), Z(t)] T be the system state of the combined queue vector, and we define the Lyapunov function as L(Θ(t)) = 1 X (t) Y (t) Z m (t)2. K K K m M (26) We also define the one-step conditional Lyapunov drift (Θ(t)) as (Θ(t)) = E [L(Θ(t + 1)) L(Θ(t)) Θ(t)]. (27) Then, we can show that (Θ(t)) B + E [ X (t) ( R r (t) ) Θ(t) ] (28) K + E [ Y (t) ( Ē e (t) ) Θ(t) ] K + E K m M [ Z m (t) ( α m (t) βm (t)) Θ(t) ], where B is a finite constant satisfying B 1 E [ R r (t) 2 Θ(t) ] E [ r (t) R Θ(t) ] (29) K K + 1 E [ Ē 2 2 +e (t) 2 Θ(t) ] E [ e (t)ē Θ(t) ] K K m M E E K m M K [ β m (t)2 + α m (t)2 Θ(t) ] [ α m (t) βm (t) Θ(t)]. We omit the derivation of (28) since it can be derived in a similar way introduced in [37]. Since the Lyapunov drift only addresses the queues for the QoS requirements, we define the following drift-plus-penalty expression to incorporate the objective function of problem (C ) into the Lyapunov optimization problem as (Θ(t)) + VE [G(t) Θ(t)], where V is a design parameter of the algorithm representing how much we emphasize the objective function. From (28), the drift-plus-penalty is bounded as (Θ(t)) + VE [G(t) Θ(t)] RHS of (28) + VE [G(t) Θ(t)]. (3) To solve the resource and tas scheduling problem, we adopt a min drift-plus-penalty algorithm in [37]. In the algorithm, an action A(t) is determined by solving the Lyapunov optimization problem in each time-slot which minimizes the right-hand-side of the inequality in (3). The Lyapunov optimization problem (c) 218 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

7 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JIOT , IEEE Internet of 7 Algorithm 1 Centralized Resource and Tas Scheduling Algorithm 1: Initialize all queues, X () s, Y () s, and Z m () s, and t = 1 2: while TRUE do 3: H-AP obtains the channel gain, queue lengths, battery level, tas arrival of each device, and the amount of its harvested renewable energy H(t) 4: H-AP obtains A(t) by solving problem (C LP(t) ) 5: All queues, Z m (t) s, X (t) s, and Y (t) s, are updated as (22), (24), and (25), respectively 6: t t + 1 7: end while in time-slot t is formulated as follows: (C LP(t) ) minimize VG(t) Z m (t) βm (t) K m M r (t)x (t) e (t)y (t) K K subject to (1), (2), (4), (5), (7), (16), (18). It is worth emphasizing that this problem can be solved only based on the current state of the system without any a priori information of the uncertainties in the system. We now develop a centralized resource and tas scheduling algorithm based on the min drift-plus-penalty algorithm in [37] which determines an action by solving the Lyapunov optimization problem. The algorithm is summarized in Algorithm 1. First, all queues are initialized (line 1 of Algorithm 1). In each time-slot t, the H-AP obtains the current system states such as the channel gain, queue lengths, and harvested renewable energy at the H-AP (line 3). Then, it determines the control policy in time-slot t, A(t), by solving the Lyapunov optimization problem, i.e., problem (C LP(t) ) (line 4). However, problem (C LP(t) ) is a mixed-integer non-linear programming (MINLP) which is hard to solve in general. Nevertheless, we can efficiently solve the problem by using well-nown algorithms to solve the MINLP such as an outer approximation algorithm (OA) and a generalized Benders decomposition (GBD) [38]. 5 After the H-AP schedules both resource and tas as the control policy A(t), the queues are updated as in (22), (24), and (25) (line 5). From (22), (24), and (25), we can see that each (virtual) queue length increases if its corresponding average constraint is instantaneously violated in each time-slot, and decreases if it is satisfied. Thus, the queue lengths represent the degree of unsatisfaction of their corresponding constraints. In the objective function in problem (C LP(t) ), each queue length assigns a weight to its corresponding quantity for the corresponding constraint, e.g., r (t) for the average data rate requirement in (1). Thus, the algorithm balances between the objective, i.e., the on-grid energy consumption, and the constraints by using the solution to the problem as the resource and tas scheduling. In the same context, by adjusting the design parameter V, we can adjust how much we emphasize the objective, i.e., 5 Since we focus on hybrid resource and tas scheduling in this paper, we do not address how to apply such algorithms to problem (C L P(t) ). Please refer to [38] for the details. minimizing the on-grid energy consumption. Note that this relation is also adapted to the algorithm in the following section. To perform the centralized algorithm, in each time-slot, each device should report its tas arrivals to the H-AP, i.e., which tass arrive at each device in each time-slot. However, such a feedbac transmission in every time-slot incurs a considerable amount of energy consumption at each device. Moreover, the computational complexity of the centralized scheduling algorithm becomes too high with a large number of devices. Specifically, the worst-case complexity of the algorithms to solve Problem (C LP(t) ) exponentially increases according to the sum of the numbers of the tas types of each device. Hence, to resolve these issues, we will study hybrid resource and tas scheduling in which each IoT device determines its own tas scheduling in a distributed manner and the H-AP determines the resource scheduling in the following section. C. Performance Analysis We derive the performance bound of the centralized resource and tas scheduling algorithm as follows. Theorem 1: Under the proposed centralized resource and tas scheduling algorithm with any control parameter V, the minimum average data rate and maximum tas performing rate requirements are satisfied. Moreover, the average on-grid energy consumption under the proposed algorithm, ĝ, satisfies: ĝ g + B/V, (31) where g is the optimal average on-grid energy consumption of problem (C) and B is the constant in (28). Proof: See Appendix A. This performance bound implies that the algorithm asymptotically achieves the optimal average on-grid energy consumption as V goes to infinity. However, when V becomes large, the average virtual queue lengths increase, which implies that the algorithm may tae longer time to satisfy the QoS requirements. Such a trade-off will be shown in the numerical results section. Remar 1: It is nown that the min drift-plus-penalty algorithm which is used to develop the proposed algorithm is robust to non-i.i.d. and non-ergodic statistic behaviors. Specifically, even in non-i.i.d. and non-ergodic environments, it can achieve the performance arbitrarily close to that of the ideal T-slot looahead policy, where the uncertainties up to T slots are perfectly nown in advance, as long as T is finite [37]. This implies that the proposed algorithm can achieve the performance close to that of the ideal T-slot looahead policy even with the practical tas arrivals and energy harvesting that have non-i.i.d. and non-ergodic statistic behaviors. IV. HYBRID RESOURCE AND TASK SCHEDULING In this section, we propose a hybrid resource and tas scheduling algorithm which consists of two algorithms: a distributed tas scheduling algorithm through which each device determines its own tas scheduling and a resource scheduling algorithm for distributed tas scheduling through which the H-AP determines resource scheduling for devices. In the hybrid algorithm, each device requires a sufficient harvested (c) 218 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

8 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JIOT , IEEE Internet of 8 energy to satisfy its tas requirements. Since the harvested energy solely depends on the resource scheduling in the H-AP, there arises the following ey challenge: how to determine the resource scheduling providing such a sufficient energy to devices. To address this challenge, we investigate a condition enabling the devices to satisfy their tas requirements by the distributed tas scheduling algorithm. Then, in the resource scheduling algorithm, we consider the average harvested energy requirements determined using the condition. Algorithm 2 Distributed Tas Scheduling Algorithm 1: Initialize queues Z m () s, and t = 1 2: while TRUE do 3: Device obtains its queue lengths and tas arrival 4: Device determines its tas scheduling β (t) by solving problem (DT LP(t) ) 5: Device updates its queues Z m (t) s as (22) 6: t t + 1 7: end while A. Distributed Tas Scheduling Algorithm In this subsection, we study the distributed tas scheduling of each device that performs its tass by using only its harvested energy. In a view of a device, its harvested energy in each time-slot depends on the resource scheduling at the H-AP and its channel condition at that time-slot. Thus, to consider the harvested energy in a distributed tas scheduling problem, we should model the harvested energy of each device in each time-slot. Hence, before formulating the problem, we first assume that the harvested energy of device in each timeslot t is given by an i.i.d. random variable ê (t) bounded as ê (t) e max. Note that this assumption is required only to apply the Lyapunov optimization framewor in theory. For each device, a distributed tas scheduling problem that finds the control policy satisfying the tas performing requirements of device in (21) is formulated as (DT ) find {β (t)} t T subject to β m (t)t m T TO, t T, (32) m M B (t) + ê (t) C (t), t T, (33) Tas queues are stable, where the control policy for tas scheduling of device is denoted by β (t) = { β m (t)} m M. In the problem, the tas performing requirements are substituted by the stability condition of the tas queues as in the centralized scheduling problem. The problem can be solved by the Lyapunov optimization framewor, where the Lyapunov optimization problem which is solved in each time-slot t is formulated by Z m (t) βm (t) m M subject to β m (t)t m T TO, m M B (t) + ê (t) C (t). (DT LP(t) ) minimize β (t) Then, we develop a distributed tas scheduling algorithm based on the min drift algorithm in [37]. The distributed tas scheduling algorithm for each device is described in Algorithm 2. Each device first initializes its tas queues (line 1 of Algorithm 2). In each time-slot, each device obtains its queue lengths and tas arrivals (line 3) and determines its tas scheduling by solving problem (DT LP(t) ) (line 4). Note that the problem is a linear programming which is easy to solve in general. After performing the tass, the tas queues are updated as in 22 (line 5). According to the performance of the min drift algorithm in [37], we can show the following theorem. We omit the proof of the theorem since it can be shown in a similar way to the proof of Theorem 1. Theorem 2: Under the distributed tas scheduling algorithm, if problem (DT ) is feasible, it is guaranteed that each device satisfies its tas constraints. We now find a sufficient condition for the feasibility of the problem. Theorem 3: If the following inequality is satisfied: 1 t 1 lim ê (τ) C m t t am, (34) τ= m M then problem (DT ) is feasible. Proof: We will prove this theorem by showing that there exists a control policy satisfying the constraints in problem (DT ) if the inequality in (34) is satisfied. Suppose that each device divides its harvested energy for each tas as C m am m M C m ê m (t) = ê (t), m M, (35) am and manages the harvested energy for tas m by using the battery level for tas m, B m (t), which is used only for tas m. The available energy of device for tas m in time-slot t is given by B m (t) + êm (t), and in time-slot t, device can perform tas m by using the available energy for tas m only. After performing tass, each device stores its surplus energy for each tas, and the dynamics of the battery level of device for tas m is given by B m (t + 1) = Bm (t) + êm (t) Cm βm (t). (36) With such energy management for each tas, we can consider a control policy of device for tas m, ˆβ m (t), with which device determines to perform tas m if B m (t) + êm (t) Cm in time-slot t. In the policy, if the total duration for performing tass exceeds the duration of the tas operation phase, some tass are postponed to the next time-slot. Then, the constraints in (32) and (33) of problem (DT ) are satisfied for all t T. We denote the performing rate of tas m in device with the control policy ˆβ m by ˆb m, and it is given by t 1 ˆb m = lim 1 t t τ= êm (τ) C m ψ m (t) (37), (t) is the number of postponed tas m of device where ψ m in time-slot t. From the assumption in (15), we have lim t ψ m (t)/t =. Then, the performing rate of tas m in device is given by t 1 ˆb m = lim 1 τ= êm (τ) 1 a m t 1 τ= t t C m = lim ê (τ) a m t t, m M C m am (38) (c) 218 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

9 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JIOT , IEEE Internet of 9 where the second equality comes from (35) and the last inequality comes from (34). This shows that there exists a control policy satisfying ˆb m a m, which implies the tas queue stability. The above theorems imply that when the equation in (34) is satisfied for each device, the device can satisfy its tas constraints by using the distributed tas scheduling algorithm in Algorithm 2. Thus, Theorem 3 provides a guideline on providing energy to the devices enabling them to satisfy their tas performing requirements. Since resource scheduling determines the amount of harvested energy at the devices, this guideline can be used for developing a resource scheduling algorithm. B. Resource Scheduling Algorithm for Distributed Tas Scheduling In this subsection, we develop a resource scheduling algorithm for distributed tas scheduling. To enable the devices to satisfy their tas performing requirements in a distributed manner, the average harvested energy of each device should be larger than the sufficient condition for the feasibility of the distributed tas scheduling problem in (34). Thus, in this algorithm, we modify the average harvested energy requirement of each device in (13) as following: ] E Ē [Ē R = max,, (39) m M C m am where Ē is the harvested energy requirement of device in (13). Note that for the constraint in (39), the H-AP should obtain the tas arrival rate of each tas in each device in advance. Such information can be obtained from the historical data, and the statistical model for the tass of the devices is already studied in the literature [39], [4]. Thus, the H-AP can obtain the information from each device when the device initially accesses to the H-AP. Then, a resource scheduling problem for distributed tas scheduling is formulated as 1 t 1 (DR) minimize lim E {G(τ)} t t τ= subject to (1), (2), (4), (5), (7), (1), (39), and the control policy is denoted by A R (t) = {q(t), p(t), ρ(t), G(t)}. The problem can be solved by the Lyapunov optimization framewor as in Section III. Since the framewor is described in the section in details, we concisely describe the process to develop the algorithm for solving problem (DR). We consider the data virtual queues, X(t), in (24) to deal with the constraint in (1). In addition, we consider the energy virtual queues, Y(t), whose dynamics is defined by Y (t + 1) = [Y (t) + Ē R e (t)] +, (4) to deal with the constraint in (39). Let Θ R (t) = [X(t), Y(t)] T be the system state of the combined queue vector. Similar to the centralized algorithm, by using the data and energy virtual queues, we can substitute the constraints in (1) and (39) as the stability constraints of the virtual queues. To adopt a min drift-plus-penalty algorithm, we formulate the Lyapunov optimization problem in time-slot t as (DR LP(t) ) minimize V R G(t) K subject to (1), (2), (4), (5), (7), Y (t)e (t) K r (t)x (t) where V R is a design parameter of the algorithm representing how much we emphasize the objective function of problem (DR). In the algorithm, the control policy A R (t) is determined by finding the optimal solution for problem (DR LP(t) ). However, problem (DR LP(t) ) is a mixed-integer non-linear programming (MINLP) which is hard and requires a high computational complexity to solve in general as mentioned in the previous section. Thus, we propose an algorithm to solve the problem with a low computational complexity. For simple presentation, we denote the set of devices except for the scheduled device l, i.e., K \ {l}, by K l, and q(t) of which q l (t) = 1 and q (t) =, K l by q l (t). In addition, we denote q(t) of which q (t) =, K by q (t). Suppose that in problem (DR LP(t) ), q(t) is given by q l (t). Then, by solving problem (DR LP(t) ) with q l (t) for each of all l K {}, and comparing the objective values, we can obtain the optimal solution of Problem (DR LP(t) ). However, the problem is still hard to solve even with given q l (t) due to the coupled variables, ρ (t) and p(t), in (8), and the piecewise linear model for the harvested energy which is non-differentiable at its edge point. Hence, we reformulate the problem into a convex programming which is easy to solve in general by introducing additional variables. We first introduce variables representing the split power of the scheduled device, p I D (t) and p E H (t), where p I D (t) is a split power for information decoding of the scheduled device from the transmission power p(t) and p E H (t) is a split power for energy harvesting of the scheduled device from the transmission power p(t). Since the sum of the split power cannot exceed the transmission power p(t), the following condition should be satisfied: p I D (t) + p E H (t) p(t). (41) Then, the power split ratio of the scheduled device in time-slot t, ρ (t), is given by p E H (t)/p(t). Moreover, for the piecewise linear model, we introduce additional variables representing the harvested energy of the devices, ē (t) s. By using the introduced variables, the Lyapunov optimization problem with given q l (t) can be formulated as (DR LP(t) l ) minimize V R G(t) Y (t)ē (t) K X l (t)w log 2 ( 1 + p I D (t)h l (t)/n W ) subject to (2), (4), (5), (41), ē (t) e max, K, (42) ē (t) ξ h (t)p(t)t DL, K l, (43) ē l (t) ξ h l (t)p E H (t)t DL. (44) (c) 218 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.