Energy harvestingbased data uploading for Internet of Things
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Abstract
Uploading data from tremendous devices is one of the most challenging tasks for Internet of Things (IoT) due to the heterogeneous data features and the energy constraints of IoT devices. In this paper, we study the data uploading problem from two tiers. In the first tier, we focus on the scheduling of data uploading from different IoT devices to a specific access point (AP) by considering the heterogeneous data features such as the freshness of the data, the data length, the data uploading period, and the energy state of the IoT device. In the second tier, we deal with the selection among different APs for one IoT device. An AP selection algorithm is proposed and we prove that the AP selection process would eventually reach a stable state. Simulation study shows that our proposed algorithm can improve the successful data uploading rate and the time slot utilization.
Keywords
Energy harvesting Data uploading Internet of ThingsAbbreviations
 AP
Access point
 IoT
Internet of Things
 NBIoT
Narrow band Internet of Things
 LORA
Longrange radio
 WiFi
WIreless FIdelity
 WEH
Wireless energy harvesting
 RF
Radio frequency
 DC
Direct current
 PMU
Power management unit
 MAC
Media access control
 ISM
Industrial scientific medical
 TDMA
Time division multiple access
 CSMA/CA
Carrier sense multiple access/collision avoidance
1 Introduction
With the expected 50 billion deployment of Internet of Things (IoT) devices in 2020, massive data is to be uploaded through wired or wireless networks [1, 2]. However, it is hard to satisfy such data uploading demands with existing network structures due to the following reasons: first, massive data is to be uploaded from the huge amount of IoT devices; second, data from different IoT devices are with heterogeneous features, such as data volume and uploading period; third, some kinds of IoT devices acquire energy from ambiance around [3, 4] which brings a high uncertainty on their energy states.
To deal with the data uploading and/or transmission requirements of IoT devices, several schemes and protocols have been proposed. For example, there already existed several power supply monitoring applications used for data acquiring by using 2G, 3G, or 4G cellular networks. Within WiFi coverage, most of IoT devices are connected by accessing into femtocells. The Bluetooth and LORA are also used by IoT devices. Along with the 5G network evolution, narrow bandInternet of Things (NBIoT) and EMTC are proposed for IoT communications. However, there are still some concerns to be solved as follows: First, the coverage of any given scheme cannot be perfect anywhere. Therefore, it is unreliable for IoT devices to rely on one specific access scheme. Second, information fusion [5] has not been considered in existing scheme which brings large information redundancy. Practically, for monitoring the environment in a given area, the acquired information from several IoT devices can be fused locally and upload the derived key information only. Third, no existing scheme considers the energy states of IoT devices. We should take the energy states of the IoT devices into consideration when scheduling their data uploading since the data uploading process cannot be conducted without enough energy supply.

In the first tier, we propose a scheduling algorithm where an emergency function is defined for each data uploading requirement by considering the freshness of the data, the data length, the data uploading period, and the energy state of the IoT device. Then, the priority of the data uploading requirements is decided according to their emergency functions.

In the second tier, we propose an AP selection algorithm where each IoT device accesses to the AP that can provide the highest expected data uploading probability. It is proved that the AP selection process would eventually reach a stable state.

A central slot utilization and also a distributive AP selection algorithm for IoT devices are proposed, to achieve the joint optimization on data uploading and energy harvesting (Table 1).
AP selection process of IoT devices
Algorithm 2 : distributive AP selection process of IoT devices.  

1:  The APs broadcast their data utilization Θ_{1},⋯,Θ_{j},⋯,Θ_{N} to devices through CC channel every \(T_{AP}, T_{AP} \gg T_{i}, \forall i\in \mathcal {M}\) period. 
2:  The devices compute the expected data uploading probability \(\tilde {A}_{i, k}^{s}\) over APs according to equation (16). 
3:  For device i,i∈1,⋯,M who selected AP j for data uploading 
4:  IF \(\max _{k} \tilde {A}_{i, k}^{s}\geq A_{i, j}^{s}+\epsilon \) do 
5:  Device i sends the request to AP k for data uploading. 
6:  end 
7:  end 
The rest of this paper is organized as follows. In Section 2, we summarize the related works on energy harvesting and data uploading. In Section 3, we describe the system model and formulate the data uploading problem. In Section 4, we analyze the data uploading of multiple IoT devices accessing to one identical AP and propose a scheduling algorithm based on the urgency functions of the IoT devices. In Section 5, the AP selection problem is solved by designing a distributive AP selection algorithm. The simulation results are given in Section 6, and we concluded our work in Section 7.
2 Related work
Wireless energy harvesting (WEH) is critical for IoT devices due to their longterm deployment and selfsustainable operation features [6]. IoT devices with WEH capability can harvest energy from environmental sources such as vibration, solar, thermal, and wireless RF [7]. The harvested energy is converted to usable power by the RFtoDC rectifier and the power management unit (PMU). Several design issues have been studied for WEH including circuit hardware design, multiantennabased WEH, energy converting, and so on [3]. Moreover, information disseminating algorithm [8, 9, 10], privacypreserving scheme [11, 12], and dominating set discovering algorithm [13] have been proposed for better utilization of the harvested energy in energy harvesting networks.
For data uploading, the wellinvestigated scheme is the harvestthentransmit protocol [8, 9, 10]. In [8], the joint optimization problem of downlink RF energy harvesting and uplink information transmission is studied based on time division multiple access (TDMA). A commonthroughput metric is proposed to address the doubly nearfar problem. Ju and Zhang [14] extend the protocol proposed in [8] by incorporating user cooperation. Sun et al. [10] propose a lowcomplexity iteration algorithm to achieve a similar throughput as in [8]. However, these work mainly focus on the fairness among multiple users while sacrificing the system throughput to a certain extent. In order to maximize the system throughput, [15, 16] schedule some users for data transmission on certain frequency blocks at given time while arranging other users for energy harvesting. Ng et al. and Sun et al. [17, 18] study the data uploading scheme that can maximize the energy efficiency. By exploring nonlinear fractional programming and Lagrange dual decomposition, an iterative algorithm is proposed to achieve better performance in average energy efficiency and system performance. However, all the abovementioned schemes are centralized that perform well in smallscale network. With the increasing number of users in the network, the computation complexity of these centralized scheme will become intractable.
To accommodate with the data uploading requirements of the large number of users/devices, the multitier network structure has been proposed in [19, 20, 21] without considering the energy harvesting capabilities of the users. Devices are divided into groups, and a device is selected as the gateway/AP within each group. The devices inside the same group may transmit their data to the gateway/AP while the gateway/AP can merge the information of the group and decide the accessing strategy to decrease the data flow in the backbone networks and improve the spectrum efficiency.
Our work is more challenging than the aforementioned ones since we take both the largescale property of the IoT network and the energy harvesting capability of the IoT devices into consideration when designing the data uploading scheme.
3 System model and problem formulation
Here, \(\xi _{k_{1}, k_{2}}^{i}, k_{1}, k_{2} \in [0, K]\) means the probability that the energy state of device i changes from state k_{1} to state k_{2}. For example, \(\xi _{0,0}^{i}\)means the probability that device i does not acquire any energy and remains in empty energy and \(\xi _{0,k}^{i}\)means the probability that device i has acquired k unit energy from state 0. Note that, although these devices may be equipped with identical energy harvesting module, they also have different Ξ_{i} due to different data sensing periods. Moreover, Ξ_{i} only represents the energy harvesting ability of device i, but not the energy consumption of data sensing and transmission. Hence, the element \(\xi _{k_{1}, k_{2}}^{i}, k_{1}>k_{2}\) has zero probability.
Note that the energy state between \(\mathcal {F} \) and \(1\mathcal {F} \) is \({e^{r}_{i}}\) for device i. Hence, we derive the energy transfer probability as Ξ_{i}H_{i} to represent the sequential process of energy harvesting and data uploading.
Here, \(\gamma _{m, n}^{i}\) represents the probability of transferring from state m,m∈[1,L_{i}] to state n,n∈[1,L_{i}]. Note that the dimension of Γ_{i} is different referring to a specified sensing object.
Therefore, this optimization problem needs an iterative process of two parts: devices select the proper AP for data uploading and the scheduling of data for devices which access the same AP. Thus, we first analyze the data uploading scheduling among devices under a given AP, then begin with the AP selection for M devices.
4 Data uploading scheduling within one identical AP
In this section, we consider the case when \(\mathcal {M}_{j}\) devices decide to upload their data through AP j. We skip the trivial case that only one device needs to upload its data for a given slot, then focus on the case when there are multiple devices, more than 2, that need to upload their data at the same time. Hence, AP j needs to figure out which device should be uploading first, and other devices wait for the next available slot and avoid possible collisions.
As for comparison, we first derive the collision probability of \(\mathcal {M}_{j}\) devices without scheduling. Taking an example of two devices, each with a data uploading period as three slots and the data volume is one slot, their data uploading probabilities are 0.3 and 0.8. It is apparent that their collision probability is 0.3*0.8/3. Hence, we begin with deriving the uploading probability for \(\mathcal {M}_{j}\) devices \({P_{i}^{S}}, i\in \mathcal {M}_{j}\) by their energy transition matrix Ξ and data transition matrix Γ. As we mentioned before, the device would upload its data under conditions: enough energy, that is, \(e_{i}\geq {e_{i}^{r}}\), and data changed compared with the previous period, that is \(d_{i}\neq d_{i}^{1}\). Therefore, we derive the data uploading probability of device \(i, i\in \mathcal {M}_{j}\) as the following lemma.
Lemma 1
Proof
Finally, by incorporating these two parts, we derive the conclusion. □
As we derived device i’s data uploading probability \({P_{i}^{S}}\), and the period s_{i} is given, we then derive the collision probability of \(\mathcal {M}_{j}\) devices without scheduling for comparison.
Proposition 1
Proof
Also the collision between four and five devices may be counted repeatedly, and we omit these parts due to complexity and comparatively small than collision between two and three devices. □

The data sequence \(\left \{d^{1}_{i}, d_{i}, {d^{1}_{i}}, \cdots, {d^{k}_{i}}, \cdots \right \}\): here, \(d^{1}_{i}\) represents the data uploading in the last period and d_{i} denotes the data to be uploaded in the current period; the accurate value of \({d^{1}_{i}}, \cdots, {d^{k}_{i}}, \cdots \) is unknown, and we only infer whether they are different from the current data d_{i} using the data transition matrix Γ.

The energy sequence \(e_{i}, {e_{i}^{1}}, \cdots \): e_{i} is the current energy state, and \({e_{i}^{1}}, \cdots \) represents the energy state in the following periods and can be inferred by energy transition matrix Ξ.

The data uploading period T_{i}: we denote the remaining slots in the current period as n_{i}, then the available slots can be n_{i}+T_{i} if there is no data to be uploaded in the next period.

The data length s_{i}: it is apparent that devices with larger data volume would endure lower successful uploading than others without considering data length s_{i}. Thus, we may incorporate data length s_{i} as a factor for data uploading scheduling to balance the fairness among devices.
here θ(n_{i}+k·T_{i}) is a decreasing factor referring to the number of slots, which reflect the inaccuracy of U_{i}(n_{i}+k·T_{i}).
We begin with deriving U_{i}(n_{i}), that is new data maybe uploaded in the next period, then only n_{i} slots can be used for uploading the current data; this can be classified into four cases:
1. The last period sensing data \(d^{1}_{i}\) was sent successfully, and also the data is unchanged in the current period, that is \(d^{1}_{i}=d_{i}\). In this case, device i need not to participate in transmission competitions, thus denote U_{i}=0.
2. The sensing data satisfies \(d_{i}\neq d_{i}^{1}\); thus, IoT device i needs to transmit. The urgency function of device i depends on the remaining slots for transmitting its sensing data. We analyze the situation in the following cases:
(a) Device i also needs to transmit new data \({d^{1}_{i}}\) in the next period; thus, we have \({e_{i}^{1}}\geq e^{req}_{i}\) and \({d^{1}_{i}}\neq d_{i}\). Hence, we have \(U_{i}(n_{i})=P\left ({e_{i}^{1}}\geq e^{req}_{i}, {d^{1}_{i}}\neq d_{i}\right)\).
(b) Device i need not to transmit in the next period but to transmit in the period following the next. Hence, we have \(U_{i}(n_{i}+T_{i})=P\left ({e_{i}^{1}} < e^{req}_{i} \text { or} {d^{1}_{i}}= d_{i}\right)\cdot P\left ({e_{i}^{2}} \geq e^{req}_{i}, {d^{2}_{i}}\neq d_{i}\right)\).
Similar to the derivation of U_{i}(n_{i}),U_{i}(n_{i}+T_{i}) above, we can derive U_{i}(n_{i}+k·T_{i}),∀k=2,⋯.
3. The last period sensing data \(d^{1}_{i}\) is not transmitted successfully, and the data in the current period is unchanged or the energy is below the threshold; this case is the same as the case above.
4. The last period sensing data \(d^{1}_{i}\) is not transmitted successfully, and also \(d^{1}_{i}\neq d_{i}\); thus, data \(d^{1}_{i}\) is discarded, and the data d_{i} in the current period needs to be sent. Hence, this case is also the same as the second case above.
Similarly, we derive the expression of U_{i}(n_{i}+T_{i}) as in Eq. (14). Hence, we derive the urgency function of device i as in Eq. (15).
5 AP selection among IoT devices

The slot utilization sequence Θ_{1},⋯,Θ_{j},⋯,Θ_{N} of AP j,j∈[1,N]. As for multiple devices that joined AP j for data uploading, AP j assigned the slots to a device with the highest utility of urgency function. Hence, AP j has the accurate statics on slot utilization irrelevant to the data uploading competitions. Note that the slot utilization E_{j} is easy to derive and broadcast through control channels by APs

The data uploading probability \({P_{i}^{S}}\) of device i,i∈[1,M]. This probability can be derived by device i using energy harvesting matrix and also data transition matrix as in Lemma 1

The actual data uploading probability \({A_{i}^{s}}\) of device i,i∈[1,M]. This probability is derived by counting on the actual uploading data.
These parameters are the overall information needed for AP selection, the first one is derived by AP broadcasting, and the latter two are derived by devices. For devices and APs to derive these parameters accurately, the AP selection should be operated periodically with a relative larger slots.
Basically, we need to find a metric for IoT devices, facilitating their selection among APs. In order to reflect the actual slot usage for devices, the metric must be accurate and brief. Fortunately, the actual data uploading probability \({A_{i}^{s}}, i \in [1, M]\) can be used as a metric to measure the data uploading performance of APs. Suppose that device i selects AP j randomly at the beginning, then perform its data uploading through AP j. After a certain time T_{s}, each AP broadcasts its slot utilization probability as Θ_{1},⋯,Θ_{N}. At the same time, data uploading probability \({P_{i}^{S}}\) and actual data uploading probability \(A_{i, j}^{s}\) of device i,i∈M are derived by device i. Before device i switches to another APs, it must derive the expected actual data uploading probability \(\tilde {A}_{i, k}^{s}, k\in [1, N], k\neq j\).
Lemma 2
Proof

Case 1: device i has data to be uploaded in the next period; thus, the remaining slots for data uploading is T_{i}−s_{i}. Hence, we can derive the successful uploading probability as the product of case 1 and other devices do not upload at these slots, that is, \({P_{i}^{s}}\cdot (1\Theta _{k})\frac {T_{i}s_{i}}{T_{i}}\).

Case 2: device i does not have data to be uploaded in the next period but in next two periods; this case has the probability of \({P_{i}^{s}}\left (1{P_{i}^{s}}\right)\). Also, the remaining slots for data uploading is 2T_{i}−s_{i}. Hence, the overall probability is \({P_{i}^{s}}\left (1{P_{i}^{s}}\right) \cdot \left (1\Theta _{k}\right)\frac {2T_{i}s_{i}}{2T_{i}}\).

Case k: device i has only 1 data to be uploaded in k period, thus has the probability of \({P_{i}^{s}}\left (1{P_{i}^{s}}\right)^{k1}\). Hence, the overall probability is \({P_{i}^{s}}\left (1{P_{i}^{s}}\right)^{k1} \cdot \left (1\Theta _{k}\right)\frac {kT_{i}s_{i}}{kT_{i}}\).
□
Hence, we finish the proof.
Therefore, device i will calculate the data utilization vector \(\tilde {A}_{i,1}^{s}, \cdots, \tilde {A}_{i,N}^{s}\) when APs broadcast their slot utilization Θ_{1},⋯,Θ_{N}, except for its current selection, that is, AP j. It is apparent that the best AP to be selected is \(\max _{k} \tilde {A}_{i,k}^{s}\). We summarize the AP selection process as in Algorithm 2 (given in Table 1). The variable ε is a minimal positive number, which avoids the pingpong effect between AP selections.
Then, the next question arises, that is, whether this AP selection process would eventually reach a stable state, no any devices change their selected AP and switch to another one. We begin with the slot utilization Θ_{j} of AP j. Considering that devices set \(\mathcal {M}_{j}=\{1, \cdots, M_{j}\}\) selected AP j currently and have the actual data uploading probability as \(A_{1,j}^{s}, \cdots, A_{M_{j},j}^{s}\), thus we can derive that the slot utilization Θ_{j} is a summation of data uploading probability of device set \(\mathcal {M}_{j}\), that is, \(\Theta _{j}=\sum \nolimits _{i=1}^{M_{j}} \frac {s_{i}}{T_{i}}{P_{i}^{s}} \). Hence, slot utilization Θ_{j} is a function of uploading period T_{i}, data volume s_{i}, and uploading probability \({P_{i}^{S}}\), that is, \(\Theta _{j}=g(T_{i},s_{i},{P_{i}^{s}})\). As we denoted in data uploading scheduling inside AP above, each device acquires the uploading opportunity by sending its urgency function, no collision is derived, but some data can be delayed and eventually discarded when new data is acquired, thus bringing the decreasing in actual data uploading probability. Hence, we conclude that the function g(·) has \(\phantom {\dot {i}\!}g^{\prime }(\cdot) \geq 0, g^{\prime \prime }(\cdot) \leq 0\). Based on this analysis, we derive the following proposition:
Proposition 2
The AP selection process leads to a stable state in finite rounds.
Proof
Consider that the current AP selected by device i is AP j, with actual data uploading probability as A_{i,j}. As the slot utilization vector broadcasting by AP is Θ_{1},⋯,Θ_{N}, device i selects AP k with \(\max _{k} \tilde {A}_{i,k}^{s}\) for data uploading. It is apparent that device i will increase its successful data uploading probability, that is, \(\tilde {A}_{i,k}^{s} >A_{i,j}\). We further denote the slot utilization of AP j without device i is \(\bar {\Theta }_{j}\) and the slot utilization of AP k by joining device i as \(\bar {\Theta }_{k}\). Thus, we have \(A_{i,j}=\left (1\bar {\Theta }_{j}\right)\left (1+\frac {s_{i} \ln (1{P_{i}^{s}})}{T_{i}}\right)\). By incorporating \(\tilde {A}_{i,k}^{s} >A_{i,j}\), we have \(\bar {\Theta }_{j}> \Theta _{k}\).
□
As we derived that \(\bar {\Theta }_{j}> \Theta _{k}\) and \(\phantom {\dot {i}\!}g^{\prime }(\cdot) \geq 0, g^{\prime \prime }(\cdot) \leq 0\), we conclude that \(\bar {\Theta }_{j}+\bar {\Theta }_{k}\Theta _{j}\Theta _{k}>0\). This result indicates that device i changes its AP selection for increasing its own successful data uploading probability and also increases the overall slot utilization of both APs. However, the slot utilization of all APs, that is, \(\sum \nolimits _{j} \Theta _{j}\), is finite, thus may achieve its maximization by finite rounds.
6 Results and discussions
Data uploading process of the proposed mechanism
Algorithm 1 : data uploading process of proposed mechanism.  

1:  The IoT devices broadcast their data transmission requests to AP through CC channel. 
2:  The AP decides whether devices’ requests can be approved according to equation (14). 
3:  while the current slot is idle, set as T=0do 
4:  The AP informs IoT devices for bids submission. 
5:  The IoT devices compute their bids by urgency function G_{i} and f(s_{i},T_{i}) according to equation (7), then submit bid b_{i} to AP for devices i∈M. 
6:  The AP selects the highest bid among devices, and the winning device begins its data transmission. 
7:  After the data uploading finished, set \(T=T+\bar {s_{i}}\), where \(\bar {s_{i}}\) is the data length of winning device. 
8:  end 
6.1 Slot utilization inside AP
Parameters of nine IoT devices
Classes  Period (slots)  Data (slots)  \({P_{i}^{S}}\) 

Class A  10  4  0.35 
Class B  6  2  0.42 
Class C  3  1  0.23 
6.2 AP selection among IoT devices
In this subsection, we evaluate the performance on the AP selection algorithm. Specifically, we need to figure out whether the proposed algorithm leads to a stable state and if the overall successful data uploading probability increases along with the iterative process. In this case, we suppose that there are 20 IoT devices and 2 AP arranged in a given area. From the scratch, 20 IoT devices select AP 1 for data uploading and no device selects AP 2, then devices decide whether to switch to another AP in each round distributively after APs broadcast their current slot utilizations.
7 Conclusions
In this work, we analyze the scenario that how to schedule the data uploading of multiple energy harvesting enabled IoT devices among multiple APs. Firstly, a multilayer data uploading process is proposed, which devices access the proper AP for data uploading and APs relay devices’ data through different network access technologies. Secondly, a lowcomplexity slot allocation algorithm is proposed for devices which select the identical AP; the urgency function of devices ensures that the uploading period, data length, and remaining slots are considered and achieve the fairness among devices. Thirdly, a distributive AP selection algorithm is proposed and thus can achieve the stable selection among devices. Finally, the simulation results indicate that our proposed algorithms well balance the data uploading requirements and also afford multiple access choices in heterogeneous networks with low cost and complexity.
8 Methods/experimental
In this paper, we designed a threelayer network framework and scheduled the data uploading from two tiers. In the first tier, we proposed a scheduling algorithm where an emergency function is defined for each data uploading requirement by considering the freshness of the data, the data length, the data uploading period, and the energy state of the IoT device. Then, the priority of the data uploading requirements is decided according to their emergency functions. In the second tier, we proposed an AP selection algorithm where each IoT device accesses to the AP that can provide the highest expected data uploading probability. Experimental results were performed using MATLAB R2009b on Intel? Core i5 system. The requirement of uploading data and the harvested energy were all constructed by an appropriate MATLAB code.
Notes
Funding
The authors would like to thank the support from the Natural Science Foundation of China (61702056, 61602062), Educational Commission of JiangSu Province (17KJB520001), the Natural Science Foundation of JiangSu Province (BK20160410), the Provincial Key Laboratory for Computer Information Processing Technology, Soochow University (KJS1521, KJS1522), CERNET innovation project (NGII20160322).
Availability of data and materials
Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.
Authors’ contributions
GS and XX conceived the scenario to be considered and carried out the theoretical analysis. GS carried out the simulations. All authors contributed to writing this paper. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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