CS计算机代考程序代写 scheme flex ER distributed system information theory algorithm Power-Delay Trade-off for Heterogenous Cloud Enabled Multi-UAV Systems

Power-Delay Trade-off for Heterogenous Cloud Enabled Multi-UAV Systems

Power-Delay Trade-off for Heterogenous Cloud
Enabled Multi-UAV Systems

Ruiyang Duan∗, Jingjing Wang∗, Jun Du∗, Chunxiao Jiang†, Tong Bai‡ and Yong Ren∗
∗Department of Electronic Engineering, Tsinghua University, Beijing, 100084, China

†Tsinghua Space Center, Tsinghua University, Beijing, 100084, China
‡University of Southampton, Southampton, SO17 3RY, United Kingdom

Email: .edu.cn

Abstract—Unmanned aerial vehicles (UAVs) have been widely
used in a range of compelling applications. However, some of
them are incompetent in tackling with computation-intensive
tasks due to limited processing capability and battery life. In
this paper, we combine the mobile edge computing and traditional
cloud computing techniques for offloading the tasks from multi-
UAV systems. Specifically, we jointly optimize the task scheduling
and resource allocation in the heterogeneous cloud architecture,
where we strike a power-delay trade-off of the system relying
on the queue theory and Lyapunov optimization, followed by
its optimal strategy analysis in each time slot. Moreover, we
conceive an iterative algorithm with a closed-form solution at each
iteration round in order to reduce the computational complexity.
Finally, numerical results demonstrate both the feasibility and
effectiveness of our proposed scheme. This paper validates that
the heterogeneous cloud structure can be the beneficial for
improving quality-of-service performance of multi-UAV systems.

Index Terms—Heterogenous cloud, task scheduling, resource
allocation, power-delay trade-off.

I. INTRODUCTION

Thanks to their low cost, high flexibility and easy de-

ployment, unmanned aerial vehicles (UAVs) have been wide-

ly used in both military and civilian applications such as

military surveillance, environment monitoring and emergency

rescue [1]. They are usually equipped with a variety of sensors

to fulfill different tasks. However, some of these tasks are

computation-intensive, which poses a great challenge to UAVs

for their limited processing capacity and battery life. Hence,

new solutions should be conceived to handle the explosive

computation demand as well as the ever-increasing require-

ment of computational quality. Mobile edge computing (MEC)

has become a promising technology for releasing the tension

between the computation-intensive tasks and resource-limited

devices [2], where devices can offload their tasks to cloud

servers which are deployed locally, and the cloud servers return

the results to the devices. Relying on MEC, quality-of-service

(QoS), such as power consumption and execution delay, can

be greatly improved.

However, in comparison to traditional cloud computing, the

resource in the edge cloud is restricted by its scale. Therefore,

the resource allocation problem becomes a critical issue in

MEC, which has attracted much attention [3]–[7]. Specially,

in [3], Sardellitti et al. proposed an iterative algorithm based
on successive convex approximation to jointly allocate the

radio resource and computational resource to multiple users

in a MIMO MEC system. Moreover, a power-delay trade-

off problem in a multi-user MEC system was formulated

in [4], where the local processing ability of devices was

considered and an optimal resource allocation scheme was

designed with the aid of Lyapunov optimization. In [5], Liu

et al. studied the delay-optimal task scheduling and resource
allocation problem under power constraints in MEC systems

modeled by a Markov decision process, which were capable

of achieving shorter average execution delay in comparison to

other schemes.

Since the traditional cloud, i.e. the remote cloud, has

abundant computational resource, the heterogenous cloud ar-

chitecture including both the edge cloud and the remote

cloud has been constructed for jointly improving the QoS

performance [8]. To elaborate a little further, in [9], Gelenbe et
al. studied the optimal load sharing problem between a local
and remote cloud, where an optimal scheme was proposed

based on the analysis of the power consumption and services

time in the context of diverse tasks with different types and

requirements. The fair resource allocation problem in the

heterogenous cloud system was investigated in [10], where

a multi-resource allocation mechanism, namely DRFH, was

designed both to guarantee the fairness of members and to

keep the service isolation among users. The delay-bounded

task offloading problem in the heterogenous cloud system was

highlighted in [11] considering both the wireless transmission

delay as well as the execution delay. Zhao et al. modeled
the arrival-service process as an M/M/1 queue, relying on

which the success probability of the delay-bounded task was

derived in the context of a single-user case and a multi-user

case. Additionally, a total power minimization assisted task

scheduling problem was studied in [12] by Gai et al.
Although many efforts have been done on the research of

UAV networks, of MEC and on heterogenous cloud, few works

focus on the combination of them. Against this background, in

this paper, we study the energy efficient network association

problem with a focus on task scheduling and resource alloca-

tion in heterogenous cloud aided multi-UAV systems, where

UAVs can offload their tasks to a heterogenous cloud system

which is composed of an edge cloud and a remote cloud. Our

main concern is to determine the percentage of the tasks to be

assigned to the edge cloud as well as the computation resource

978-1-5386-8088-9/19/$31.00 ©2019 IEEE

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Fig. 1. The structure of the heterogeneous cloud aided multi-UAV system.

to be allocated to different tasks from UAVs. Moreover, the

queue theory is used for modeling the execution delay. Thus,

we formulate the energy efficient network association problem

as a power consumption minimization problem under system

stability constraints. Additionally, a power-delay trade-off is

struck based on the Lyapunov optimization and an iterative

algorithm is designed in order to find the optimal strategy.

The rest of the paper is organized as follows. The system

model is introduced in Section II. In Section III, the power-

delay trade-off is struck based on Lyapnuov optimization con-

sidering the power consumption and execution delay involved.

Moreover, an iterative algorithm is invoked to find the optimal

strategy in each time slot. Simulation results are provided

in Section IV to evaluate the performance of our proposed

scheme, followed by our conclusions in Section V.

II. SYSTEM MODEL

We consider a heterogeneous cloud aided multi-UAV sys-

tem, which consists of multiple UAVs, the edge cloud and the

remote cloud, as shown in Fig. 1. These UAVs carry sensed

data related to different tasks. We assume that the tasks are

computation-intensive, and hence they need to offload the tasks

to two kinds of clouds considered. The UAVs are able to

communicate with the clouds through a radio access network

(RAN). In our model, the edge cloud can be viewed as a small-

scale processing center with limited computational capability

installed at the wireless access point (AP), while the remote

cloud is a large-scale processing center with powerful process-

ing ability with the aid of the easy access to the Internet. The

system is operated under a high dynamic circumstance because

of the high mobility of UAVs. For the simplicity of analysis,

the dynamic of the system is characterized by discrete time

slots, i.e. t ∈ T = {1, 2, 3, …}. In each time slot t, UAVs first
transmit corresponding sensed data to an AP over the air, and

then the data is processed by the virtualized machines (VMs)

either in the edge cloud or in the remote cloud.

A. The UAV Model

We assume that there are total N UAVs to execute N
different tasks in the multi-UAV system, which can be denoted

as N = [1, 2, …, N ]. The tasks are assigned by the ground

control station (GSC). Once being assigned a task, the related

UAV will fly to certain area according to the pre-defined

path, collect related data and then navigate to the nearby AP

to offload the data. These UAVs are equipped with sensor

units, control units, management units and communication

units to fulfill the tasks. Specifically, the communication units

are composed of multiple modules configured by various

protocols [1], so that the UAVs can communicate with the AP

via Wi-Fi, long-term evolution (LTE), etc. as the circumstance

may require. Relying on the high flexibility, these UAVs can

fly close to and hover around an AP to ensure the reliable

wireless transmission. Under this assumption, we neglect the

occurrence of the transmission outage resulted from the poor

channel condition between the AP and UAVs. Let Ai(t) denote
the number of packets arriving at the AP from UAV i in time
slot t, while A(t) = [A1(t), A2(t), …, AN (t)] represent the
packet arrival vector in time slot t, where Ai(t) in different
time slots is independent and identically distributed (i.i.d.). The

number of the arrival packets is bounded between Ai,min and
Ai,max, i.e. Ai,min ≤ Ai(t) ≤ Ai,max. Let λi = E [Ai(t)] be
the average packet arrival rate from UAV i in time slot t.

B. Cloud Execution Model

In our paper, the packets from different UAVs are offloaded

and processed at the clouds. In time slot t, after receiving the
packets transmitted from related UAVs, part of these packets

from UAV i, denoted as Ae,i(t), will be locally processed at
the edge cloud, while Ar,i(t) packets will be tackled at the
remote cloud. Hence, we have Ai(t) = Ae,i(t) +Ar,i(t).

1) Edge Cloud: In the edge cloud, there are total N
VMs exclusively used by N UAVs. When packets reach
the edge cloud, the corresponding VM allocates appropriate

computational resources to support the data processing task.

The computational resource is decided by the CPU-cycle

frequency [4]. In this paper, we assume that the available CPU-

cycle frequency allocated to UAV i at time slot t is represented
by fi(t), where fi(t) ≤ fi,max. We define the number of the
packets that can be served by the VM i in the edge cloud as:

μi(t) = Δtfi(t)L
−1
i , (1)

where Δt denotes the duration of the time slot, while Li is
the minimum CPU cycles needed to process one packet from

UAV i. Moreover, the power consumption during the whole
execution process in the edge cloud can be approximately

formulated by:

Pe,i(t) = κf
3
i (t), (2)

where κ represents the capacitance coefficient.

The newly arrived packets will be queued in the buffer of the

edge cloud when the corresponding VM is busy with dealing

with early arrived packets. Let Qi(t) denote the queue length
in the ith VM related to UAV i and we have Qi(0) = 0 at
the beginning. Then the dynamic of the queue length can be

expressed as:

Qi(t+ 1) = max{Qi(t)− μi(t), 0}+Ae,i(t). (3)

Because of the local deployment of the edge cloud, the

execution delay in the edge cloud mainly stems from the

queue. Relying on the Little’s Law [13], the average queueing
delay can be derived from the average queue length, which is

calculated by Eq. (3).

2) Remote Cloud: By contrast, the power consumption in
the remote cloud is closely related to the variation of the

workload, which is formulated by:

Pr,i(t) = Ce
Ar,i(t), (4)

where C is a constant coefficient. As for the execution delay
in the remote cloud, given that it is equipped with a multi-

core high-speed CPU, we assume that the arrived packets

can be processed without the queueing time. Hence, the time

delay largely depends on the Internet transmission process.

Moreover, referring to [14], the Internet transmission delay

follows an empirical distribution. For simplicity, we assume

that Internet transmission process has a deterministic delay D.

III. TASK SCHEDULING AND RESOURCE ALLOCATION

SCHEME

As mentioned before, task scheduling is an important issue

in heterogeneous cloud aided systems. Specifically, if all the

packets are locally processed at the edge cloud, it is difficult

to keep the system stable because both the computational

capability and the buffer capacity in the edge cloud are limited.

On the other hand, if all the packets are offloaded and tackled

at the remote cloud, the power consumption is too high. In this

section, our goal is to find an optimal scheme to determine the

percentage of packets processed at the edge cloud as well as

the amount of computational resources allocated for different

tasks considering both the average power consumption and the

cloud execution delay.

A. Problem Formulation

The power consumption for handling the packets from UAV

i in time slot t is composed of two parts, i.e. the power
consumption in the edge cloud and the power consumption

in the remote cloud. Let Pi(t) = Pe,i(t) + Pr,i(t) denote the
power consumption for fulfilling the task from UAV i in time
slot t. Considering a total number of N UAVs, the system’s
power consumption can be calculated as P (t) =

∑N
i=1 Pi(t).

Then, the average power consumption is given by:

P̄ = lim
t→∞

1

t
E

[
t−1∑
τ=0

P (t)

]
. (5)

Since the Internet transmission delay in the remote cloud

is a constant, the average execution delay largely hinges on

the sojourn time in each edge cloud’s queue. Relying on the

Little’s Law [13], we use the average queue length in the task
buffer as a measurement of the average execution delay, which

is expressed as:

Q̄i = lim
t→∞

1

t
E

[
t−1∑
τ=0

Qi(t)

]
. (6)

Definition 1. The queue system in the edge cloud related to
UAV i is strong stable, if:

lim
t→∞

1

t
E

[
t−1∑
τ=0

Qi(t)

]
< ∞. (7) Note that if all the queues are stable, the system’s average service rate is equal to the packet arrival rate, i.e. lim t→∞ 1 t t−1∑ τ=0 ui(t) = lim t→∞ 1 t t−1∑ τ=0 Ae,i(t), (8) which guarantees that the arrived packets can be processed in terms of finite time delay. In this paper, we aim to find a task scheduling and re- source allocation scheme for the sake of minimizing the average power consumption under the constraint that all the tasks can be executed with finite time delay. Let η(t) = [η1(t), η2(t), ..., ηM (t)], where ηi(t) = Ae,i(t) Ai(t) , and f(t) = [f1(t), f2(t), ..., fM (t)]. Hence, the problem can be formulated as: P1 : min η(t),f(t) P̄ s.t. 0 ≤ ηi(t) ≤ 1, i = 1, 2, ..., N, t ∈ T , (9a) 0 ≤ fi(t) ≤ fi,max, i = 1, 2, ..., N, t ∈ T , (9b) lim t→∞ 1 t E [ t−1∑ τ=0 Qi(t) ] < ∞, i = 1, 2, ..., N. (9c) To elaborate, (9a) requires that the packets from UAV i should be processed by either the edge cloud or the remote cloud, while (9b) denotes that the CPU-cycle frequency meets the given threshold. Moreover, (9c) allows that the packets tackled in the edge cloud can be processed within finite time delay. B. Lyapunov Optimization Based Greedy Solution P1 is a stochastic optimization problem since η(t) and f(t) is time-varying. In this section, we design an online algorithm to determine the optimal task scheduling and resource alloca- tion strategy in each time slot based on Lyapunov optimization. Lyapunov optimization is designed to greedily minimize the queue backlogs by solving a deterministic problem. Detailed descriptions concerning to Lyapunov optimization can be referred to [15]. First of all, we define the function L (Q(t)) as the sum of squares of backlogs in the queue, which is expressed as: L (Q(t)) = 1 2 N∑ i=0 Q2i (t). (10) Then, the conditional Lyapunov drift for time slot t can be given by: Δ(Q(t)) = E [L (Q(t+ 1))− L (Q(t)) |Q(t)] . (11) If we minimize Δ(Q(t)) in each time slot, it may stabilize the whole system. However, the average power consumption is substantially large. Alternatively, we define a drift-plus-penalty function ΔV (Q(t)) to strike a trade-off between the power consumption and queue backlogs, i.e. ΔV (Q(t)) = Δ (Q(t)) + V · E [P (t)|Q(t)] , (12) where V is the weighting parameter. A large value of V is beneficial of optimizing the average power consumption yet with the expense of large average delay. Thus, the drift-plus- penalty function provably strikes a balance between the power consumption and cloud execution delay. Lemma 1. For any η(t) and f(t) such that ηi(t) ∈ [0, 1] , fi(t) ∈ [0, fi,max] , i = 1, 2, ..., N , ΔV (Q(t)) is upper bounded by ΔV (Q(t)) ≤ 1 2 E [ N∑ i=1 ( A2e,i(t) + μ 2 i (t)− 2Ae,i(t)μi(t) ) |Q(t) ] − E [ N∑ i=1 Qi(t) (μi(t)−Ae,i(t))|Q(t) ] + V · E [P (t)|Q(t)] (13) Proof: Relying on Eq. (3), the difference of the Lyapunov function in adjacent time slots can be given by: L (Q(t+ 1))− L (Q(t)) = 1 2 N∑ i=1 ( Q2i (t+ 1)−Q2i (t) ) = 1 2 N∑ i=1 [( max {Qi(t)− μi(t), 0}+A2e,i(t) )2 −Q2i (t) ] ≤ 1 2 N∑ i=1 [ A2e,i(t) + μ 2 i (t)− 2Ae,i(t)μi(t) ] − N∑ i=1 [Qi(t) (μi(t)−Ae,i(t))], (14) where the last deduction of expression (14) relies on the conclusion: (max {Q− μ, 0}+A)2 ≤ Q2 + μ2 +A2 + 2Aμ− 2Q(μ−A), (15) for any Q ≥ 0, μ ≥ 0, A ≥ 0. Then, calculate the drift-plus- penalty function defined in Eq.(12), and we can obtain the upper bound in Lemma 1. For the sake of achieving a superior task scheduling and resource allocation scheme, in this paper we conceive the Algorithm 1 aiming to greedily minimize the upper bound of the ΔV (t) in each time slot, where hc (η(t),f(t)) = 1 2 N∑ i=1 [ A2e,i(t) + μ 2 i (t)− 2Ae,i(t)μi(t) ] − N∑ i=1 [Qi(t) (μi(t)−Ae,i(t))] + V · P (t). (16) In Algorithm 1, solving the stochastic optimization problem P1 is reduced to deal with a deterministic optimization problem P2 in each time slot. By changing the value of V , we can achieve the power-delay trade-off. Moreover, the proposed algorithm is capable of minimizing the power consumption and of driving the queue backlog towards a low congestion state. Algorithm 1 A Lyapunov Optimization Based Task Schedul- ing and Resource Allocation Algorithm 1: At the begin of the time slot t, obtain {Qi(t)} and {Ai(t)}. 2: Calculate P2 : {η(t),f(t)} =argmin hc (η(t),f(t)) s.t. (9a), (9b). 3: Update {Qi(t)} according to Eq. (3) and set t = t+ 1. C. A Low-complexity Iterative Algorithm In this section, we provide a low-complexity iterative al- gorithm to solve P2 based on its structure feature. Since P2 is a combinational optimization problem in terms of two variables, the minimization optimization can be achieved by searching the solution in accordance with the decreasing gradient direction of either of them. Hence, by fixing one of the two variables, we can obtain the optimal value of the other one. Plugging Eq. (1), Eq. (2) and Eq. (4) into Eq. (14), and we have: hc (η(t),f(t)) = 1 2 N∑ i=1 [η2i (t)A 2 i (t) + Δt 2f2i (t)L −2 i −2ηi(t)Ai(t)Δtfi(t)L−1i ] − N∑ i=1 [ Qi(t) ( Δtfi(t)L −1 i − ηi(t)Ai(t) )] + V N∑ i=1 [ κf3i (t) + Ce (1−ηi(t))Ai(t) ] . (17) Optimal CPU-cycle Frequency: By fixing η(t), the objec- tive function of P2 reduces to: hc (η(t),f(t)|η(t)) = 1 2 N∑ i=1 [ Δt2f2i (t)L −2 i − 2ηi(t)Ai(t)Δtfi(t)L −1 i ] − N∑ i=1 Qi(t)Δtfi(t)L −1 i + V N∑ i=1 κf3i (t). (18) Hence, the single-variable optimization problem can be given by: P3 : min η(t) hc (η(t),f(t)|η(t)) s.t. 0 ≤ fi(t) ≤ fi,max, i = 1, 2, ..., N. (19a) Since fi(t) ′s are i.i.d., the optimal solution can be achieved by solving ∂hc(η(t),f(t)|η(t)) ∂fi(t) = 0, which is expressed as: f∗i (t) = −Δt2L−2i + √ Δt4L−4i + 12V κΔtL −1 i (ηi(t)Ai(t) +Qi(t)) 6V κ . (20) We can verify that ∂2hc(η(t),f(t)|η(t)) ∂fi 2(t) ∣∣∣ fi(t)=f ∗ i (t) ≥ 0. Hence, f∗i (t) is the global minimum point. Because fi(t) is bounded by fi,max, thus the optimal solution can be given by: f̂i(t) = min {f∗i (t), fi,max} , i = 1, 2, ..., N. (21) Optimal Data Diffluence: By fixing f(t), the objective of of P2 reduces to: hc (η(t),f(t)|f(t)) = 1 2 N∑ i=1 [ η2i (t)A 2 i (t)− 2ηi(t)Ai(t)Δtfi(t)L−1i ] + N∑ i=1 [Qi(t)ηi(t)Ai(t)] + CV N∑ i=1 e(1−ηi(t))Ai(t). (22) Then, the optimization problem can be rewritten as: P4 : min η(t) hc (η(t),f(t)|f(t)) s.t. 0 ≤ ηi(t) ≤ 1, i = 1, 2, ..., N. (23a) Similarly, P4 can be solved by solving: ∂hc (η(t),f(t)|f(t)) ∂ηi(t) = Ai(t)CV e (1−ηi(t))Ai(t) − ηi(t)A2i (t) +Ai(t)Δtfi(t)L−1i −Qi(t)Ai(t) = 0 (24) Eq. (24) is a transcendental equation, which can be easily solved by numerical methods such as Newton’s method or secant method. Let η∗i (t) be the solution of Eq. (24), and we can also verify that η∗i (t) is the global minimum point. Considering ηi(t) ∈ [0, 1], the optimal solution can be given by: η̂i(t) = max {0,min {η∗i (t), 1}} , i = 1, 2, ..., N. (25) Relying on the optimal solution obtained by Eq. (21) and Eq. (25), we provide a low-complexity iterative algorithm to find the optimal solution for P2. The algorithm is detailed in Algorithm 2. IV. SIMULATION RESULTS In this section, numerical results are provided to evaluate the performance of our proposed scheme. The length of one time slot is set to be 30 ms. We assume that Ai,min = 10, Ai,max = 100 and Ai(t) is uniformly distributed within the range of [10, 100]. Further set κ = 10−27, L = 3 × 106, fi,max = 3 GHz and C = 10 −20. The simulation results are averaged over 100 time slots. Algorithm 2 A Low-complexity Iterative Algorithm for Solv- ing P2 1: Initialize η(t), set k = 0 and ε as the threshold. 2: Calculate {f̂ki (t)} according to Eq. (21). 3: Calculate {η̂ki (t)} by solving Eq. (25). 4: Calculate hkc according to Eq. (17). 5: repeat 6: Update {f̂k+1i (t)} according to Eq. (21). 7: Update {η̂k+1i (t)} by solving Eq. (25). 8: Update hk+1c according to Eq. (17). 9: Update k = k + 1. 10: until ∣∣hkc − hk−1c ∣∣ ≤ ε 11: Obtain f̂ opt i (t) = f k i (t), η opt i (t) = η̂ k i (t) 1 5 10 15 20 Number of Iterations 4500 5000 5500 6000 6500 7000 7500 8000 h c N = 5 N = 10 N = 20 Fig. 2. The convergence performance of Algorithm 2. Fig. 2 presents the convergence performance of Algorithm 2, where we set V = 4000. It can be inferred that given a set of randomly generated η0(t), the proposed algorithm is capable of achieving the convergence in 2 steps. Moreover, the increment of UAVs almost has no influence on the rate of convergence. Therefore, we validate that our algorithm can achieve fast convergence with lower computational cost, comparing with solving P2 with interior-point methods, . Fig. 3 shows the relationship between the average power consumption of task execution/average queue length per user and the control parameter, where we set N = 10. It can be observed that the average power consumption decreases with the increment of V, and converges to the minimum value when V is sufficiently large. In contrast, the average queue length per user increases with V and also converges when V is sufficiently large. It can be explained that when V is sufficiently large, the optimal data diffluence tends to be a constant, so do the average power consumption and average queue length. These results verify the tradeoff between the power consumption and execution delay caused by the control parameter. Fig. 4 depicts the comparison of the average pow- er consumption with respect to queue length perfor- mance of systems between the scenarios with and with- 0 1 2 3 4 Control parameter V ×104 0 10 20 30 40 50 60 70 A ve ra ge p ow er c on su m pt io n 0 1 2 3 4 Control parameter V ×104 0 100 200 300 400 500 600 700 800 900 A ve ra ge q ue ue le ng th p er u se r Fig. 3. Average power consumption and queue length versus the control parameter. 0 500 1000 1500 2000 2500 Average queue length per user 0 50 100 150 200 250 300 A ve ra ge p ow er c on su m pt io n With Remote Cloud Without Remote Cloud V=50 V=4000 Fig. 4. The comparison of average power consumption and queue length performance of systems with and without the remote cloud. out the remote cloud. Here we set N = 10 and V ∈ {50, 100, 200, 300, 400, 500, 1000, 2000, 4000}. It is shown that in general, the average power consumption decreases with the increment of average queue length for the both systems. Therefore, it is necessary to carefully select a suitable V to balance the power consumption and execution delay. Moreover, the falling range of the power consumption of the system without the remote cloud is much larger than the system with the remote cloud, which indicates that the control parameter has more influence on the system without the remote cloud. In addition, more power is consumed for the system without the remote cloud while leading to longer delay. This is because the edge cloud cannot stabilize its task buffers, due to its limited computational capacity if not equipped with the remote cloud. In this case, Fig. 4 verifies that the superiority of heterogenous cloud system on improving the quality of computation experience. V. CONCLUSIONS In this paper, we studied the energy efficient network association problem in heterogenous cloud aided multi-UAV systems. We dedicate on the optimization of task scheduling and resource allocation. We formulated the problem as a power consumption minimization problem under system stability constraints. A power-delay trade-off was struck as well as an optimal solution relying on Lyapunov optimization was designed. Numerical results showed that our proposed scheme can reach the optimal solution within a few iterative rounds and can yield an improved QoS performance. ACKNOWLEDGEMENT This work is supported by the China Postdoctoral Sci- ence Foundation (2018M640130), the National Natural Sci- ence Foundation of China (91338203), the Pre-research Fund of Equipments of Ministry of Education of China (6141A02022615). REFERENCES [1] J. Wang, C. Jiang, Z. Han, Y. Ren, R. G. Maunder, and L. 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