Online Computation Offloading and Trajectory Scheduling for UAV-Enabled Wireless Powered Mobile Edge Computing

Han Hu,Xiang Zhou,Qun Wang,Rose Qingyang Hu,*

1 The Jiangsu Key Laboratory of Wireless Communications,Nanjing University of Posts and Telecommunications,Nanjing 210003,China

2 The Engineering Research Center of Health Service System Based on Ubiquitous Wireless Networks,Ministry of Education,Nanjing University of Posts and Telecommunications,Nanjing 210003,China

3 The Department of Electrical and Computer Engineering,Utah State University,Logan,UT,USA.

Abstract:The unmanned aerial vehicle(UAV)-enabled mobile edge computing(MEC)architecture is expected to be a powerful technique to facilitate 5G and beyond ubiquitous wireless connectivity and diverse vertical applications and services,anytime and anywhere.Wireless power transfer(WPT)is another promising technology to prolong the operation time of low-power wireless devices in the era of Internet of Things(IoT).However,the integration of WPT and UAV-enabled MEC systems is far from being well studied,especially in dynamic environments.In order to tackle this issue,this paper aims to investigate the stochastic computation offoading and trajectory scheduling for the UAV-enabled wireless powered MEC system.A UAV offers both RF wireless power transmission and computation services for IoT devices.Considering the stochastic task arrivals and random channel conditions,a long-term average energyeffciency(EE)minimization problem is formulated.Due to non-convexity and the time domain coupling of the variables in the formulated problem,a lowcomplexity online computation offoading and trajectory scheduling algorithm(OCOTSA)is proposed by exploiting Lyapunov optimization.Simulation results verify that there exists a balance between EE and the service delay,and demonstrate that the system EE performance obtained by the proposed scheme outperforms other benchmark schemes.

Keywords:energy effciency;mobile edge computing;UAV-enabled;wireless power transfer;trajectory scheduling

I.INTRODUCTION

The fast advancement of Internet of Things(IoT)and 5G wireless technologies greatly facilitate the proliferation of new IoT applications,such as Industrial Internet of Things(IIoT),augmented reality,surveillance,and e-Healthcare[1].They also increase the tension between the computation-intensive requirements and the limited computation capacities of the mobile IoT devices(MIDs)[2].Mobile edge computing(MEC)that aims to support computation-intensive and delay-sensitive services is envisioned as a promising paradigm to tackle this issue.With MEC,the IoT devices can offoad partial or their entire computation tasks to MEC servers that locate much closer to the local devices.In recent years,many research efforts have been dedicated to developing effective offoading schemes in the MEC-enabled ground-based IoT systems[3–6].However,with the fast-escalating demands on pervasive communication and computing,traditional terrestrial MEC systems may not meet the needs in various ways.With the advantages of UAVs,such as,autonomy,fexibility,and mobility,MEC servers or cloudlets can be mounted on UAVs to offer effcient and reliable computing services in some geographically constrained areas[7].Such a UAVenabled MEC architecture[8–10]is expected to be a promising mechanism to facilitate B5G/6G ubiquitous wireless connectivity and computing services,anytime and anywhere.

In the meanwhile,many ground IoT devices are normally constrained by the limited computation capacity and battery lifetime.Lately,energy harvesting becomes an appealing technique that can effectively prolong the effective working duration of small IoT devices[11].Compared to the traditional energy harvesting technologies,such as solar or wind charging,wireless power transfer(WPT)is more attractive since it can offer controllable and stable power supply by using radio frequency(RF)signals[12,13].It has been proved that the integration of MEC and WPT can signifcantly enhance the computation performance[14–18].However,the harvested power level can be significantly degraded by the severe propagation loss.Recently,the UAV-enabled WPT architecture has been proposed to provide wireless energy towards devices on the ground[19–22].Due to the swift deployment and high quality of line-of-sight(LoS)energy harvesting links,it can bring many new benefts in contrast to the ground mobile WPT chargers.

To unlock the potential of the UAV-enabled wireless powered MEC system,several works[23–28]have been focusing on computation offoading and trajectory scheduling under different scenarios.However,most of the approaches[24–26]are built upon the oneshot optimization,in which the optimization problem needs to be frequently revisited due to the highly dynamic environment,leading to the diffculty in guaranteeing the long-term performance.In fact,massive computation-intensive tasks could be offoaded any time via UAV to MEC.The task pattern and size are both diffcult to predict.Besides,most existing works[23–26]focus on the pure energy consumption or delay performance of the UAV-enabled wireless powered MEC systems,and the balanced trade-off between energy effciency(EE)and service queuing delay has not been well explored.Actually,EE and delay are two correlated performance metrics notably affected by the wireless channel conditions,e.g.,postponing the energy transfer and task offoading when channel conditions are poor can improve the EE performance but leads to a longer queuing delay.Moreover,channel conditions between UAV and MIDs are decided by the UAV locations,which are controlled by the UAV trajectory.Consequently,it is important to balance EE and delay by designing a low-complexity online computation and trajectory algorithm in a UAV-enabled wireless powered MEC system.

Motivated by the issues mentioned above,in this paper,a joint online computation and trajectory scheduling scheme is explored for UAV-enabled wireless powered MEC systems.We frst formulate the EE minimization problem to balance a tradeoff between EE and service queuing delay by considering the stochastic task arrivals and dynamic channel conditions,and then propose an online algorithm by jointly optimizing computation resource allocation and trajectory scheduling for the UAV-enabled wireless powered MEC system to solve this problem.The major contributions of the paper are summarized as follows:

·We develop a stochastic UAV-enabled wireless powered MEC system,where a UAV is deployed to assist task offoading and provide energy supply to the ground devices as well.

·A stochastic optimization problem is formulated to optimize the long-term average network EE,under the constraints on the task queue stability both at device and UAV,maximum CPU-cycle frequency and transmit power at each MID,the energy causality,as well as the trajectory scheduling of the UAV.

·To effciently solve the formulated EE-delay tradeoff problem,a low-complexity online computation offoading and trajectory scheduling algorithm(OCOTSA)is proposed by exploiting the Lyapunov optimization method.

·The simulation results demonstrate the proposed OCOTSA algorithm can balance EE and the service delay through adjusting the control parameterV,and the MEC system performance with the proposed OCOTSA algorithm is superior to the benchmark counterparts.

The remaining of the paper is organized as follows.Section II discusses the related works.Section III presents the system model.In Section IV,the average long-term EE minimization problem is formulated.In Section V,the online computation offoading and trajectory scheduling algorithm is given for the system.Simulation results are provided in Section VI.Finally,we conclude the paper in Section VII.

II.RELATED WORK

Many studies have investigated how to use UAVs in MEC networks to enhance the coverage in the scenarios with limited or no infrastructure[8–10,29].In[8],the authors studied the computation effciency maximization problem under partial computation offoading mode,wherein offoading time,power control,and trajectory are jointly optimized.In[9],the authors proposed a theoretical model for the propulsion energy consumption of fxed-wing UAVs as a function of the UAV’s fying velocity and acceleration.The sum power minimization problem with latency and coverage constraints was formulated in[29]by jointly optimizing user association,power control,computation capacity allocation,and location planning.The authors in[10]investigated three-layer online data processing in a UAV-enabled MEC system.By exploiting Lyapunov optimization and deep reinforcement learning,an online edge processing algorithm and an online path planning algorithm are proposed,respectively.However,these works did not consider the limited battery energy of devices,and no energy harvesting technology was taken into account.

Recently,the authors in[24–26]studied the resource scheduling problem of using WPT technology to realize energy harvesting in the MEC system driven by UAV.Duet.al.in[24]formulated a problem to minimize the total energy consumption of UAV based on the TDMA workfow model,and proposed an alternative algorithm to solve the problem.Luet.al.in[25]considered the‘double near-far’effect in UAV-assisted wireless powered cooperative MEC systems,and studied the power optimization problem under the constraint of the delay and task size constraint.Liuet.al.in[26]investigated a UAV-enabled wireless powered cooperative MEC system,in which devices complete the computing tasks with the help of both UAV and neighboring idle devices.A successive convex approximation(SCA)-based algorithm was proposed to minimize UAV energy consumption by jointly optimizing CPU frequency,offoading amount,transmit power,and UAV trajectory.Nevertheless,the approaches in the above works[24–26]were built on the one-short optimization,and the task streaming for a certain period in the UAV-enabled WPT MEC system was not explored.The recent work in[23]studied the space-air-ground network in a dynamic environment,and leveraged the Lyapunov optimization approach to design an online algorithm to maximize the long-term time-averaged system computation rate.

Different from the existing research,we develop an online resource allocation and trajectory scheduling scheme and explore the tradeoff between EE and service queuing delay.This work flls the gap by building a stochastic optimization framework and designing a corresponding algorithm to realize network EE minimization for UAV-assisted wireless powered MEC system.

III.SYSTEM MODEL

As shown in Figure 1,a UAV-enabled wireless powered MEC system forMMIDs is considered,where a radio frequency energy transmitter and an MEC server are mounted on the UAV to provide computation offoading services and energy supply to the MIDs,e.g,UAV transmits energy and each MID implements energy harvesting from the power transmitter.In military and civilian applications,such as disaster rescue,the fre alarm in monitoring areas,the UAV-assisted MEC system with WPT can provide fexible deployment and stable energy supplement for the MIDs,especially when the conventional communication system is destroyed.

Figure 1.System model and frame structure.

Each MID can also offoad some computation tasks to the UAV for remote processing while the remaining tasks are processed locally.Similar to works[20,23,29],we assume that MIDs can perform energy harvesting,local computing,and wireless offoading.UAV can process task computation and energy transmission simultaneously.The UAV has a mission to fy from the appointed initial position to the fnal position .During that fight time,it provides WPT and data process services to MIDs.Considering a 3-D Cartesian coordinate system,MIDs are distributed on the ground,i.e.,each MID has a zero altitude and the position of MIDmcan be denoted as qm=(xm,ym),m ∈M.The UAV is assumed to fy at a fxed altitudeH.The horizontal coordinate of the UAV attis denoted as qc(t)=(xc(t),yc(t)).Let the mission completion time beT,which is discretized intoNequal time slots.The length of each time slot isτ=T/N.We assumeτis small enough such that the location of the UAV is approximately unchanged in each time slot.For convenience,we denote the set of MIDs and the time slot asand,respectively.

As shown in the frame structure in Figure 1,each time slot duration is further divided into three stages,i.e.,energy harvesting,task offoading,and edge computing/downloading.In the energy harvesting stage,each MID frst receives the energy transmitted from the UAV radio frequency by the energy transmitter,and the duration of energy harvesting is represented asτ0(t).In the offoading phase,in order to eliminate interference among the MIDs,TDMA scheme is used.The offoading phase is further divided intoMsmall time durations,each of which is allocated to one MID for offoading.The occupancy duration ofτm(t)represents the offoading duration of MIDmatt,m ∈M,t ∈T.The time for MEC computing and task download are negligible and omitted here since the UAV has much stronger computation capacities than the MIDs and the size of computed outcomes is relatively small[14,19].

A block fading channel model is adopted,i.e.,the channel remains static during each time slottbut varies across time slots.Assume that the wireless channels between UAV and MIDs are dominated by LoS links[9,29].Thus,the channel power gain be-tween MIDmand UAV is given as

whereg0is the channel power gain at a reference distance ofd0= 1m.dm(t)represents the Euclidean distance between MIDmand UAV at time slott.‖·‖represents the Euclidean norm.

For convenience of reference,we list the key notations of our system model in Table 1

Table 1.Summary of key notations.

3.1 Task Queuing Model

LetAm(t)denote the computing task bits that arrive at the MIDmduringt.To capture the dynamics of the network,we assume thatAm(t)∈[0,Am,max]is independently and identically distributed(i.i.d)at different time slots with an average rateλm(t)[14,30].Each MID has a buffer that stores and processes the arrival tasks.

LetQm(t)be the task queue backlog maintained at MIDmin time slott,whereQm(0)= 0.Att,Dl,m(t)bits are processed by MIDmwhileDo,m(t)bits are offoaded to UAV-enable MEC.Thus,the evolution equation ofQm(t)is expressed as

where[a]+=max(a,0).

The MEC server at UAV is assumed to haveMsimilar large-capacity parallel buffers to store tasks received from each MID.LetDc,m(t)be the bits that MEC server processed for MIDmin time slott,which is assumed to be a random number with the maximum valueDc,max[31].Similarly,the task queue backlogHm(t)maintained at UAV for MIDmshould satisfy the following update process:

3.2 Local Computing

At each MID,local computing is performed simultaneously with the task offoading.LetCmdenote the processing density,which is the number of CPUfrequency cycles required to process one-bit task.By adjusting the CPU frequency in each time slot,the energy consumed by local computing can be adaptively controlled[19].Letfl,m(t)≤fl,maxrepresent the CPU frequency of the MIDmintwith a unit of cycles per second,andfl,maxis the maximum computing power of each MID.The total number of locally computed in time slottis expressed as

The corresponding energy consumption is expressed as

whereκis the effective switching capacitance coeffcient determined by the CPU hardware structure[19].

3.3 TDMA-Based Task Offloading

LetWbe the communication bandwidth.The transmit power of the MIDmattis denoted asPm(t).σ2represents the noise power,andvmrepresents the communication overhead during task offoading.Since the time duration allocated to MIDmfor offoading isτm(t),according to Shannon-Hartley formula,the amount of dataDo,m(t)from MIDmto UAV is given by

Based on the above descriptions,we only need to consider the energy harvesting duration and the offoading duration.The sum time for all the MIDs to performing energy harvesting and offoading cannot exceed the duration of one time slot,i.e.,

LetEoff,m(t)denote the offoading energy consumption of MIDmin time slott.We have

3.4 Energy Queuing Model

The energy harvested by MID is used for local computing and task offoading[13,14,19].UAV sends energy signals to MIDs withinτ0(t).With a linear energy harvesting model,the energy harvested by MIDmin time slottis

whereηm ∈(0,1]represents the effciency of energy harvesting at MIDm,andP0(t)is the UAV transmit power.LetBm(t)represent the energy queue size at MIDmin time slott.Its dynamics can be captured by the following equation:

whereEMID,m(t)=El,m(t)+Eoff,m(t)is the total energy consumption of MIDmin time slott.

The energy consumption of MIDmin time slottcannot exceed the available energy stored in its battery,i.e.,

3.5 Energy Consumption of UAV

1)UAV service energy consumption:UAV service energy consumptionEserincludes two parts,one is used for energy harvesting and one is used for offoaded task computation[14].Since the MEC server normally has a powerful computation capacity,we only focus the frst part on the service energy consumed by the UAV.Therefore,the UAV service energy consumption is expressed as

2)UAV flying energy consumption:Similar to the existing studies[25–27],we assume that the UAV fies in a straight line with a constant speed inside each time slot.Since a constant altitude fight does not affect the consumption of gravitational potential energy,the speedv(t)is defned as the ratio of the UAV’s horizontal distance increment to the length of the time slot,which is expressed as

Accordingly,the energy consumption for fying can be expressed as

IV.PROBLEM FORMULATION

4.1 Average EE Minimization Problem

In this section,we aim to minimize the long-term average EE of the UAV-enabled wireless powered MEC system,subject to resource allocation,network stability,energy causality,and fying trajectory of the UAV.

Based on the discussions above,the total amount of computing tasks that can be processed is given as

where the frst term is the local computing amount and the second term is the offoading amount.

The total energy consumption includes the computation energy and offoading energy of MIDs,and the communication energy and fying energy of UAV at time slott,which is expressed as

wherewsandwcare the weight factors of the energy consumption of MID and UAV,andws+wc= 1.γis the fight energy penalty coeffcient,which aims to alleviate the difference in amplitude.

We defne the system EE as the ratio of the longterm total energy consumption of the system to the corresponding long-term aggregated processed computation tasks,i.e.,

Note that the common defnition of EE in the existing works[32,33]is based on an instantaneous perspective.Here,we defne the EE from a long-term time-average perspective,based on which can refect the average energy consumption for executing the onebit task.Similar defnition of EE can be found in[14,34].

The parameter vector for optimization in time slottis defned asX(t)={fl,m(t),Pm(t),τm(t),qc(t)}.Then,the long-term average EE minimization problem can be formulated as

The constraints above can be explained as follow.C1 andC2 are the local CPU-cycle frequency and power constraints of MIDs,respectively.C3 is the time constraint that the total time of energy harvesting and task offoading cannot exceed one time slot.C4 represents the time constraints.C5 indicates that the total energy consumption by each MID cannot exceed the energy available in the battery.C6 denotes the range of the fying speed of the UAV.C7 denotes the initial position and the fnal position for UAV.C8 means that the history of the UAV trajectory cannot be modifed,where qc′(t)is the UAV trajectory obtained at the previous time slot.C9 guarantee the task queue stability.

4.2 Lyapunov Optimization

In this section,an online algorithm based on Lyapunov optimization theory is developed to solve the stochastic optimization problem P2.By maintaining the task queue stable,a balance between the queuing delay and EE is achieved.First,we defne the Lyapunov function as follows:

where Θ(t)={Q(t),H(t)}represents the current backlog of all task queues of at time slott.We further introduce the one-step conditional Lyapunov drift function as follows.

By incorporating queue stability,we defne a Lyapunov drift-plus-penalty function[37]as

whereVis a non-negative weight constant that represents the trade-off among the queue stability and system utility.

Instead of minimizing ΔV L(Θ(t))directly,we can minimize its upper bound and the near-optimal system EE can still be achieved.The following Lemma gives the upper bound of ΔV L(Θ(t))under any feasibleX(t).

Lemma 1.For an arbitrary queue backlog,the upper bound of drift-plus-penalty function can be derived as

whereCis a constant.

Proof.Please refer to the Appendix.

Based on Lemma 1,the original problem is transformed into a series of per-time slot optimization problems P3,which only require the information of current queue lengths and control parameters,given as

V.ONLINE ALGORITHM FOR COMPUTATION OFFLOADING AND TRAJECTORY SCHEDULING

Due to the coupling between the optimization variables and the non-convex part of the trajectory,problem P3is still a non-convex optimization problem.In this section,problem P3is decoupled into two subproblems and an effective online algorithm for computation and trajectory scheduling is proposed.The two subproblems are established for different optimal variables: 1)P3.1aims to fnd the optimal CPU cycle frequency,transmission power and time allocation;2)P3.2aims to achieve the optimal trajectory scheduling of UAV.

5.1 Optimal CPU-Cycle Frequency,Transmit Power and Time Allocation

Given that only partial tasks inQm(t)are offoaded to UAV buffer queueHm(t)and assuming that edge server always has powerful processing,one always hasQm(t)-Hm(t)+V ηEE(t)≥0.It can be easily proved that the problem P3.1is convex,and the Lagrange duality method can be used to solve it[38].The specifc steps are as follows.

5.1.1 Lagrange duality decomposition method

With the given fying trajectory of the UAV,the Lagrange duality can be used to obtain the CPU cycle frequency and transmit power.The Lagrange function of P3.1can be written as follows

whereµm ≥0 andθ ＞0 respectively represent the dual variables related to constraintsC5 andC3.ψdenotes the set of the variables in P3.1.

Defne the Lagrangian dual problem of P3.1as

The Lagrangian dual problem of(29)can be represented as

To obtain the optimal power control,the Karush-Kuhn-Tucker(KKT)conditions of P3.1should be satisfed[39].Thus,let the derivation of(28)with respect tofl,m(t)andεm(t)be zero,one has

Given UAV trajectory qc(t),the optimal time allocation can be obtained by solving the following equation.

Algorithm 1.Online computation offloading and trajectory scheduling algorithm(OCOTSA).1: At current slot t:2: Initialization:3: Θ(t),Am(t),Bm(t),ηEE(t),qI,qF,qm and qc(t).4: Repeat:5: Solve the P3.1 problem,and determine the optimal CPU cycle frequency fopt l,m(t),transmit power Popt m(t)and time allocation τoptm(t)of MID according to(27)-(33).6: Slove the P3.2 problem,and get the optimal UAV fight trajectory qopt c(t)according to(34)-(38).7: Update Qm(t),Hm(t),Bm(t)and ηEE(t)according to(2)(3)(11)(20).8: Update the time slot t=t+1.9: Until the fying mission is completed at t=N.10: Obtain solutions:fopt l,m(t),Poptm(t),τoptm(t)and qoptc(t).

5.1.2 The update of Lagrangian multiplies

After obtaining the local computing resource allocation,transmit power,and time allocation,the subgradient method can be used to update the dual variables as shown in Lemma 2.

Lemma 2.The following sub-gradient method is used to update the values of the dual variables[19].

5.2 Trajectory Scheduling of UAV

For the given CPU frequency,transmit power,and time allocation,the trajectory optimization problem can be formulated as P3.2

The objective of problem P3.2consists of energy consumption for fight and energy consumption for wireless offoading.Both parts are affected by the position and trajectory of the UAV.In addition,trajectory scheduling needs to determine the locations of UAVs fying in all time slots[29].The latter part of the objective function is to minimize the total fight energy consumption of all time slots instead of the fying energy consumption in a certain time slot.In other words,a complete UAV fying trajectory can be obtained by solving the problem P3.2.

Note that thatC6 andC8 are convex quadratic constraints,andC7 is a linear constraint.SinceC5 is non-convex,problem P3.2is non-convex.The successive convex approximation(SCA)technique can be exploited to solve the optimization problem while the obtained solutions satisfy the Karush-Kuhn-Tucker(KKT)conditions of P3.2[9].By using the SCA technique,we have the following Theorem 1.

Theorem 1.In order to solve the problem P3.2,we introduce a slack variable zm(t)≥0,m ∈M,t ∈T to deal with non-convex problems by adding new constraints.

The constraint in C5 can be rewritten as

P3.2.1is a convex optimization problem,which can be easily solved with standard convex optimization methods[38].

In summary,a low-complexity online computation offoading and trajectory scheduling algorithm(OCOTSA)that jointly optimize local CPU cycle frequency,time allocation,power control and UAV trajectory scheduling in an online manner summarized in Algorithm 1.

VI.SIMULATION RESULTS AND DISCUSSION

The simulation settings are based on the works in[24]and[29].Assume that there areM= 4 MIDs distributed within an area of 15m ×15m.The location of each MID is(0,0),(0,15),(15,15),(15,0).Each MID has a computation task arrival in every time slot,and the arrival task sizeAm(t)follows the uniform distribution within[0,Am,max].UAV fies from the initial position qI=[0,0]to the fnal position qF=[15,0]at a constant altitudeH= 10m.In addition,the total time for the UAV mission completion isT= 2s,which is divided intoN= 50 time slots.The remaining parameters used in the simulations are set asW= 1MHz,g0= 10-2,σ2= 10-9W,fl,max= 1GHz,Pm,max= 0.1W,P0= 50dBm,κ= 10-25,Cm= 1000cycle/bits,Vmax= 10m/s,Mg=9.65kgunless otherwise specifed.

6.1 Performance Analysis

Figure 2-4 show the variation of the system’s average energy consumption,average EE,and average queue length with the control parameterV,respectively.The evolution of average energy consumption withVis illustrated in Figure 2.The average system energy consumption of all the settings decreases with the increase ofV.This is due to the fact that a larger value ofVleads to smaller energy consumption of the system,which can be seen from(26).In addition,it can be observed that the average energy consumption increases withwcandAm,max.The energy consumption of UAV is much higher than the energy consumption of MID[29].Whenwcincreases,the proportional weight of UAV energy consumption increases greatly whereas the achievable rate of the system does not increase that much,leading to a worse overall EE performance.Furthermore,the large value of task sizeAm,maxrequires a higher task processing rate in order to maintain the stability of buffer queue.Thus the energy consumption inevitably increases accordingly.

Figure 2.Average energy consumption v.s.control parameter V.

Figure 3.Average energy efficiency v.s.control parameter V.

Figure 3 shows the relationship between the average EE and control parameterV.It can be seen from the fgure that the system EE decreases with the growth ofV.The reason is that the system gives a higher priority for minimizing the EE with a larger value ofV,which is in conformity of(25).Due to the larger magnitude of the UAV’s energy consumption,the growth ofwcmeans the value of system energy consumption signifcantly increases while the amount of processing data keeps stable,leading to a worse EE performance.Since larger task arrivals require more processing resources to maintain the stability of the queue,it is evident that EE is getting worse withAm,max.Figure 4 shows the impact of the control parameterVon the average queue length.It is quite evident that the average queue length increases as the value ofVincreases,which further verifes that the parameterVcan be a control factor to balance EE and the queuing length in Lyapunov optimization.With the given task size,the buffer queue length slightly increases with the growth ofwc.The reason can be explained as follows.With a higherwc,the weight for UAV is much higher,the total energy consumption for MIDs and corresponding achievable rate is reduced,leading to a higher queue length.

Figure 4.Average queue length v.s.control parameter V.

Figure 5.Average energy efficiency v.s.time slot.

Figure 6.Optimal trajectories of the UAV under different schemes.

AsAm,maxincreases,the average queue length also increases.Obviously,a largerAm,maxcauses a significant increase in the average queue length.The observations from Figure 3 and Figure 4 further reveal that there exists a tradeoff between EE and average queue length,i.e.,the network EE is negatively correlated with the average queue length.Therefore,the control parameterVshould be selected according to different service quality.

Figure 5 illustrates the EE performance over the large time scale.It can be observed that as the number of time slots increases,the system EE slowly decreases,and the proposed algorithm based on different settings fnally converges to a stable performance.It also demonstrates that with a largerV,the system can achieve a lower EE and faster convergence.

Figure 7.Average energy efficiency v.s.maximum data arrivals under different schemes.

Figure 8.Average energy consumption v.s.maximum data arrivals under different schemes.

Figure 9.Processing data v.s.maximum data arrivals under different schemes.

6.2 Scheme Comparison

In this part,the superiority of the proposed method with respect to minimizing system EE is verifed.The control parameter is set asV= 109for the following simulation.We compare our proposed algorithm with the following three benchmark schemes.

1)Complete local: all computing tasks are processed locally by MIDs.Thus,UAVs will only serve as energy supply and use the same trajectory scheduling with our proposed method.

2)Complete offoading: MIDs don’t have local process capability and need to offoad all their computing tasks to the MEC server on the UAV for processing.The trajectory scheduling is the same as our proposed method.

3)Without trajectory optimization: the UAV only applies the initial trajectory without any trajectory optimization strategies.MIDs can partially offoad their tasks to UAV with the same resource allocation algorithms proposed in our method.

Figure 6 shows the trajectory scheduling in different schemes.MID frst receives the energy transmitted from the UAV,then offoads partial tasks to the UAV for processing.Therefore,UAV needs to be as close to each MID as possible.Furthermore,since the energy consumption of UAV increases with fight distance,UAV needs to optimize its trajectory to save more energy as well as guarantee the performance of each MID.The ‘Complete local’ method has a lower fight distance since the UAV only needs to transmit energy without waiting for offoading data.The proposed method has a lower distance compared with the other two benchmarks,because it can fnd the optimal tradeoff between energy harvesting and task offoading for different MIDs.The ‘Complete offoad’method has a higher distance since the MIDs cannot perform the local computing,UAV has to fy farther and wait for all the tasks offoaded from all the MIDs.

Figure 7-9 present the system performance versus maximum arrival taskAm,max.

Figure 7 depicts the impact ofAm,maxon system average EE.From the fgure,we can see that all the curves increase with maximum arrival data.The reason is that more task arrivals require a larger processing rate,and more energy consumption to maintain the buffer queue length at a stable level,leading to a worse performance of EE.Compared with other benchmarks,the proposed method can achieve the best EE.The ‘Complete local’ method has the worst EE performance due to MIDs’ limited computing ability and energy supply.This also indicates that the deployment of a UAV-based MEC server can signifcantly improve the system performance.Another thing worth noting is that the gap between different methods becomes larger with the change ofAm,max.The reason is that when the size of tasks is at a low level,all the methods can easily satisfy the processing requirement and maintain a higher EE.However,when the task size keeps increasing,the benchmarks have to sacrifce their EE to maintain the system stable.But the proposed method still maintains a better EE-delay tradeoff since it can exploit all the benefts from local computing and task offoading with optimal UAV trajectory.

Figure 8 shows the average energy consumption versus theAm,max.The energy consumption of all the methods keeps increasing with the size of arrival tasks,which is similar to the observation in Figure 7.The proposed method can achieve the lowest energy consumption compared with other benchmarks.One thing worth noting is that the energy consumption of the‘Complete local’ method is close to other methods whenAm,maxis small,but the limited local computing speed of MIDs make the achievable rate and corresponding EE lower than other benchmarks.Note that although in the beginning,the proposed method has a slightly higher energy consumption than‘Complete offoading’,but the achievable rate and EE are much better than that method,which verifes the proposed method can achieve a better EE tradeoff.

The average amount of processed data versus maximum arrival dataAm,maxis presented in Figure 9.The trends of curves are similar as in Figure 7 and Figure 8,which verifes the observations discussed above.The proposed method can achieve the highest amount of processed data.The performance of ‘Without trajectory optimization’,‘Complete offoading’,and‘Complete local’ methods are in a descending order.The reason behind this is that based on our settings,the deployment of UAV can signifcantly help the system increase the processing capacity and EE even without trajectory optimization.However,since the UAV fight consumes more power,the EE performance of the‘Without trajectory optimization method is worse than the‘Complete offoading’method,as observed previously.The average amount of processed data achieved by the ‘Complete local’ and ‘Complete offoading’methods is lower than the other methods.This is because neither of them can adaptively adjust the optimal task allocation based on the dynamic changes of environment.Therefore,based on the discussions above,the proposed UAV-enabled method can help to improve the system performance.

VII.CONCLUSION

In this article,we investigate CPU cycle frequency,power control,time management,and UAV trajectory scheduling in the UAV-enabled wireless power MEC system by jointly taking stochastic task generating and wireless channel environment into consideration.The time average network EE minimization problem with queue stability constraint was formulated.In order to solve the non-convex problem,an optimization algorithm based on Lyapunov optimization was exploited to decompose the target problem into two manageable sub-problems.The simulation results validate the tradeoff between EE and service queue delay and verify that EE obtained by the proposed algorithm outperforms other benchmark schemes.

ACKNOWLEDGEMENT

This work was supported in part by the U.S.National Science Foundation under Grant CNS-2007995;in part by the National Natural Science Foundation of China under Grant 92067201,62171231;and in part by Jiangsu Provincial Key Research and Development Program under Grant BE2020084-1.

APPENDIX

The inequality(max[a-b,0]+c)2≤a2+b2+c2+2a(c-b),∀a,b,c ≥0 always holds.By applying the above inequality to(2)and(3),we can get

Therefore,the difference between the Lyapunov function in the current time slot and the previous time slot can be calculated by

Among them,Cis a constant and defned as

whereAm,max(t),Dl,max(t)andDo,max(t)are the upper bounds ofAm(t),Dl,m(t)andDo,m(t),respectively.Thus the upper bound of Lyapunov driftplus-penalty function can be given as: