I Introduction
The industrial application of IoT, or IIoT, as a new industrial concept, combines intelligent machines, advanced analysis and machine-human collaboration together, making industrial operation intensely efficient and intelligent[1-2]. With the development of wireless sensor-actuator networks (WSAN), and wireless sensor networks (WSN), more and more IoT devices (IoTDs) are deployed in oil production platforms, underground mines[3], container ports and hydroelectric stations to measure important operational and environmental parameters. IIoT is anticipated to have the capability to transform many industries, including manufacturing, agriculture, engineering industry and energy industry. However, many IIoTDs have limited computing capability and batteries due to their limited size,and is difficult to replace due to the work environment. In order to maintain the quality of service (QoS), it is necessary to assist these kinds of IIoTDs in processing data.
As for the above problems, PEC and Wireless Power Transfer (WPT) are recognized as the feasible solutions. Faced with the data computation, PEC is a emerging computing paradigm with great potential to enhance the performance of devices by task offloading[4], where data can be processed on the edge of the network[5], with the assistance of intelligent devices. Faced with the energy supplement, WPT is a technology to realize the vision of IIoT[6], which is designed to provide a stable and controllable wireless power[7]. With the Energy Harvesting (EH), the IIoTDs can power themselves by harvesting the wireless signal. Howerver, due to the limited hardware capacity and propagation loss, the radio frequency (RF) signals over long distances lead to poor performance of the WPT and EH systems.
Thanks to their high mobility, flexible deployment and low cost[8-9], UAVs have been widely used in various scenarios (e.g. search and rescue, cargo delivery, surveillance and monitoring, etc.) as moving relays and flying BSs to enlarge network coverage and enhance the communication quality. Distinguished from the fixed location BSs on the ground, UAVs can not only satisfy different quality-of-service (QoS) requirements, but also more likely to establish the line-of-sight (LoS) links with IIoTDs by adjusting their locations flexibly, which can achieve better communication channels and more reliable transmission quality.
In this paper, we present a global joint resource allocation scheme for UAV service of PEC in IIoTDs system, as illustrated in Fig. 1, in which a moving UAV is deployed as a PEC server and a mobile power source. Specifically, we consider the environments where the terrestrial wireless connection between IIoTDs and ground BSs or APs can’t be be established, since there is no such wireless infrastructures exist or have been badly damaged. Besides, the IIoTDs can not perform the sensing tasks while data calculation due to the limitation of hardware. Therefore, a UAV deployed to provide task offloading opportunities and energy supply to IIoTDs in such environments, and the collected data from IIoTDs needs to be execute rapidly. We formulate the system process as a optimization problem aiming at minimizing the sum service latency of all IIoTDs consisting of task computation latency and offloading latency, by joint optimizing the task offloading decisions, charging resources allocation, connection management, and UAV computation resources allocation.
However, the above formulated optimization problem is indeed challenging to tackle. There are two main reasons.On the one hand, there exists correlation among different optimization variables, such as the charging power, the UAV CPU frequency allocation and the variables related to the connection management, making the objective function and constraints non-convex. On the other hand, the variables related to the offloading and connecting decisions are binary, making the problem a mixed integer non-convex optimization problem.
The main contributions of our work are summarized as follows: 1) We propose the collaborative UAV-IIoTDs resource allocation scheme for PEC in IIoTs systems where the UAV is deployed to provide PEC and power-charging services for IIoTDs; 2) Considering the limitation and the QoS requirement of IIoTDs, we formulate the global joint resources allocation as an optimization problem under the proposed system, with the goal of minimizing the sum latency of all IIoTDs; 3) We present an alternating optimization algorithm based on the block-coordinate descent (BCD) method to decouple the optimization variables and develop an heuristic adjusting-approaching algorithm to solve the subproblem relating to the task offloading decisions optimization; 4) To illustrate the performance of the proposed scheme, massive evaluations were conducted. Performance analysis demonstrate that our algorithm can enhance the performance of PEC IIoT systems significantly, compared to several conventional schemes.
The rest of this paper is organized as follows. In Section II, we present the related work. We introduce our system model in Section III. The optimization problem is formulated and solved by the proposed method in Section IV. In Section V, we present our performance analysis. Finally, we conclude the paper and mention the future work in Section VI.
Ii Related Work
Ii-a Resource Allocation in EC
Extensive efforts have been dedicated on the resource allocation in edge computing (EC) that aims at optimizing operating cost[10-11], system latency[12], energy consumption[13-14] and network throughput[15]. Wang et al. in [10] studied the mobility-agnostic online resource allocation by solving the optimization problem of allocation costs, reconfiguration, service quality and migration under unpredictable resource prices and user movement. Wang et al. in [11] proposed a dynamic optimization scheme for the IoT fog computing system with multiple mobilr devices, aiming at minimizing the system cost by joint optimizaing the radio and computational resources and offloading decisions. Zhao et al. in [12] formulated a cloud-MEC collaborative computation offloading problem through jointly optimizing computation offloading decision and computation resource allocation. In [13], Zhang et al. studied the joint optimization of bits allocation, time slot scheduling, power allocation and UAV trajectory design, aiming at minimizing the total energy consumption. In [14], Yang et al. investigated joint resource allocation and trajectory design in a MEC network where multiple UAVs are deployed to compute users’ offloading tasks,aiming at minimizing the sum energy consumption. Ning et al. in [15] put forward a hybrid computation offloading framework for real-time traffic management aiming at maximizing the sum offloading rate by joint optimizing task distribution, sub-channel assignment and power allocation.
All these studies assume users or devices have sufficient batteries to complete the task transmission and execution. However, it is utmost important to take the limited batteries into consider for enhancing the system endurance. In the view of the above consideration, we propose to deploy a UAV in the PEC IIoTs system to assist the IIoTDs task offloading and wireless charging processes.
Ii-B UAV-assisted WPT
There are a number of studies on UAV-assisted WPT that aims at trajectory design[16-17], trajectory design based on energy optimization[18-19], communication quality optimization[20] and charging resource allocation[21-22]. Yang et al.
in [16] proposed a genetic algorithm based successive hover-and-fly scheme to design the optimal UAV trajectory with the objective to maximize the minimal received energy among all users under UAV speed constraints. Ku
et al.[17] applied Q-learning among reinforcement learning techniques to design UAV trajectory in a WPT system where UAV broadcasts power to energy receivers (ERs) on the ground to solve the fairness problem. Beak
et al. in [18] deployed UAV as a flying data collector and wireless power source in wireless charging sensor networks (WCSNs). The problem of joint optimization of the UAV hovering location and duration under data collection along with UAV energy consumption constraints,aims at maximizing the minimum energy consumption of sensors after data transmission and energy harvesting. Xie et al. in [20] formulated the system throughput maximization problem under two paradigms of delay-tolerant case and delay-sensitive case by joint optimizing the time slot scheduling, power allocation along with UAV trajectory constrained by a so-called neutrality constraints. Yin et al. in [21] studied the sum of download rate maximization problem in a UAV-assisted cellular network where UAVs are powered by a ground wireless charging station,by joint optimization for user association,resource allocation and station placement. Chen et al. in [22] presented an investigation on the optimal the overall power transmission efficiency considering the UAV’s trajectory along with the power of the charging, where the UAV is deployed to collect data reliably form a group of sensors.To the best of our knowledge, the resource allocation for UAV service of PEC in IIoTs systems has not been well investigated. Therefore, a new model is required in such systems, which is discussed in the following section.
Parameter | Description |
---|---|
N | Number of IIoTDs |
M | Number of UAV hovering positions |
Set of IIoTDs | |
Set of IIoTDs in local execution mode | |
Set of IIoTDs in task offloading mode | |
Set of UAV hovering positions | |
Horizontal coordinate of IIoTD i | |
Horizontal coordinate of j-th hovering position | |
H | Altitude of the UAV |
Computation task of IIoTD i | |
Data size of task | |
Number of CPU cycles of task | |
Total service latency of task | |
Distance between j-th hovering position and IIoTD i | |
Connection status indicator | |
Average pathloss of the IIoTD i at j-th position | |
Channel power gain of the IIoTD i at j-th position | |
Offloading transmission rate of the IIoTD i at j-th position | |
Charging power allocated to the IIoTD i at j-th position | |
On-chip computing capability of the IIoTD i | |
Computing resources allocated to the IIoTD i at j-th position | |
Total harvesting energy of IIoTD i | |
Total local computation energy consumption of IIoTD i | |
Total task offloading energy consumption of IIoTD i | |
Total energy harvesting latency of IIoTD i | |
Task local computation latency of IIoTD i | |
Total task offloading transmission latency of IIoTD i | |
Total task offloading computation latency of IIoTD i | |
Task offloading decision indicator of IIoTD i | |
The energy conservation efficiency | |
The effective switched capacitance constant of IIoTD i |
Iii System Model
Iii-a Set-Up
As shown in the Fig.1, we consider a global joint resource allocation scheme for UAV service of PEC in IIoTs system, where a UAV equipped with multiple orthogonal isotropic antennas, is deployed to provide task offloading opportunities and energy supplement to N IIoTDs equipped with one single antenna, each of which has an computation-intensive and latency-critical task. The task completion process includes: i) energy transmission and harvesting; ii) task local execution or offloading execution (data migration and assistance computation); iii) result uploading for local execution or beacon post-back for task offloading. We ignore the latency of step iii) due to the small amount of data. We assumed that each IIoTD has an individual computation-intensive and latency-critical task. It is also assumed that the UAV can perform energy transmitting and offloading computing while IIoTDs can perform energy harvesting and local computing or task offloading. For data transmission, in order to avoid interference among IIoTDs, we consider the orthogonal frequency division multiplexing (OFDM) scheme. The main sysbols mentioned in the paper are summarized in Table I.
Without loss of generality, a three-dimensional (3D) Euclidean coordinate is adopted, whose coordinates are measured in meters, and all the devices in the wireless IIoT system are distributed in the first quadrant. We assume that there are a total of N IIoTDs randomly distributed in the area and locations of all the IIoTDs are fixed on the ground with zero altitude, with = (,) representing the location of IIoTD i, where i and = {1,2,…,N}. Denote as the amount of transmission data and as the required processing CPU cycles for task i. Thus,we can express the task of IIoTD i as:
(1) |
In addition, we assume that the UAV flies above the area at a fixed altitude H and hovers at M given locations, with = (,) representing the location of UAVs j-th hovering position, where j and = {1,2,…,M}. Therefore, at the hovering position j, the distance between UAV and IIoTD i is shown as:
(2) |
Assume each IIoTD can select one and only one UAV hovering position to harvest energy and offload its data, while UAV can serve more than one IIoTD at each hovering position. Therefore, we define binary variables
to indicate the connection status between UAV and IIoTDs, where = 1 means the IIoTD i chooses the j-th UAV hovering position to harvest energy and offload data; otherwise, = 0. It yields the following constraints:(3) |
(4) |
Iii-B Channel Model
In the UAV-enabled wireless powered mobile edge network, we consider the effect of the environment on the occurrence of LoS and an air-to-ground propagation model in suburban environment proposed in [23-25]. In hovering position j, the LoS and NLoS pathloss between UAV and IIoTD i is given by:
(5) |
(6) |
where denotes the free space pathloss given by , and f is the system carrier frequency. and represent the additional attenuation factors in cases of the LoS and NLoS connections respectively.
The probability of LoS connection is given by:
(7) |
where a and b are constants depending on the environment and denoted the elevation angle given by .
The average pathloss of the IIoTD i at j-th hovering position is given by:
(8) |
We define the B as the channel bandwidth and as the transmitting power of IIoTD i, along with the as the noise power. Then, the transmission rate of IIoTD i at j-th hovering position is given by[25]:
(9) |
Iii-C Wireless Energy Harvesting Model
In the proposed system,the energy consumption of the IIoTDs for local computing and task offloading all comes from the harvested energy. Similar to the [26-27], we applied the linear energy harvesting model in this paper. Thus,the energy harvested by IIoTD i at j-th the hovering position is given as:
(10) |
where is the channel power gain of the IIoTD i at j-th the hovering position, represents the received power at the reference distance = 1 m. And (0,1] denotes the energy conservation efficiency, denotes the charging power allocated to the IIoTD i at j-th hovering position and denotes the corresponding energy harvesting time.
Iii-D Working Pattern Model
As mentioned above, each IIoTD can choose computing its task locally, which is the local execution mode, or offloading task to the UAV, which is the task offloading mode. Thus, if IIoTD i choose the local execution mode, it will allocate the frequency for its own task data processing. On the contrary, if IIoTD i choose the task offloading mode and offload its task at the j-th hovering position, the UAV will allocate the frequency for the task data processing.
In order to distinguishing the two working pattern of IIoTDs preferably, we denote and as the set of IIoTDs choosing computing locally and offloading task, respectively. Therefore, and , where denotes the null set.
Iii-D1 Local Execution Mode
For the local execution mode, the computational task of IIoTDs are performed locally. The local execution time is given as:
(11) |
The corresponding energy consumption is given as:
(12) |
where denotes the effective switched capacitance of IIoTD i and denotes the positive constant.
At j-th hovering position, the local computing energy consumption of IIoTD i should not be more than the total harvesting energy. Thus, one can have:
(13) |
Iii-D2 Task Offloading Mode
For the task offloading mode, IIoTDs will offload their task to the UAV. Based on the channel model mentioned above, the transmission delay and energy consumption for IIoTD is task offloading at the j-th hovering position are given as:
(14) |
and
(15) |
The task computation time on the UAV is given as:
(16) |
At j-th hovering position, the task offloading energy consumption of IIoTD i should not be more than the total harvesting energy. Thus, one can have:
(17) |
Iv Our Proposed GJRA Scheme
In order to specify the service delay of IIoTDs, we make following assumptions: (i)IIoTDs cannot execute or offload its task until completing the energy harvesting; (ii)the UAV cannot computing a task until receiving its entire data. Therefore, the service latency of IIoTD i is given as:
(18) |
Assume that the locations of IIoTDs and the UAV’s hovering positions are fixed and known[28]. Let , , . Our problem becomes to the joint optimization of the task offloading decisions(i.e., and ), the IIoTD connection management(i.e., ), the charging resources allocation(i.e., ) and the UAV computation resources allocation(i.e., ), with the goal of minimizing the overall service delay of all IIoTDs. Then, it can be formulated as the following optimization problem:
(19a) | ||||
(19b) | ||||
(19c) | ||||
(19d) | ||||
(19e) | ||||
(19f) | ||||
(19g) | ||||
(19h) | ||||
(19i) | ||||
(19j) |
where denotes the maximum computing frequency of the UAV while denotes the maximum computing frequency of the IIoTD i, and denotes the maximum charing power of the UAV. and represent the energy consumption should not be more than the harvesting energy for each IIoTD choosing either local execution mode or task offloading mode, respectively. means the computation resources allocated to all IIoTDs in task offloading mode cannot exceed the total computation capability of the UAV. guarantees that the offloading computation resources allocated to each IIoTD is non-negative. Similarly, means the charing power allocated to all IIoTDs cannot exceed the total wireless power capability of the UAV. guarantees that the charing power allocated to each IIoTD is nonnegative. and represent that all of the IIoTDs can select one and only one UAV hovering position to connect to the UAV. is the task offloading decision constraint. P1 is a MINLP problem, which is NP-hard and difficult to be optimally solved in general.
To solve the formulated problem P1, we obtain the approximate optimal solution for each variable in problem P1 by the BCD method. Based on it, we proposed an overall optimization algorithm to get an approximation solution of the formulated problem P1. The details of the proposed algorithm are presented as follows.
Iv-a Task Offloading Decisions Optimization
In order to efficiently solve P1, a binary variable denoted by is introduced, where and . = 0 means that the IIoTD i performs local execution mode while = 1 means that the IIoTD i performs task offloading mode. Moreover, the task offloading decision indicator variable is relaxed as a sharing factor . Further, we can combine the constraints to . Thus, P1 can be rewritten as follow:
(20a) | ||||
(20b) | ||||
(20c) | ||||
Given , and , the subproblem of task offloading decisions optimization can be given as:
(21a) | ||||
(21b) | ||||
(21c) |
To achieve the goal of minimizing the overall service latency, the IIoTD will make its offloading decision based on the tradeoff between the achievable minimum task completion time and the necessary resources consumption. Hence, for any given , and , the IIoTD offloading decision scheme depends on the achievable minimum sum service latency.
In this case, while the IIoTD i performs local execution mode, the minimum service latency of task i can be obtained by constraint as . And similarly, while the IIoTD i performs task offloading mode, the minimum service latency of task i can be expressed as by constraint .
Therefore, the partial optimal IIoTD task offloading decision scheme constrained by can be obtained by
(22) |
(23) |
(24) |
where is denoted as the service latency of task i in local execution mode and is denoted as the service latency of task i in task offloading mode.
Considering the existence of constraint , we developed an heuristic method to find out the optimal solution of problem P2.1 by continuously adjusted based on the partial optimal scheme obtained above. The proposed heuristic adjusting-approaching method is specified as Algorithm 1.
Iv-B UAV Computing Resource Allocation Optimization
Given , , . The sub-problem with regard to is:
(23) | ||||
Problem P2.2 is a convex problem. Thus, P2.2 can be solved by the convex optimization technique such as the interior-point method[29]. To gain more insights on the structure of the optimal solution, we leverage the Lagrange method to obtain a well-structured solution. The Lagrange multipliers associated with the constraints in is given as . The partial Lagrangian function of P2.2 is
(26) |
The dual function of P2.2 is given as
(27) |
Then the dual problem of P2.2 is given as
(28) |
Since the convex problem P2.2 satisfies the Slater’s condition, strong duality holds between problem P2.2 and problem (28). Therefore, one can solve problem P2.2 by equivalently solving its dual problem (28).
Iv-B1 Derivation of the Dual Function
Given any , we can obtain by solving problem (27). Notice that problem (27) can be decomposed into the following subproblems:
(29) |
According to to monotonicity of objective function, the optimal solution of problem (27) is given as
(30) |
Iv-B2 Obtaining to Maximize
Solving dual problem (28) means obtaining in the defined domain to maximize . Putting eq.29 into problem (28), thus we can obtain:
(31a) | ||||
(31b) |
Notice that problem (31) can be decomposed into the following M subproblems, one can have:
(32) |
According to the monotonicity of the objective function, one can have:
(33) |
Therefore, the optimal solution to can be obtained by
(34) |
Iv-C UAV Charging Power Optimization
With given , , , the sub-problem on optimizing is:
(35a) | ||||
(35b) | ||||
Lemma 1.
For problem P2.3, the equal sign always holds for (35b).
Proof.
As mentioned above, the service latency for any IIoTD i consists of two parts: 1) energy harvesting time ; and 2) task computation time, the local computation time or the sum of transmission latency and offloading computation latency .
To achieve the goal of minimizing the overall service latency of all IIoTDs in the system is to minimize the service latency of every IIoTD, which is to minimize the both two parts time consumption mentioned above for every IIoTD. In other words, the optimal energy harvesting time for IIoTD i, , is its lower bound, which is characterized by constraint (35b). This thus proves the lemma.
∎
Thus, we can obtain:
(36a) | ||||
(36b) | ||||
Since the optimal task offloading decisions and have been obtained above, as well as is pre-defined, we can rewrite the P2.4 as :
(37) | ||||
(50) |
It can easily proved that problem P2.5 is convex. Therefore, as solving problem P2.2, we can leverage the Lagrange method to solve this problem similarly. The Lagrange multipliers associated with the constraints in is given as and the partial Lagrangian function of P2.5 is
(38) |
Then the dual function of P2.5 is given as
(39) |
Thus, the dual problem of P2.5 is
(40) |
Strong duality holds between problem P2.5 and problem (40) since problem P2.5 is convex and it also satisfies the Slater’s condition. Therefore, one can solve problem P2.5 by equivalently solving its dual problem (40).
Iv-C1 Derivation of the Dual Function
Given any , we can obtain by solving problem (39). Notice that problem (39) can be decomposed into the following subproblems.
(41) |
Let .
(42) |
where .
Let , one can have
(43) |
Iv-C2 Obtaining to Maximize
Solving dual problem (40) means obtaining in the defined domain to maximize . Putting (43) into problem (40), thus we can obtain:
(44a) | ||||
(44b) |
Notice that problem (43) can be decomposed into the following subproblems.
(45) |
According to the monotonicity of objective function, one can have
(46) |
Therefore, the optimal solution to can be obtained by
(47) |
Iv-D IIoTD Connection Management Optimization
With obtained , and task offloading decision, the sub-problem on optimizing IIoTD connection management can be formulated as:
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