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IEEE INTERNET OF THINGS JOURNAL 1
Stochastic Optimization-Aided Energy-Efficient
Information Collection in Internet-of-Underwater
Things Networks
Zhengru Fang , Student Member, IEEE, Jingjing Wang , Senior Member, IEEE,JunDu ,Member, IEEE,
Xiangwang Hou, Student Member, IEEE, Yong Ren ,Senior Member, IEEE,andZhuHan ,Fellow, IEEE
Abstract—In the face of deeply exploring and exploiting marine
resources, the Internet-of-Underwater Things (IoUT) networks
have drawn great attention considering its widely distributed
low-cost and easy-deployment smart sensing nodes. However,
given the hostile underwater environment, it is critical to con-
ceive energy-efficient information collection because of limited
underwater energy supply and inefficient artificial recharge
methods. Characterized by high flexibility and maneuverabil-
ity, autonomous underwater vehicles (AUVs) are regarded as a
promising solution for information collection in the IoUT relying
upon delicate AUVs’ trajectory and information collection strat-
egy design with the spirit of balancing their energy consumption
and information processing capability. In this article, we pro-
pose a heterogeneous AUV-aided information collection system
with the aim of maximizing the energy efficiency of IoUT nodes
taking into account AUV trajectory, resource allocation, and the
Age of Information (AoI). Moreover, based on the particle swarm
optimization (PSO), we obtain the trajectory of AUVs with low
time complexity. Additionally, a two-stage joint optimization algo-
rithm based on the Lyapunov optimization is constructed to strike
a tradeoff between energy efficiency and system queue backlog
iteratively. Finally, simulation results validate the effectiveness
and superiority of our proposed strategy.
Index Terms—Energy efficiency, Internet of Underwater
Things (IoUT), Lyapunov optimization, trajectory scheduling,
underwater information collection.
Manuscript received February 11, 2021; revised May 11, 2021; accepted
June 7, 2021. This work was supported in part by the National
Natural Science Foundation of China under Grant 62071268 and Grant
61971257; in part by the Young Elite Scientist Sponsorship Programs
by CAST under Grant 2020QNRC001; and in part by the Project “The
Verification Platform of Multi-Tier Coverage Communication Network
for Oceans” of Peng Cheng Laboratory under Grant LZC0020. The
work of Zhu Han was supported in part by NSF under Grant EARS-
1839818, Grant CNS1717454, Grant CNS-1731424, and Grant CNS-1702850.
(Corresponding author: Jingjing Wang.)
Zhengru Fang, Jingjing Wang, Jun Du, and Xiangwang Hou are with
the Department of Electronic Engineering, Tsinghua University, Beijing
100084, China (e-mail: fangzhengru@gmail.com; chinaeephd@gmail.com;
blgdujun@gmail.com; xiangwanghou@163.com).
Yong Ren is with the Department of Electronic Engineering, Tsinghua
University, Beijing, 100084, China, and also with the Network and
Communication Research Center, Peng Cheng Laboratory, Shenzhen 518055,
China (e-mail: reny@tsinghua.edu.cn).
Zhu Han is with the Department of Electrical and Computer Engineering,
University of Houston, Houston, TX 77004 USA, and also with the
Department of Computer Science and Engineering, Kyung Hee University,
Seoul 446-701, South Korea (e-mail: zhan2@uh.edu).
Digital Object Identifier 10.1109/JIOT.2021.3088279
I. INTRODUCTION
AUTONOMOUS underwater vehicles (AUVs) play a vital
role in surveillance and monitoring tasks by flexibly
providing seamless coverage for the Internet-of-Underwater
Things (IoUT) networks. These AUVs are usually equipped
with diverse payloads for acoustic communications energy
supply and information processing, which can be viewed as
underwater mobile nodes constituting AUV-assisted IoUT [1].
To elaborate, AUVs along with seabed fixed nodes and surface
base stations construct an oceanic heterogeneous information
network, which is capable of sensing and collecting data expe-
ditiously in wide-area underwater scenarios, manual operation,
as well as traditional cast-and-collect-based underwater wire-
less sensor networks (UWSNs) in terms of both timeliness
and coverage. More explicitly, the seabed sensor nodes are
unable to be discretionarily deployed in complex underwater
terrain because of the high operational cost and, thus, fixed
nodes can only apply to high measurement in limited geo-
graphic scope. In contrast, due to high maneuverability, AUVs
are beneficial of improving the spatial and temporal scale of
the information sensing and of providing persistent and syn-
chronous information collection capability, which can support
the underwater extensive surveillance anytime and anywhere.
Due to the requirement of reliable underwater tasks, AUV
trajectory optimization is a hotspot that needs further consid-
eration [2]. In [3], Huang et al. investigated a two-phase AUV
trajectory optimization mechanism to effectively reduce the
AUV trajectory distance. Then, an in-cluster data collection
mechanism based on the matrix completion was proposed to
make a tradeoff among each IoUT node. As for optimizing
energy consumption of AUV’s maneuvering, Nam et al. in [4]
formulated an enhanced lawn mower pattern path to facili-
tate both the long-duration cooperation and the energy cost of
IoUT nodes. In general, the aforementioned studies only con-
sider the energy-efficient trajectory scheduling, but overlook
the effect of turbulence and communication status.
Most applications of IoUT require data “freshness” in order
to make timely and efficient decisions, e.g., underwater rescue
and recovery. In regards to the quest for a suitable standard of
freshness-sensitive applications, Age of Information (AoI) has
recently attracted attention as a proper metric that evaluates
task-oriented packet delivery’s timeliness [5]. AoI is different
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2 IEEE INTERNET OF THINGS JOURNAL
from latency, because AoI is applied to measure the time since
the generation of the packet that was most recently delivered
to the destination [6], while packet latency measures the time
interval between the generation and transmission of a given
packet. However, in face of the AoI-sensitive and energy-
efficient applications in AUV-aided IoUT, few considered AoI
and the queue backlogs of networks in designing the AUVs’
trajectory and resource allocation algorithms. Furthermore,
the existing underwater information collection approaches are
designed for deterministic tasks, which are not adequate for
the time-varying and stochastic optimization problems in the
context of the spatiotemporal complexity of the underwater
environment.
Considering the above-mentioned open challenges, we pro-
pose a stochastic optimization-aided multi-AUV information
collection architecture to strike a tradeoff between system
energy efficiency, queue stability, and AoI for IoUT consid-
ering the turbulent currents. Our main contributions can be
summarized as follows.
1) To the best of our knowledge, this is the first work
that studies the energy-efficient underwater information
collection scheme in the context of the multi-AUV het-
erogeneous acoustic communication model considering
the turbulent ocean environments, which also balance
the AoI and the stability of network backlogs.
2) We obtain the approximate optimal AUV trajectory strat-
egy relying on the swarm optimization. Moreover, a
two-stage joint optimization algorithm is investigated for
the power control and computational resource allocation
scheme in our proposed system. Both Lyapunov-based
approach [7]–[9] and augmented Lagrange multiplier
(ALM) method are used to approximately solve a series
of convex subproblems.
3) For the sake of evaluating the feasibility and superiority
of our proposed stochastic optimization, simulations are
conducted in terms of the energy efficiency, time average
AoI, as well as the congestion of network queues within
instabilities and currents.
The remainder of this article is structured as follows. The
system model is detailed in Section III. Then, problem for-
mulation and its solutions are proposed in Section IV, where
the stochastic optimization is utilized to transform the non-
convex problem and a two-stage joint optimization algorithm
is also developed. In Section V, we conduct performance
analysis for the proposed multi-AUV-assisted information
collection scheme for IoUT, followed by our conclusion
in Section VI.
II. RELATED WORKS
As a burgeoning underwater communication facilitator,
AUV-assisted underwater networks are characterized by flex-
ibility and robustness [10]–[12]. Nevertheless, the chal-
lenges of time-varying and frequency-dependent channel
have a great impact on the communication of AUV-assisted
IoUT [13]–[17]. For instance, the radio waves are strongly
absorbed, and acoustic communication is the only feasible
technique for large-area underwater environments. However, in
comparison to radio-wave communication, the acoustic com-
munication leads to large latency due to the its transmission
speed in water, which is about 1.5×103m/s. Specifically,
Jiang [18] summarized the effect of slow propagation speed
on mobile IoUT devices, which caused abominable distortion
and Doppler effect leading to high dynamics of channel states.
Many mobile or fixed underwater nodes in real-world sce-
narios are equipped with the frequency synchronization for
efficient reception accordingly. Moreover, the underwater ener-
getic flows, instabilities, and rapids can strongly threaten the
safety deployment of AUV. Mahmoudzadeh et al. [19] investi-
gated the turbulent characteristics of oceans, which disturb the
velocity and direction of AUV. In order to address the afore-
mentioned issues, researchers have designed various methods
for the AUV’s trajectory scheduling in underwater environ-
ments. Specifically, Mahmoudzadeh et al. [20] presented a
differential evolution (DE) algorithm for AUV path planning
within a complex 3-D underwater environment incorporated
with turbulent current vector fields. In [21], Yao et al. proposed
an improved GA (IGA) incorporating grey wolf optimization
(GWO) to optimize the feasible path within the ocean envi-
ronment with complicated static and dynamic obstacles as
well as the ocean current. In [22], Li et al. introduced a
mission-planning method to generate mobile charger trajec-
tories considering environmental constraints, such as currents
and obstacles. However, they mostly focused their attention on
kinematical planning and optimization. Particularly, in the case
of the underwater static or dynamic obstacle avoidance, few
considered the requirement of reliable, energy-efficient, and
timely information collection for IoUT under the condition of
the dynamics acoustic channel.
The trajectory scheduling methods in AUV-aided IoUT
networks have been widely investigated in the literature. For
instance, Han et al. in [23] proposed a stratification-based
data collection scheme for 3-D IoUT, which combined the
advantages of the multihop sensor networks and AUV-aided
scheme to reduce the energy consumption and to prolong the
network lifetime. In [24], Gjanci et al. defined a greedy and
adaptive AUV path-finding heuristic to improve the Value of
Information (VoI) of the data by solving an integer linear pro-
gramming (ILP) problem. Overall, the aforementioned studies
mainly focused their attention on the network architectures
and protocol design for IoUT without considering network
stability. However, IoUT networks are generally resource-
constrained system with limited memory and energy, which
results in network congestion and lifetime decrease [25]. For
the purpose of striking a tradeoff among energy efficiency
and other network metrics, energy-efficient techniques for
Internet of Things (IoT) have been widely investigated in
the literature [26], [27]. Specifically, considering the diffi-
culties of smoke detection, Khan et al. [28] proposed an
energy-efficient system based on deep convolutional neural
networks. Zhou et al. [29] developed a flexible framework,
namely, BEGIN, to combine big data analytics with vehicular
edge computing, and its the superiority of energy efficiency
has been verified. In [30], Ji et al. investigated a coopera-
tive secrecy transmission mechanism based on UAV selec-
tion and energy harvesting (EH) schemes. Pang et al. [31]
FANG et al.: STOCHASTIC OPTIMIZATION-AIDED ENERGY-EFFICIENT INFORMATION COLLECTION 3
TAB LE I
SUMMARY OF KEY NOTATIONS
conceived a hybrid precoding and power allocation scheme to
maximize the energy efficiency of mmWave-enabled NOMA-
UAV networks. In [32], Wang et al. proposed a UAV-assisted
NOMA scheme to realize simultaneous wireless information
and power transfer (SWIPT) and ensure the secure trans-
mission for ground passive receivers (PRs). Nevertheless, the
aforementioned articles mostly payed attention to the network
facilities on land, but ignored the energy efficiency of the
IoUT.
In carefully considering the timeliness of the data, making
a tradeoff between AoI and energy efficiency is critical. For
instance, Arafa et al. [6] proposed an optimal renewal pol-
icy to minimize the AoI of the sensor with finite batteries.
Zhang et al. [33] has proposed a joint sensing, transmission
and trajectory optimization algorithm for minimizing the UAV-
aided networks’ AoI. However, the aforementioned works
mainly focused on the AoI of wireless sensor networks on
land. Therefore, taking into account the underwater emergency
and energy-limited applications, it is significant to strike a bal-
ance between AoI and energy efficiency for IoUT under the
constraint of underwater spatial-temporal complexity.
III. SYSTEM MODEL
In this section, we first illustrate a heterogeneous AUV-
aided information collection architecture is proposed in
Fig. 1. Illustration of the multi-AUV-assisted data-sensing model.
Section III-A, and we also investigate the dynamic char-
acteristics of queue backlogs in IoUT networks. Then, the
underwater acoustic channel analysis is modeled based on
frequency-division multiple access (FDMA) in Section III-B.
In Section III-C, we model the turbulent ocean environment
based on the Navier–Stokes equation. Finally, the analysis of
AoI is conducted to measure the timeliness of information
collection.
A. Multi-AUV-Assisted Data Sensing and Processing Model
In this work, we formulate a heterogeneous AUV-aided
information collection architecture as illustrated in Fig. 1,
which has KIoUT node clusters. We deploy one AUV named
H-AUV for each cluster, which can only move horizontally at
a fixed depth. Specifically, we consider one H-AUV is able to
get mission trajectory and serves the kth sensor cluster with
MIoUT nodes. Equipped with the acoustic communication
unit, H-AUV is capable of collecting information by the peri-
odic movement from starting point to the IoUT node cluster
and back to it again. For the purpose of saving the information
storage space as well as improving the transmission efficiency,
H-AUV needs to process data, such as media data compres-
sion. Furthermore, we deploy one AUV named V-AUV that
only moves vertically. V-AUV is assigned to receive H-AUV
data processed at fixed position. After exchanging information
with H-AUV, V-AUV surfaces and uploads the information to
the off-shore stations or satellites, then it returns to the fixed
position.
Let Mk,idenote the ith IoUT node in the kth cluster Mk,
which has MIoUT nodes. For the sake of introducing the
stochastic optimization approach, the underwater information
collection system is analyzed in discrete time. Tkdenotes the
number of time slots elapsed in H-AUV’s trajectory, and τ
denotes the time slot length. For simplicity, we assume that τ
is small sufficiently to ensure the channel state and the position
of AUV approximately unchanged during the same time slot.
Due to the uncertainty of observation signals, we assume
that the nonnegative value of ak,i(t)represents the amount
of packets updated at sensor nodes Mk,iduring time slot t.
The value of bk,i(t)denotes the amount of data of H-AUV
received in the time slot t. For the underwater acoustic chan-
nel, bk,i(t)is assumed to be nonnegative. It is noted that
4 IEEE INTERNET OF THINGS JOURNAL
H-AUVs are designed to deal with compressed/encoded data
from each IoUT node and gk,i(t)represents the data executed
by H-AUV from Mk,iin the time slot t, namely, the com-
putational capacity of H-AUV. Let Qk,i(t)denote the data
backlogs in Mk,iover discrete time slots t∈Tk. Thus,
the queue backlogs in the cluster Mkcan be defined as
Qk(t)={Qk,1(t), Qk,2(t),...,Qk,M(t)}. Because the future
system states are driven by stochastic arrival ak,i(t)and the
computational capacity of H-AUV, backlogs Qk,i(t)can be
obtained by the following dynamic equation:
Qk,i(t+1)=maxQk,i(t)−bk,i(t), 0+ak,i(t). (1)
After IoUT nodes’ packets are transmitted in the time slot
t, H-AUV has corresponding Mindependent queue buffers
Lk(t)={Lk,1(t), Lk,2(t),...,Lk,M(t)}to store the received
packets. For the sake of saving storage, H-AUV has to com-
press received data by making full use of CPU computational
capabilities. Similarly, we can obtain the iteration equation of
the data backlogs in H-AUV as
Lk,i(t+1)=maxLk,i(t)−gk,i(t), 0+bk,i(t). (2)
The processing density can be given by ρc, which means the
amount of CPU cycle required to handle one bit of data. We
define fA
k,i(t)as the dynamic CPU frequency of H-AUV in the
time slot t
fA
k,i(t)=ρcgk,i(t)
τ.(3)
According to [34], the relationship between the CPU-cycle
frequency and total CPU energy consumption of task process-
ing can be obtained by:
ES→H
Ck(t)=
M
i=1
κfA
k,i(t)3
τ(4)
where ES→H
Ck(t)denotes the unit energy consumption for H-
AUV computing in the ith cluster in the time slot t.Letκbe
the effective switched capacitance of the CPU. Considering
ak,i(t)≥0 and bk,i(t)≥0, (1) and (2) indicate that Qk,i(t)
and Lk,i(t)are nonnegative. In order to avoid the queue conges-
tion and facilitate the energy efficiency of IoUT networks, we
utilize the Lyapunov optimization to make a tradeoff between
system stability and energy consumption in Section IV.
B. Underwater Acoustic Channel Analysis
The communication between AUV and IoUT nodes is
carried out by acoustic signals, which is governed by the atten-
uation of underwater acoustic propagation. Moreover, in the
context of the short-distance transmission in shallow sea areas,
our scenario only considers the line-of-sight (LOS) trans-
mission. In order to obtain the underwater acoustic channel
capacity for LOS path, we need to investigate the environment
noise of the underwater channel, which is affected by variable
factors, such as bubbles, shipping activities and surface wind
fields. In [35], Stojanovic proposed a noise model consider-
ing turbulence shipping, wind, and other factors. Therefore,
the different types of power spectral density (p.s.d) of noisy
sources components in dB are μPa per Hz and can be obtained
as follows:
10 log Nt(fi)=17 −30 log fi(5a)
10 log Ns(fi)=40 +20s−1
2+26 log fi
−60 log(fi+0.03)(5b)
10 log Nw(fi)=50 +7.5w1
2+20 log fi−40 log(fi+0.4)
(5c)
10 log Nth(fi)=−15 +20 log fi(5d)
where fidenotes the transmitting frequency of the ith node.
Nt(fi), Ns(fi), Nw(fi), and Nth(fi)denote the corresponding
noisy sources: the turbulence, shipping, waves, and thermal
noise, respectively. Moreover, sin (5b) is the shipping activity
ranging from 0 to 1, and win (5c) denotes wind speed mea-
sured in m/s. Thus, the combined noise N(f)in the acoustic
channel yields
N(fi)=Nt(fi)+Ns(fi)+Nw(fi)+Nth(fi).(6)
Furthermore, we analyze the signal attenuation model of the
LOS path for the purpose of getting the capacity of underwater
acoustic channel. Let A(li,fi)be the acoustic path loss versus
communication frequency fiand distance libetween AUV and
the ith IoUT node, which is given by
A(li,fi)=lika(fi)li(7)
where krepresents the spreading factor, and a(fi)is the absorp-
tion coefficient, which can be expressed empirically in dB pre
km as
10 log a(fi)=0.11f2
i
1+f2
i
+44f2
i
4100 +f2
i
+2.75 ·10−4f2
i+0.003.
(8)
Due to the harsh environment of the underwater acoustic chan-
nel, we denote the frequency bandwidth by B. Moreover, the
lower bounds function of channel attenuation coefficient can
be obtained as γ(li,fi)=[A(li,fi)N(fi)]−1.
According to [36], we can get the lower band of the under-
water acoustic channel capacity, which provides a reference
for our derivation of the AUV transmission power. In order
to guarantee the simultaneous transmission of IoUT nodes in
the same cluster, we consider the communication unit of AUV
applies FDMA. Assuming that the channel is Gaussian. Then,
given a frequency band Bwithin a wide range around a sub-
channel frequency fi, the capacity for LOS path C(li,fi)at the
subchannel over distance lican be expressed as
C(li,fi)=Blog21+ηPtrγ(li,fi)
2πH·(1μPa)·B(9)
where ηdenotes the overall efficiency of electronic circuitry
and Hrepresents the depth of AUV. Then, Ptr represents the
transmission power of the ith node. Substituting bk,i(t)=
C(lL,fi)τ into (9), the corresponding transmission energy
consumption for the kth cluster on slot tcan be given by
ES→H
Tk(t)=
M
i=1
2πH·(1μPa)·B
ηγ (lL,fi)2bk,i(t)
B·τ−1τ(10)
FANG et al.: STOCHASTIC OPTIMIZATION-AIDED ENERGY-EFFICIENT INFORMATION COLLECTION 5
where τdenotes the time slot width, and bk,irepresents the
data departing from the ith IoUT node queue in the kth
cluster. Furthermore, the extremely large-scale deployment of
AUV-assisted sensor networks in the ocean environment is
characterized by the acoustic signal attenuation and under-
water spatiotemporal variability, whereas, the latter has the
negative effect on AUV’s path planning. Therefore, for the
purpose of obtaining the trajectory solution with low time
complexity, we first approximate the features of the underwater
turbulence in the following section.
C. Turbulent Ocean Environments Modeling
The operation environment of AUV is often characterized
by the complex spatiotemporal variability, specifically for the
strong current fields, which poses a threat to underwater mis-
sions. Therefore, in order to carry out safety and optimum
operations, AUVs are equipped with the horizontal acoustic
Doppler current profiler (H-ADCP) that is an acoustic monitor-
ing unit to measure the water current velocities in a horizontal
line up to hundreds of meters in front of the AUV. The ADCP
manufacturer claims to have high velocity accuracy, i.e., 1%
of measured velocity ±5 mm/s [37]. With the aid of the H-
ADCP, AUVs can sense the surrounding turbulence and avoid
the damage of energetic flows through the optimization of
trajectory scheduling. Garau et al. [38] and Yao et al. [39]
showed more information about H-ADCP, turbulence model,
and the energy cost model for AUV’s movement.
Owing to the rotation of the Earth, the current strength
of horizontal scales is much larger than the vertical strength.
Therefore, the impact of the horizontal current field remains
dominant in AUVs’ motions, considering the case of horizontal
plane. In order to more accurately model real-world turbulent
regions, the ocean current field can be modeled by the 2-D
Navier–Stokes equation as follows:
∂ω
∂t+
VC∇ω=νω (11)
where
VC=(Vx,Vy)represents the velocity field and ω
denotes the vorticity of current. Besides, νis the viscosity
of the fluid. ∇and are the gradient and Laplacian oper-
ators, respectively. To simplify this process, we provide the
2-D Navier–Stokes equation in a very approximate manner as
follows:
Vx(P(t))=− 0·(y−y0)
2πP(t)−P02
2
·⎛
⎝1−e−P(t)−P02
2
r2
0⎞
⎠(12a)
Vy(P(t))=0·(x−x0)
2πP(t)−P02
2
·⎛
⎝1−e−P(t)−P02
2
r2
0⎞
⎠(12b)
ω(P(t))=0
πr2
0
·e−P(t)−P02
2
r2
0(12c)
where P(t)and P0denote the H-AUV coordinate of the
2-D ocean plane in the time slot tand the center of Lamb
vortex, respectively. The radius and strength of the vor-
tex can be described as r0and 0, respectively. As shown
in Figs. 3 and 4, we capitalize (12) for modeling 2-D ocean
Fig. 2. H-AUV-assisted underwater information collection procedures.
current behavior in the simulation section. The main energy
consumption of AUV motions is to overcome the underwater
resistance generated by the current field. We assume H-AUVs
move along the segment at constant speed Vk·ek(t), where
ek(t)is the unitary vector. At point P(t),
VRk(P(t)) denotes
the relative velocity between H-AUV and current, which is
given by
VRk(P(t))=Vk·ek(t)−
VC(P(t)).(13)
Based on the computational fluid dynamics (CFD) meth-
ods[40], the relationship between the drag force of AUV and
its actual physical structure can be obtained by
Fd=1
2ρLACd
VRk(P(t))
2
2(14)
where Cddenotes the drag coefficient, Ais the cross-sectional
area if the AUV moves along the current direction, and ρL
is the density of seawater. According to the water resistance
function above, we can get the energy consumption of H-
AUV during the trajectory of information collection in the time
slot t
EH→V
Pk(t)=1
ζ·Fd·
VRk(P(t))
2·τ
=1
2ζ·ρL
VRk(P(t))
3
2·A·Cd·τ(15)
where ζis the conversion efficiency of electricity. The drag
force function and (15) show that it is possible to take
advantage of the energetic current that locally favors AUVs’
trajectory scheduling.
D. Analysis of AoI
In our proposed scenario, the average AoI of information
collection is mainly determined by the trajectory of H-AUV,
IoUT nodes’s sampling and transmission rate. Without loss of
generality, the storage space in IoUT nodes conform the first-
in, first-out (FIFO) principle. In order to reduce the average
AoI, each IoUT node discards data sampled before the H-
AUV reaches the data sensing area, namely, the cluster Mk.
Moreover, the nth update cycle for H-AUV’s information col-
lection is shown in Fig. 2. We use B(n)
k,S(n)
k,S(n)
k,D(n)
kand
V(n)
kdenote the nth moment of begin of the parts I, II, III,
and IV, respectively. Let T(n)
Wrepresent the moment of end of
part IV. Specifically, part I is the procedure of H-AUV moving
from the V-AUV’s position to the cluster Mk, and part II
represents the procedure of H-AUV’s information collection.
Moreover, part III denotes the procedure of H-AUV leaving
the cluster Mkto the V-AUV’s position. Besides, part IV
6 IEEE INTERNET OF THINGS JOURNAL
represents the procedure that H-AUV exchanges data with V-
AUV. T(n)
k=(D(n)
k−S(n)
k)/τ denotes the time slot elapsed in
part II. Furthermore, let the average AoI Akdenotes the aver-
age elapsed time of data collected from the sampling time to
the V-AUV receiving time, which yields
Ak=1
NT
k
M
i=1
Tk
t=1
ak,i(t)Ak,i(t)(16)
where NT
k=M
i=1Tk
t=1bk,i(t)denotes the total number of
packets collected by H-AUV. Moreover, A(n)
k,i(t)represents the
AoI of the ith IoUT nodes in the time slot t, which yields
A(n)
k,i(t)=T(n)
W−t,T(n)
W−t<Amax
Amax,T(n)
W−t≥Amax
(17)
where Amax denotes the maximum allowed AoI. Moreover,
the time elapsed ςis related to the H-AUV trajectory in
part III without relation to information collection. Therefore,
ς=V(n)
k−D(n)
kis considered as a constant vacation period.
In our scenario, the arrival of H-AUVs from different clusters
do not affect the probability of others, because the number
of H-AUVs is large and the event of each arrival is relatively
sparse with a stable rate. Therefore, it is almost impossible
that the arrival of H-AUVs occurs at the same time. Without
loss of generality, it can be assumed that the event of the H-
AUV arrival follows a Poisson process [41]. Moreover, due
to the constraint of storage, the number of H-AUVs served
by V-AUV does not exceed N,which can be modeled as
a limited service queue. We assume that service time yields
a general distribution. After the queue is empty, i.e., all H-
AUVs have been served, the V-AUV leaves for surface and
transmits data with surface stations or satellites. The time
elapsed of the V-AUV floating and diving is seen as a typ-
ical vacation period since V-AUV cannot serve H-AUV after
leaving seabed. Hence, we use a limited service M/G/1 vaca-
tion queueing system1to model this queueing system. Then,
according to [36], we can get the closed-form expression of
the waiting time as follows:
E[Wk]=ET(n)
W−V(n)
k
=1
2(N−λξ )·λξ 2+2ξ(N−λξ )
−1
λ(2)
N(1)+N(N−1)(1−N(1))−ξ
2
(18)
where ξ=TU+TDrepresents the floating and diving time
of V-AUV, and M(Z)=M−1
i=0piZidenotes the sum of
1Typically a queue can be illustrated as three variables, i.e., A/S/K,where
Aand Sdenote the arrival and service distributions, respectively. Krepresents
the number of servers. As for M/G/1 queueing system, G means the general
distribution, and M means that the interval of arrivals or the service time
yields exponential distribution.
the first Mterms of the generation function of the queue-
ing length ϒn. Since H-AUV stops the transmission procedure
when it leaves the cluster Mk. Therefore, IoUT nodes dis-
card the sensing data without transmission. Additionally, the
packets collected by H-AUV in the time slot tshould sat-
isfy T(n)
k
t=t+1bk,i(t)≥Qk,i(t), because all packets transmitted
from IoUT nodes in the time slot tshould be received by H-
AUV without considering bit error. We assume that A(n)
k,i=0
when T(n)
k
t=t+1bk,i(t)<Qk,i(t). Accordingly, A(n)
k,i(t)should
be revised as (20), as shown at the bottom of this page.
Considering (20) and (16), we can reduce the average AoI by
keeping the information up to date, which relies on the queue
stability of IoUT nodes. Therefore, the queue control scheme
based on stochastic optimization is carried out to facilitate the
queue stability in our article.
IV. PROBLEM FORMULATION
In this section, we will first illustrate the problem of mini-
mizing the weight sum of energy consumption, which can be
transformed by stochastic optimization method, namely, the
Lyapunov optimization, in Section IV-B. Finally, we decom-
pose the problem into two subproblems and address the issues
with a two-stage joint optimization algorithm.
A. Energy Cost Minimization Problem
Because the information collection and the arrivals of
H-AUV in different clusters are independent, we can decouple
the subproblem of one cluster from the optimization problem
of the whole system. After solving all the subproblems, we
can obtain the near-optimal solution for the whole system.
Therefore, we only focus on the optimization problem in
one cluster. First, we define the weighted sum of energy
consumption in the kth IoUT cluster in the time slot tas
follows:
k(t)=
M
i=1ω1ES→H
Tk,i(t)+ω2ES→H
Ck,i(t)+ω2EH→V
Pk(t)
(21)
where ω1denotes the weight of the IoUT nodes power, and
ω2represents the H-AUV’s energy consumption in the kth
cluster (ω1+ω2=1). Therefore, we formulate the following
optimization problem, which subjects to the constraints of time
average AoI, power, and trajectory as follows:
min
{bk,fk,Pk}
ETk
t=1
(t)
s.t. (22a):0≤φS→H
Tk,i(t)≤φS→H
Tmax ,t∈Tk,i∈Mk
(22b):0≤bk,i(t)≤bU
k,i(t), t∈Tk,i∈Mk
(22c):0≤gk,i(t)≤gU
k,i(t), t∈Tk,i∈Mk
A(n)
k,i(t)=⎧
⎨
⎩
minς+E[Wk]+(T(n)
W−t)τ, Amax ,T(n)
k
t=t+1bk,it≥Qk,i(t)
0,T(n)
k
t=t+1bk,it<Qk,i(t)
(20)
FANG et al.: STOCHASTIC OPTIMIZATION-AIDED ENERGY-EFFICIENT INFORMATION COLLECTION 7
(22d):
M
i=1
fA
k,i(t)≤fU
k,t∈Tk,i∈Mk
(22e):0≤φH→V
Pk(t)≤φH→V
Pmax ,t∈Tk
(22f):Pk(t)−Pk(t−1)2≤Dmax,t∈Tk
(22g):Pk(1)=PI
k,Pk(Tk)=PL
k
(22h): lim
t→∞EQk,i(t)
t=0,t∈Tk,i∈Mk
(22i): lim
t→∞ELk,i(t)
t=0,t∈Tk,i∈Mk
(22j):Ak≤Amax,t∈Tk(22)
where bkdenotes the sensor offload rate matrix {bk,i(t)}in the
kth cluster, and fkdenotes H-AUV’s CPU frequency allocated
to each task in the kth cluster. Pkrepresents the variable of
H-AUVs trajectory. Equation (22a) illustrates that each sensor
has a maximum transmission power limit of φS→H
Tmax . Moreover,
in (22b) and (22c), we assume that bU
k,i(t)=min{Qk,i(t), bmax}
and gU
k,i(t)=min{Lk,i(t), gmax}are the rate upper bounds of
the IoUT nodes transmission and H-AUVs computing capacity.
Due to the restriction of H-AUV design, the propeller power
of H-AUV does not exceed φS→H
Pmax . Furthermore, (22f)and
(22g)are the constraints of the H-AUV trajectory. Due to the
resource limits of each nodes, all the queueing system should
satisfy the mean rate stability condition in (22h) and (22i). In
order to keep the freshness of packets, the maximum-allowable
time average AoI is imposed by (22j).
The problem in (22) is a stochastic problem that is difficult
to solve. Due to its nonconvex and time-varying characteris-
tic, we cannot get satisfying results when we use traditional
approaches. Therefore, a Lyapunov optimization-based method
is introduced to solve this problem by making optimal deci-
sions in each time slot.
B. Problem Analysis
In the considered IoUT system, it is impossible to find
the global optimum of time average energy cost due to the
time-varying constraints of channels, the backlogs of nodes as
well as the ocean turbulent environment. Thus, the allowable
decisions depends only on the current system state and the
influence of action history is negligible. To solve the stochas-
tic optimization problem, we utilize a Lyapunov optimization
technique based on iterative solution by solving a single
deterministic problem in each time slot.
In this article, the Lyapunov optimization method is adopted
to make transmission and processing rate decisions under the
constraints of queue backlog, the upper bound of power as
well as the trajectory. First, we define the quadratic Lyapunov
function for the queue backlogs in the kth cluster in the time
slot tas follows:
L(k(t))
=1
2Q2
k(t)+L2
k(t)
=1
2
M
i=1Q2
k,i(t)+L2
k,i(t)(23)
where we define k(t)
=[Qk(t), Lk(t)]. Furthermore, Qk(t)
is the vector of queues in underwater acoustic IoUT nodes
from the kth cluster, and Lk(t)denotes the data queues in
the corresponding H-AUV. For the purpose of defining the
expected change in queues, we use the one-slot conditional
Lyapunov drift (k(t)) to as follows:
(k(t))
=E[L(k(t+1))−L(k(t))|k(t)].(24)
The advantage of using the Lyapunov drift is that (k(t))
depends on the current and last system states to represent the
system stability without a-priori knowledge of traffic rate or
channel probabilities. Because we hope to decrease the power
of system and keep the queue backlogs in a low congestion, the
objective function in (22) is revised as the following expression
through a drift-plus-penalty technique:
(t)
=(k(t))+VE[k(t)|k(t)].(25)
The reason of substituting the original objective function
in (22) with (25) is that we can make a tradeoff among the
energy consumption and system stability by adjusting the non-
negative value V. According to Lemma 1 and Proposition 1,
the optimization problem in (22) is rewritten as follows
min
{bk,fk,Pk}VE[(t)|(t)]
+
Tk
t=1
M
i=1Qk,i(t)ak,i(t)−bk,i(t)
+Lk,i(t)bk,i(t)−gk,i(t)
s.t. (22a),(22b),(22c),(22e),(22f),(22g)and (22j).
(26)
Since the stochastic optimization problem is still too com-
plex to solve, problem (26) requires further decomposition.
Therefore, in the following, we reformulate problem (26) as
the AUV path scheduling and two convex optimization prob-
lems. Then, a two-stage joint optimization is provided to tackle
the previous problems under the constraints.
Lemma 1: For any α≥0, β≥0 and γ≥0, we have the
following inequality:
max(α−β, 0)+γ2−α2≤β2+γ2+2α(γ−β).(27)
Proof: See Appendix A.
Proposition 1: The expression of drift-plus-penalty (t)is
given by (25). Moreover, we define the upper bounds of the
below variables bk,i(t),ak,i(t), and gk,i(t)as bU
k,i,aU
k,i, and gU
k,i.
Suppose there are Qk,i(t)≥0, bk,i(t)≥0, and ak,i(t)≥0for
all time slot t∈{0,1,...,}. For all possible (t),wehave
(t)≤ϒ+VE[(t)|(t)]+
K
k=1
M
i=1
k,i(28)
where
k,i=Qk,i(t)ak,i(t)−bk,i(t)+Lk,i(t)bk,i(t)−gk,i(t)(29)
8 IEEE INTERNET OF THINGS JOURNAL
and the constant ϒdenotes the upper bound of information
collection system states as bU
k,i,aU
k,i, and gU
k,iand yields
ϒ=1
2
K
k=1
M
i=12bU
k,i2+aU
k,i2+gU
k,i2.(30)
Proof: See Appendix B.
C. PSO-Based AUV Trajectory Scheduling
In the context of the nonconvex and NP hard characteristics,
the trajectory scheduling problem is equivalent to combination
optimization that is difficult to find the global optimal solution.
Due to the feature of low complexity and fast convergence,
the improved PSO-based algorithm is used to settle the near-
optimum solution of the above problem.
Here, we only consider one cluster and divide the trajectory
into Ntsegments that also is the dimensions of each parti-
cle. The cost function of the kth cluster can be formulated as
follows:
ϑk=
Tk
t=1M
i=1ω1ES→H
Tk,i(t)+ω2ES→H
Ck,i(t)
+ω2EH→V
Pk(t)+α0ϑv
k(31)
where Tkdenotes the number of time slots elapsed in H-AUV’s
trajectory (part II in Fig. 2). The above cost function is the
basis of the choosing the optimal dynamic routing of H-AUV.
The algorithm aims to find the near-optimum path to minimize
ϑk. We assume that v={v1,v2,...,vNv}denotes the posi-
tion set of ocean vortexes, where Nvis the amount of ocean
vortexes in cluster k.α0represents the coefficient of the dis-
tance between the vortexes, which can tear down H-AUVs.
The penalty function ϑv
kis given by
ϑv
k=
Nt
n=1
Nv
k=1
max1−dn,k
r0,0(32)
where dn,kdenotes the distance between the nth segment of
AUV path and the kth vortex center. Thus, we define ϑv
k=
ϑv
k/Npas the risky index to evaluate the safety condition of
H-AUV. For the (n+1)th iterations, the velocity update of
each particle υcan be obtained by
υ(n+1)
j=θ1·υ(n)
j+θ2r1· P(n)
j−X(n)
j!
+θ3r2· G(n)−X(n)
j!(33)
where θi(i=1,2,3)denote the weights of the inertial
part, self-component, and social-component, respectively. Let
ri(i=1,2)be the random coefficient for enhancing the ability
of searching solutions. X(n)
jis the position of the jth particle
in the nth iteration. P(n)
jand G(n)are the local optimal path
found by the jth particle and the global optimum from niter-
ations, respectively. Moreover, the dimension and number of
particles are Dpand Np, respectively. The algorithm details
are shown in Algorithm 1.
Algorithm 1 Particle Swarm Optimization-Based AUV Path
Planning
1: Initialize initial random path X(0)
j, and the iteration step
threshold .
2: Initialize aC
k,i,bC
k,i,gC
k,i.
3: Set iteration indicator n:=1.
4: repeat
5: Update iteration indicator n:=n+1.
6: for j=1toNpdo
7: υ(n+1)
j=max(υ(n+1)
j,υmin).
8: υ(n+1)
j=min(υ(n+1)
j,υmax).
9: Obtaining the path by: X(n+1)
j=X(n)
j+υ(n+1)
j
10: Getting the penalty coefficient (32) and obtaining
(31) to evaluate the function values.
11: Calculating the global best path for each iteration.
12: end for
13: Updating the velocities υ(n+1)
k,iby solving (33).
14: θ1=w×θ1, where wis damping ratio.
15: until n>,ϑk≤ϑmax are satisfied.
16: Set X
k=X(n)
kand ϑ
k=ϑ(n)
k.
D. Two-Stage Joint Optimization Solution
In this section, we propose a two-stage joint optimization
algorithm for the energy cost minimization problem in (26).
First, we decompose the original problem into two
optimization subproblems and solve them with the ALM
method. First, we obtain the near-optimal trajectory Pkby
Algorithm 1 and utilize the following convex problem to get
the optimal transmission policy at each time slot:
min
bk(t)
M
i=1ω1VES→H
Tk,i(t)+Lk,i−Qk,i(t)bk,i(t)
s.t. (22a)and (22b).(34)
In order to get the approximating optimum transmission
resource allocation bk(t)with low complexity, we introduce
a nonnegative slack vector zk(t)to convert (34) to the ALM
standard form as follows:
min
bk(t)
M
i=1ω1Vϕ·2bk,i(t)
B·τ·τ+Lk,i−Qk,i(t)bk,i(t)
s.t. bk,i(t)+zk,i(t)=ck,i(t)and (22b)(35)
where ck,i(t)=min [Blog2(1+φS→H
Tmax (t)/ϕ), Qk,i(t)] and
ϕ=([2π·(1μPa)·B·H]/[ηγ (lL,f)min]). Then, the aug-
mented Lagrangian for the problem defined in (35) is given
by
Lρ(bk(t), λk(t))=
M
i=1ω1Vϕ·2bk,i(t)
B·τ·τ+Lk,ibk,i(t)−Qk,i(t)
+λk,i(t)bk,i(t)+zk,i(t)−ck,i(t)
+ρ
2
bk,i(t)+zk,i(t)−ck,i(t)
2
2(36)
FANG et al.: STOCHASTIC OPTIMIZATION-AIDED ENERGY-EFFICIENT INFORMATION COLLECTION 9
where the nonnegative value ρis called the penalty parameter,
which can adjust the speed of ALM convergence. The advan-
tage of the penalty term is that the dual function Gρ(λk(t)) =
infb(t)Lρ(bk(t), λk(t)) becomes easier to satisfy the derivative
condition of the original function. Similar to the dual ascent
method, the ALM algorithm consists of iterating the following
equations:
b(n+1)
k,i(t)=arg min
bk,i(t)
Lρ b(n)(t), λ(n)(t)!(37a)
z(n+1)
k,i(t)=arg min
ck,i(t)
Lρ b(n+1)(t), λ(n)(t)!
=maxck,i(t)−b(n+1)
k,i(t)−λ(n)
k,i(t)/ρ, 0(37b)
λ(n+1)
k,i(t)=λ(n)
k,i(t)+ρ·b(n+1)
k,i(t)−ck,i(t)+z(n+1)
k,i(t)
(37c)
where ρdenotes a step size, and (37a) and (37b) are known
as the method of multipliers for problem (35). The method
of multipliers has good global convergence and convergence
speed compared to the dual ascent. Moreover, the stopping
criterion of ALM is that the primal and dual residuals must
be sufficiently small, i.e.,
r(n+1)
λ
2=ρ
b(n+1)
k,i(t)−ck,i(t)−z(n+1)
k,i(t)
2≤pri (38)
r(n+1)
z
2=
ck,i(t)−b(n+1)
k,i(t)−λ(n)
k,i(t)/ρ
2≤scal (39)
where pri >0 and scal >0 are feasibility tolerances for the
primal and scale feasibility conditions, respectively. Therefore,
if conditions (38) and (39) are satisfied, the iterative opera-
tion stops and obtains the optimal solution with IoUT nodes
transmission rate b
k(t)=b(n+1)
k(t). For the purpose of sav-
ing storage space, the data uploaded from the acoustic IoUT
nodes need to be compressed and processed by H-AUV’s CPU.
Furthermore, our goal is to reasonably allocate the computing
resources for uploading data from different IoUT nodes under
the conditions of trajectory Pk(t)and transmission rates b(t),
which can be illustrated as the following subproblem:
min
fk(t)
M
i=1Vω2·κfk,i(t)3τ−τ
ρcLk,i(t)fk,i(t)
s.t. (22c)and (22d).(40)
The feasible set of problem (40) is convex, and the objective
function and all inequality constraint functions are convex.
Therefore, the above optimization problem is convex. In
order to solve the inequality constrained minimization prob-
lems, the optimization of computational capability fk,i(t)can
be obtained separately by each H-AUV, because the objec-
tive function and the constraints of problem (40) can be
decomposed for individual fk,i(t). Furthermore, let α[fk,i(t)]=
Vω2κ[fk,i(t)]3−(τ/ρc)Lk,i(t)fk,i(t)denotes the objective func-
tion of problem (40). Thus, we derive α[fk,i(t)] with respect
to fk,i(t)yields
∂αfk,i(t)
∂fk,i(t)=3Vω2κfk,i(t)2−τ
ρcLk,i(t).(41)
Algorithm 2 Two-Stage Joint Resource Allocation and
Trajectory Scheduling
1: Initialize , b(0)
k(t),λ(0)
k(t),z(0)
k(t)and ck(t).
2: Set the maximum number of iteration indicators imax =
and nmax.Leti:=0 and n:=0, respectively.
3: Initialize H-AUV hovering depth d0and utilize the
Algorithm 1 to obtain the near optimum trajectory P
k=
(Pk(1), Pk(2), . . . , Pk(Tk)) and the amount of time slot Tk.
4: for t=1toTkdo
5: for i=1toMdo
6: repeat
7: n:=n+1.
8: Calculate the partial derivative of (36) to get
b(n+1)
k,i(t).
9: Update the slack variable z(n+1)
k,i(t)and Lagrangian
variable λ(n+1)
k,i(t), respectively.
10: until n=nmax or arrive the convergence:
r(n+1)
λ
2≤pri and
r(n+1)
z
2≤scal.
11: Solve the H-AUV local CPU frequency allocation
problem in (40) relying on the barrier method.
12: Get f
k,i(t)by (42).
13: end for
14: end for
15: Calculate the weighted sum of energy consumption
Tk
t=1(t)relying on (21).
By considering [(∂α[fk,i(t)])/(∂fk,i(t))]=0 and fk,i(t)<
fmax,wehaveα[fk,i(t)] is decreasing with fk,i(t)when
0<fk,i(t)<"([Lk,i(t)]/[3ρcVω2κ]), and increasing when
fk,i(t)≥"([Lk,i(t)]/[3ρcVω2κ]). Therefore, by minimizing
α[fk,i(t)], the optimal solution of the computational capability
fk,i(t)can be given by
f
k,i(t)=⎧
⎨
⎩
min#Lk,i(t)
3ρcVω2κ,fA
max,ω
2>0
fA
max,ω
2=0
(42)
where fA
max(t)=([ρcgmax]/τ), and f
k,irepresents the optimal
CPU computing resources allocated by H-AUV for each
IoUT node, and the procedure of two-stage joint optimization
algorithm for IoUT is summarized in Algorithm 2.
E. Algorithmic Complexity Analysis
The computational complexity of Algorithm 1 can be esti-
mated as O(·Np·Tk), where Tkrepresents the number of time
slots elapsed in H-AUV’s trajectory. Specifically, we define
as the upper bound of iterations of the Algorithm 1, and each
iteration needs to find the optimal solution within Npparti-
cles. Thus, Algorithm 1 consists of three nested loops, i.e., the
outermost-loop (Algorithm 1, Lines 4–15), the loop of differ-
ent particles (Algorithm 1, Lines 6–12), and the innermost-
loop (Algorithm 1, Line 10). Furthermore, the computational
complexity of Algorithm 2 is O(Tk·( ·Np+M·nmax)),
because it contains Algorithm 1 and Lyapunov optimization
method. The complexity of the latter method increases with
10 IEEE INTERNET OF THINGS JOURNAL
TAB LE I I
PARAMETERS OF THE PSO ALGORITHM
TABLE III
SIMULATION PARAMETERS
the number of time slots Tk, the amount of IoUT nodes Mand
the upper bound of iteration nmax.
V. SIMULATION RESULTS AND DISCUSSIONS
In our simulation, we consider a 400 m×300 m underwater
rectangular region, where five IoUT nodes are deployed at reg-
ular intervals (i.e., 50 m), and the positions of the vortexes are
randomly generated, which can be shown in Fig. 3. Relying on
FDMA, H-AUV receives the packets transmitted by five IoUT
nodes at the same time. Moreover, H-AUV is a small-size
AUV with ellipsoid hull, which has the length of major axis
L=1,800 mm and length of minor axis L =200 mm [43].
Unless otherwise specified, the arrival data rate of each IoUT
node is 2 ×104bps. Table II shows the parameters of PSO
algorithm for AUV path planning. The essential parameters
are summarized in Table III.
In Fig. 3, we validate the trajectory planning scheme with
different ω1(ω2=1−ω1) in the context of spatiotemporal
variability. In order to maximize the energy efficiency of the
IoUT nodes, we set ω1=0.9, namely, the MEN scheme. For
Fig. 3. AUV trajectory scheduling with the help of H-ACDP, αv
0=2×103.
improving the energy efficiency of AUV, we set ω1=0.1,
namely, the MEA scheme. If we tend to maximize the total
energy efficiency of system, we have ω1=0.5, namely, the
MTES scheme. For minimizing the trajectory distance of AUV,
the Greedy scheme denotes the shortest path without consid-
ering current. As shown in Fig. 3, the direction of the arrow
represents the direction of the turbulent velocity vector, and
the color of the arrow denotes the strength of the flow. It can be
observed that the schemes based on PSO (i.e., MEN, MEA,
and MTES) avoid the risk of ocean vortexes. Furthermore,
for the purpose of improving the energy efficiency of IoUT
nodes, the trajectory based on MEN is closer to IoUT nodes.
Otherwise, the trajectory based on MEA tries to take advan-
tage of the current field that facilitates the energy efficiency of
H-AUV’s movement. In order to make a tradeoff between five
IoUT nodes and H-AUV, the trajectory based on the METS
scheme is much closer to IoUT nodes than the MEA scheme,
which also tends to reduce energy consumption by flow resis-
tance. The Greedy scheme gets the shortest path but ignores
the risk of vortexes, which poses a threat to the H-AUV’s
mission.
Fig. 4 demonstrates the impact of the distance coefficient
of ocean vortexes α0on H-AUV’s trajectory based on MTES.
First, the paths with α0=1×102and α0=1×103encounter
the underwater risky area, because they are too closer to the
vortexes and result in the risk of mission. If α0=2×103or
α0=4×103, the paths have longer distance than the previous
schemes, but guarantee safety by avoiding danger of vortexes.
Therefore, it can be observed that higher α0can reduce the risk
of lapsing into vortexes. Fig. 5 represents the influence of dif-
ferent coefficients α0on the risk index of the AUV trajectory
with the fixed arrival data rate λn=20 kbps. As for trajectory
based on the MEN, MEA, and MTES schemes, the decrease
of ϑv
kresults from a higher α0. Moreover, the MEN and MEA
schemes have similar lower risk index values compared to the
Greedy-based trajectory. It is because Algorithm 1 can reduce
the risk of encountering turbulence by the cost function.
Fig. 6 portrays the performance of the energy efficiency
of IoUT nodes versus different arrival data rates. It can be
FANG et al.: STOCHASTIC OPTIMIZATION-AIDED ENERGY-EFFICIENT INFORMATION COLLECTION 11
Fig. 4. Capability of avoiding the risky area through Algorithm 1.
Fig. 5. Risky index ϑv
kversus the distance coefficient of ocean vortexes α0.
observed that low arrival data rate is beneficial in terms
of improving the energy efficiency of IoUT nodes. That is
because the energy consumption of underwater acoustic com-
munication races up as the growing arrival data rate λn, which
leads to the canceling effect of the high-throughput. As shown
in Fig. 6, optimized MEN scheme has better energy efficiency
for IoUT nodes with different arrival data rate. In Fig. 7, we
compare the performance of energy efficiency among four tra-
jectory schemes with λn=20 kbps versus different weighted
parameter Vin the IoUT cluster. The lower bounds of differ-
ent trajectory schemes represent the energy efficiency of IoUT
nodes based on corresponding algorithms without Lyapunov
optimization. It can be observed that each optimized scheme
is superior to the original one. That is because the Lyapunov
technique is able to optimize the transmission power and com-
putational resources in each time slot. According to the feature
of the drift-plus-penalty algorithm, reducing Vcan push the
queue backlog toward a lower congestion, and the growth
of Vleads to the higher energy efficiency of IoUT nodes.
Fig. 6. Average energy efficiency of IoUT nodes versus arrival data rate λn
(bit/s), V=2×108bit2·W−1,andα0=2×103.
Fig. 7. Average energy efficiency of IoUT nodes versus V(bit2·W−1),
λn=20 kbps, and α0=2×103.
Additionally, it can be observed that the energy efficiency of
IoUT nodes based on the MEN scheme is superior to other
schemes.
Fig. 8 depicts the average queue length of queues in
IoUT nodes (E[Lk(t)]) and H-AUV (E[Q(t)]) versus the
number of time slots. Besides, the average queue length
of IoUT nodes yields E[Lk(t)]=(1/M)M
i=1E[Lk,i(t)],
and the average queue length of H-AUV yields E[Q(t)]=
(1/M)M
i=1E[Qk,i(t)]. E[Qk(t)] based on different schemes
become unstable with V=109, because the Lyapunov
optimization is unable to make a power and congestion trade-
off when Vis large. Otherwise, E[Lk(t)] can converge when
V=109and 107, because the service rate of H-AUV is
much higher than the data transmission rate of IoUT nodes.
Compared to different schemes, the MEA scheme and greedy
scheme have low probability of congestion, which benefit from
12 IEEE INTERNET OF THINGS JOURNAL
Fig. 8. Average queue length of the IoUT nodes and the task buffers in
H-AUV versus time, λn=20 kbps, and α0=2×103. (a) Optimized MEA.
(b) Optimized MEN. (c) Optimized MTES. (d) Optimized Greedy.
Fig. 9. Average queue length of the IoUT nodes and the task buffers in
H-AUV versus V(bit2·W−1), λn=20 kbps, and α0=2×103.(a)Qk(t).
(b) Lk(t).
the shorter trajectory distance. Furthermore, IoUT nodes guar-
antee the stability of queue with V=107. However, Vcannot
be set by an arbitrary small number, because it leads to a
higher energy consumption.
In Fig. 9, we demonstrates the performance of
queue stability in IoUT nodes and H-AUV ver-
sus a different weighted parameter V. Moreover,
Qk(t)=(1/MTk)
1
M
i=1
k,
Tk
t=1E[Qk,i(t)] and
Lk(t)=(1/MTk)M
i=1Tk
t=E[Li(t)] denote the time
average queue length of IoUT nodes and H-AUV, respec-
tively. It can be observed that Qk(t)decreases rapidly with
the growth of V. It is because with the lower V, our proposed
algorithm tends to maintain the stability of queue by transmit-
ting more data from IoUT nodes. However, Lk(t)is always
at low levels without large oscillation, because the service
rate of H-AUV is greater than the acoustic transmission rate.
Fig. 10 shows the impact of the arrival data rate λnon Qk(t)
Fig. 10. Average queue length of the IoUT nodes and the task buffers in
H-AUV versus arrival data rate λn(bit/s), V=2×108bit2·W−1,and
α0=2×103.(a)Qk(t).(b)Lk(t).
Fig. 11. Average AoI of IoUT nodes versus V(bit2·W−1), and α0=
2×103. (a) Optimized MEA. (b) Optimized MEN. (c) Optimized MTES.
(d) Optimized Greedy.
and Lk(t), respectively. It can be seen that Qk(t)and Lk(t)are
increasing with the growth of λn. Intuitively, this is because
the energy consumption of communication is growing rapidly
when transmission rate becomes larger, and our proposed
algorithm has to reduce the transmission rate, which leads to
the growth of Qk(t). Figs. 9 and 10 imply that the proper V
and arrival data rate can reduce the congestion of the IoUT
nodes, and the queue in H-AUV Lk(t)is not very sensitive to
different settings.
Fig. 11 shows the influence of Vand arrival data rate on
the average AoI based on different schemes. The average AoI
of IoUT nodes increases with the growth V, because a large V
leads to the queue backlogs congestion in IoUT nodes, which
blocks the latest information updates. When Vis small, the
backlogs of IoUT nodes achieve queue stability, which guar-
antee the transmission of latest information and reduce the
average AoI. In this case, the average AoI decreases at higher
arrival data rate. However, when Vis large, it can be observed
FANG et al.: STOCHASTIC OPTIMIZATION-AIDED ENERGY-EFFICIENT INFORMATION COLLECTION 13
that a higher arrival data rate aggravates the performance of
average AoI, because there are more packets blocked in the
queues of IoUT nodes. Compared to different schemes, the
greedy scheme has a lowest average AoI for the shortest path.
Because MEN scheme tends to minimize the transmit power
of IoUT nodes, it takes a longer path, which leads to large
AoI. According to Figs. 7 and 11, we can conclude that our
proposed algorithm makes a tradeoff between the average AoI
and energy efficiency by adjusting V. However, the average
AoI can be expected to be aggravated considerably by an
excessive V.
VI. CONCLUSION
In this article, we formulated a two-stage joint power con-
trol, computational resource allocation and trajectory schedul-
ing for IoUT networks considering the turbulent ocean envi-
ronments in the context of a multi-AUV-aided heterogeneous
network for energy-efficient information collection. Since the
problem was a nonconvex stochastic problem, we divided
the problem into three subproblems associated with trajectory
scheduling, transmission power control, and computational
resource allocation. Then, based on the PSO algorithm, we
addressed the issue of avoiding the risk of vortexes and
obtained an AUV trajectory with low time complexity. For the
sake of maximizing the energy efficiency, a Lyapunov-based
technique was applied to adjust the transmission power and
AUV’s computational capability under the constraints of queue
stability. Finally, the simulation was conducted and results
showed that the performance of the MEN scheme got bet-
ter energy efficiency than MEA, MTES, and Greedy-based
algorithms. Both Vvalue and the weight factors portrayed
the tradeoff between energy efficiency and queue stability.
Furthermore, we can improve the data arrival rate to reduce
the average AoI in the condition of relatively small V.
APPENDIX A
PROOF OF LEMMA 1
Now, assume that (α −β) ≥0, the left-hand side of the
above inequality can be derived as follows:
β2+γ2+2αγ −2αβ −2βγ ≤β2+γ2+2α(γ−β)
(43)
where α≥0, β≥0, and γ≥0. Therefore, (27) is true since
(−2βγ) ≤0. Likewise, if (α −β) < 0, the left-hand side of
the above inequality can be derived as follows:
γ2−α2≤β2+γ2+2α(γ−β).(44)
Rearranging the terms in the above inequality yields (β−α)2+
2αγ ≥0. Therefore, Lemma 1 holds for all nonnegative α,β,
and γ.
APPENDIX B
PROOF OF PROPOSITION 1
Because (t)is the sum of the iterated expression
E[L((t+1)) −L((t))|(t)] and the weighted system
energy consumption VE[(t)|(t)]. Besides, Vis a parame-
ter that denotes the weight index on how much we emphasize
power efficiency minimization. Moreover, the Lyapunov drift
function can be expressed as follows:
((t))=L((t+1)) −L((t))
=1
2
K
k=1
M
i=1Q2
k,i(t+1)−Q2
k,i(t)
+L2
k,i(t+1)−L2
k,i(t) (45)
where Qk,i(τ ) ≥0 and Lk,i(τ ) ≥0, τ∈{1,2,...,}.The
Lyapunov drift function is utilized to represent the congestion
level of the underwater information system. Substituting (1)
and (2) in (45), we have
((t))=1
2
K
k=1
M
i=1maxQk,i(t)−bk,i(t),0+ak,i(t)2
−Q2
k,i(t)+maxLk,i(t)−gk,i(t),0
+bk,i(t)2−L2
k,i(t)
(46)
where Qk,i(t)≥0, bk,i(t)≥0, and ak,i(t)≥0. In order to solve
the optimization problem in each time slot, we can obtain the
bound of (t)to avoid the calculation of the iterations in (46).
According to Lemma 1, the above inequality can be simplified
as follows:
((t))≤
K
k=1
M
i=1ak,i(t)2
2+gk,i(t)2
2+bk,i(t)2+k,i
≤
K
k=1
M
i=1⎧
⎪
⎨
⎪
⎩
aU
k,i(t)2
2+gU
k,i(t)2
2
+bU
k,i(t)2+k,i⎫
⎪
⎬
⎪
⎭
=ϒ+
K
k=1
M
i=1
k,i.(47)
Substituting (25) into the above inequality, namely, we add
VE[(t)|(t)] to both sides of (47), the bound of the drift-
plus-penalty expression yields Proposition 1.
REFERENCES
[1] G. Han, X. Long, C. Zhu, M. Guizani, and W. Zhang, “A high-
availability data collection scheme based on multi-AUVs for under-
water sensor networks,” IEEE Trans. Mobile Comput., vol. 19, no. 5,
pp. 1010–1022, Mar. 2020.
[2] C.Lin,G.Han,J.Du,Y.Bi,L.Shu,andK.Fan,“Apathplanning
scheme for AUV flock-based Internet of Underwater Things systems to
enable transparent and smart ocean,” IEEE Internet Things J.,vol.7,
no. 10, pp. 9760–9772, Oct. 2020.
[3] M. Huang, K. Zhang, Z. Zeng, T. Wang, and Y. Liu, “An AUV-assisted
data gathering scheme based on clustering and matrix completion for
smart ocean,” IEEE Internet Things J., vol. 7, no. 10, pp. 9904–9918,
Oct. 2020.
[4] H. Nam, “Data-gathering protocol-based AUV path-planning for long-
duration cooperation in underwater acoustic sensor networks,” IEEE
Sensors J., vol. 18, no. 21, pp. 8902–8912, Nov. 2018.
14 IEEE INTERNET OF THINGS JOURNAL
[5] I. Kadota, A. Sinha, and E. Modiano, “Optimizing age of information
in wireless networks with throughput constraints,” in Proc. IEEE
Conf. Comput. Commun. (INFOCOM), Honolulu, HI, USA, Apr. 2018,
pp. 1844–1852.
[6] A. Arafa, J. Yang, S. Ulukus, and H. V. Poor, “Age-minimal transmission
for energy harvesting sensors with finite batteries: Online policies,” IEEE
Trans. Inf. Theory, vol. 66, no. 1, pp. 534–556, Jan. 2020.
[7] Y. Li, S. Xia, M. Zheng, B. Cao, and Q. Liu, “Lyapunov optimization
based trade-off policy for mobile cloud offloading in heterogeneous
wireless networks,” IEEE Trans. Cloud Comput., early access, Aug. 30,
2019, doi: 10.1109/TCC.2019.2938504.
[8] K. W. Choi and D. I. Kim, “Stochastic optimal control for wireless pow-
ered communication networks,” IEEE Trans. Wireless Commun., vol. 15,
no. 1, pp. 686–698, Jan. 2016.
[9] N. Moghadam, H. Li, H. Zeng, and L. Liu, “Lyapunov scheduling and
optimization in network coded wireless multicast network,” IEEE Trans.
Veh. Technol., vol. 67, no. 6, pp. 5135–5145, Jun. 2018.
[10] I. Jawhar, N. Mohamed, J. Al-Jaroodi, and S. Zhang, “An architecture
for using autonomous underwater vehicles in wireless sensor networks
for underwater pipeline monitoring,” IEEE Trans. Ind. Informat., vol. 15,
no. 3, pp. 1329–1340, Mar. 2019.
[11] M. T. R. Khan, S. H. Ahmed, and D. Kim, “AUV-aided energy-efficient
clustering in the Internet of Underwater Things,” IEEE Trans. Green
Commun. Netw., vol. 3, no. 4, pp. 1132–1141, Dec. 2019.
[12] C. Lin, G. Han, M. Guizani, Y. Bi, J. Du, and L. Shu, “An SDN
architecture for AUV-based underwater wireless networks to enable
cooperative underwater search,” IEEE Wireless Commun., vol. 27, no. 3,
pp. 132–139, Jun. 2020.
[13] J. Yan, X. Yang, X. Luo, and C. Chen, “Energy-efficient data collection
over AUV-assisted underwater acoustic sensor network,” IEEE Syst. J.,
vol. 12, no. 4, pp. 3519–3530, Dec. 2018.
[14] Z. Gong, C. Li, and F. Jiang, “AUV-aided joint localization and time
synchronization for underwater acoustic sensor networks,” IEEE Signal
Process. Lett., vol. 25, no. 4, pp. 477–481, Apr. 2018.
[15] T. Wang, D. Zhao, S. Cai, W. Jia, and A. Liu, “Bidirectional
prediction-based underwater data collection protocol for end-edge-cloud
orchestrated system,” IEEE Trans. Ind. Informat., vol. 16, no. 7,
pp. 4791–4799, Jul. 2020.
[16] S. Guan, J. Wang, C. Jiang, R. Duan, Y. Ren, and T. Q. S. Quek,
“MagicNet: The maritime giant cellular network,” IEEE Commun. Mag.,
vol. 59, no. 3, pp. 117–123, Mar. 2021.
[17] T. Qiu, Z. Zhao, T. Zhang, C. Chen, and C. L. P. Chen, “Underwater
Internet of Things in smart ocean: System architecture and open issues,”
IEEE Trans. Ind. Informat., vol. 16, no. 7, pp. 4297–4307, Jul. 2020.
[18] S. Jiang, “On reliable data transfer in underwater acoustic networks:
A survey from networking perspective,” IEEE Commun. Surveys Tuts.,
vol. 20, no. 2, pp. 1036–1055, 2nd Quart., 2018.
[19] S. Mahmoudzadeh, D. M. W. Powers, A. M. Yazdani, K. Sammut, and
A. Atyabi, “Efficient AUV path planning in time-variant underwater
environment using differential evolution algorithm,” J. Mar. Sci. Appl.,
vol. 17, no. 4, pp. 585–591, Sep. 2018.
[20] S. Mahmoudzadeh, D. M. W. Powers, and A. Atyabi, “UUV’s hierarchi-
cal DE-based motion planning in a semi dynamic underwater wireless
sensor network,” IEEE Trans. Cybern., vol. 49, no. 8, pp. 2992–3005,
Aug. 2019.
[21] P. Yao, Z. Zhao, and Q. Zhu, “Path planning for autonomous underwater
vehicles with simultaneous arrival in ocean environment,” IEEE Syst. J.,
vol. 14, no. 3, pp. 3185–3193, Sep. 2020.
[22] B. Li, B. R. Page, J. Hoffman, B. Moridian, and N. Mahmoudian,
“Rendezvous planning for multiple AUVs with mobile charging sta-
tions in dynamic currents,” IEEE Robot. Autom. Lett., vol. 4, no. 2,
pp. 1653–1660, Apr. 2019.
[23] G. Han, S. Shen, H. Song, T. Yang, and W. Zhang, “A stratification-
based data collection scheme in underwater acoustic sensor networks,”
IEEE Trans. Veh. Technol., vol. 67, no. 11, pp. 10671–10682, Nov. 2018.
[24] P. Gjanci, C. Petrioli, S. Basagni, C. A. Phillips, L. Bölöni, and
D. Turgut, “Path finding for maximum value of information in multi-
modal underwater wireless sensor networks,” IEEE Trans. Mobile
Comput., vol. 17, no. 2, pp. 404–418, Feb. 2018.
[25] H. Luo, K. Wu, R. Ruby, Y. Liang, Z. Guo, and L. M. Ni, “Software-
defined architectures and technologies for underwater wireless sensor
networks: A survey,” IEEE Commun. Surveys Tuts., vol. 20, no. 4,
pp. 2855–2888, 4th Quart., 2018.
[26] J. Du, C. Jiang, J. Wang, Y. Ren, and M. Debbah, “Machine learning
for 6G wireless networks: Carry-forward-enhanced bandwidth, massive
access, and ultrareliable/low latency,” IEEE Veh. Technol. Mag., vol. 15,
no. 4, pp. 123–134, Dec. 2020.
[27] J. Wang, C. Jiang, H. Zhang, Y. Ren, K.-C. Chen, and L. Hanzo,
“Thirty years of machine learning: The road to Pareto-optimal wireless
networks,” IEEE Commun. Surveys Tuts., vol. 22, no. 3, pp. 1472–1514,
3rd Quart., 2020.
[28] S. Khan, K. Muhammad, S. Mumtaz, S. W. Baik, and
V. H. C. de Albuquerque, “Energy-efficient deep CNN for smoke
detection in foggy IoT environment,” IEEE Internet Things J.,vol.6,
no. 6, pp. 9237–9245, Dec. 2019.
[29] Z. Zhou, H. Yu, C. Xu, Z. Chang, S. Mumtaz, and J. Rodriguez,
“BEGIN: Big data enabled energy-efficient vehicular edge computing,”
IEEE Commun. Mag., vol. 56, no. 12, pp. 82–89, Dec. 2018.
[30] B. Ji, Y. Li, D. Cao, C. Li, S. Mumtaz, and D. Wang, “Secrecy
performance analysis of UAV assisted relay transmission for cognitive
network with energy harvesting,” IEEE Trans. Veh. Technol., vol. 69,
no. 7, pp. 7404–7415, Jul. 2020.
[31] X. Pang, J. Tang, N. Zhao, X. Y. Zhang, and Y. Qian, “Energy-efficient
design for mmwave-enabled NOMA-UAV networks,” Sci. China Inf.
Sci., vol. 64, Jul. 2021, Art. no. 140303.
[32] W. Wang et al., “Joint precoding optimization for secure SWIPT in
UAV-aided NOMA networks,” IEEE Trans. Commun., vol. 68, no. 8,
pp. 5028–5040, Aug. 2020.
[33] S. Zhang, H. Zhang, Z. Han, H. V. Poor, and L. Song, “Age of
information in a cellular Internet of UAVs: Sensing and communica-
tion trade-off design,” IEEE Trans. Wireless Commun., vol. 19, no. 10,
pp. 6578–6592, Oct. 2020.
[34] J. Zhang et al., “Stochastic computation offloading and trajectory
scheduling for UAV-assisted mobile edge computing,” IEEE Internet
Things J., vol. 6, no. 2, pp. 3688–3699, Apr. 2019.
[35] M. Stojanovic, “On the relationship between capacity and distance in
an underwater acoustic communication channel,” ACM SIGMOBILE
Mobile Comput. Commun. Rev., vol. 11, no. 4, pp. 34–43, Oct. 2007.
[36] Z. Fang, J. Wang, C. Jiang, Q. Zhang, and Y. Ren, “AoI inspired
collaborative information collection for AUV assisted Internet of
Underwater Things,” IEEE Internet Things J., early access, Jan. 5, 2021,
doi: 10.1109/JIOT.2021.3049239.
[37] Z. Zeng, K. Sammut, A. Lammas, F. He, and Y. Tang, “Efficient path
re-planning for AUVs operating in spatiotemporal currents,” J. Intell.
Robot. Syst., vol. 79, no. 1, pp. 135–153, 2015.
[38] B. Garau, A. Alvarez, and G. Oliver, “AUV navigation through turbulent
ocean environments supported by onboard H-ADCP,” in Proc. IEEE Int.
Conf. Robot. Autom. (ICRA), Orlando, FL, USA, 2006, pp. 3556–3561.
[39] X. Yao, F. Wang, J. Wang, and X. Wang, “Bilevel optimization-based
time-optimal path planning for AUVs,” Sensors, vol. 18, no. 12, p. 4167,
Nov. 2018.
[40] K. M. Tan, T.-F. Lu, and A. Anvar, “Drag coefficient estimation model
to simulate dynamic control of autonomous underwater vehicle (AUV)
motion,” in Proc. 20th Int. Congr. Model. Simulat. (MODSIM), Adelaide,
SA, Australia, Dec. 2013, pp. 963–969.
[41] L. Kleinrock, Queueing Systems, vol. 1. New York, NY, USA: Wiley,
1974.
[42] A. T. De Almeida, F. J. T. E. T. E. Ferreira, and J. A. C. Fong, “Standards
for efficiency of electric motors,” IEEE Ind. Appl. Mag., vol. 17, no. 1,
pp. 12–19, Jan./Feb. 2011.
[43] J. V. N. de Sousa, A. R. L. De Macêdo, W. F. de Amorim, Jr., and
A. G. B. De Lima, “Numerical analysis of turbulent fluid flow and drag
coefficient for optimizing the AUV hull design,” Open J. Fluid Dyn.,
vol. 4, no. 3, pp. 263–277, Sep. 2014.
Zhengru Fang (Student Member, IEEE) received
the B.S. degree in electronics and information engi-
neering from Huazhong University of Science and
Technology, Wuhan, China, in 2019. He is currently
pursuing the M.S. degree in electronics and com-
munication engineering from Tsinghua University,
Beijing, China.
His research interests lie in the areas of Internet
of Underwater Things, age of information, queueing
theory, and mobile-edge computing.
Mr. Fang has been serving as a Reviewer for
IEEE INTERNET OF THINGS JOURNAL, IEEE SYSTEMS JOURNAL, IEEE
ACCESS, IEEE GLOBECOM and IEEE ICCC.
FANG et al.: STOCHASTIC OPTIMIZATION-AIDED ENERGY-EFFICIENT INFORMATION COLLECTION 15
Jingjing Wang (Senior Member, IEEE) received
the B.S. degree in electronic information engi-
neering from Dalian University of Technology,
Dalian, China, in 2014, and the Ph.D. degree in
information and communication engineering from
Tsinghua University, Beijing, China, in 2019, both
with the highest honors.
From 2017 to 2018, he visited the Next
Generation Wireless Group chaired by Prof. Lajos
Hanzo, University of Southampton, Southampton,
U.K. He is currently a Postdoctoral Researcher with
the Department of Electronic Engineering, Tsinghua University. His research
interests include resource allocation and network association, learning theory-
aided modeling, analysis and signal processing, as well as information
diffusion theory for mobile wireless networks.
Dr. Wang was a recipient of the Best Journal Paper Award of IEEE ComSoc
Technical Committee on Green Communications and Computing in 2018, and
the Best Paper Award from IEEE ICC and IWCMC in 2019.
Jun Du (Member, IEEE) received the B.S. degree
in information and communication engineering from
Beijing Institute of Technology, Beijing, China,
in 2009, and the M.S. and Ph.D. degrees in
information and communication engineering from
Tsinghua University, Beijing, in 2014 and 2018,
respectively.
From October 2016 to September 2017, she was
a Sponsored Researcher, and she visited Imperial
College London, London, U.K. She currently holds
a Postdoctoral position with the Department of
Electrical Engineering, Tsinghua University. Her research interests are mainly
in resource allocation and system security of heterogeneous networks and
space-based information networks.
Dr. Du is the recipient of the Best Student Paper Award from IEEE
GlobalSIP in 2015, the Best Paper Award from IEEE ICC 2019, and the
Best Paper Award from IWCMC in 2020.
Xiangwang Hou (Student Member, IEEE) received
the B.E. degree from Shandong University of
Technology, Zibo, China, in 2017, and the M.E.
degree from Xidian University, Xi’an, China, in
2020. He is currently pursuing the Ph.D. degree with
Tsinghua University, Beijing, China.
He has worked as an Algorithm Engineer with
2012 Laboratory, Huawei Technologies Co., Ltd.,
Hong Kong, and the Department of Electronic
Engineering, Tsinghua University, from 2020 to
2021. His research interests include edge intelli-
gence, UAV networks, and wireless AI.
Mr. Hou received the Outstanding Graduate Award of Shandong Province
in 2017 and the China Postgraduate National Scholarship Award in 2019.
Yong Ren (Senior Member, IEEE) received the B.S.,
M.S., and Ph.D. degrees in electronic engineering
from Harbin Institute of Technology, Harbin, China,
in 1984, 1987, and 1994, respectively.
He has worked as a Postdoctoral Fellow with
the Department of Electrical Engineering, Tsinghua
University, Beijing, China, from 1995 to 1997,
where he is currently a Full Professor with the
Department of Electronic Engineering and serves as
the Director of the Complexity Engineered Systems
Laboratory. He has authored or co-authored more
than 400 technical papers in the area of computer network and mobile
telecommunication networks. His current research interests include complex
system theory and its applications to the optimization of the Internet, Internet
of Things, and ubiquitous network, cognitive networks, and cyber–physical
systems.
Prof. Ren has served as a reviewer for more than 40 international journals
or conferences.
Zhu Han (Fellow, IEEE) received the B.S. degree
in electronic engineering from Tsinghua University,
Beijing, China, in 1997, and the M.S. and Ph.D.
degrees in electrical and computer engineering from
the University of Maryland, College Park, MD,
USA, in 1999 and 2003, respectively.
From 2000 to 2002, he was a Research and
Development Engineer with JDSU, Germantown,
MD, USA. From 2003 to 2006, he was a Research
Associate with the University of Maryland. From
2006 to 2008, he was an Assistant Professor with
Boise State University, Boise, ID, USA. Currently, he is a John and Rebecca
Moores Professor with the Electrical and Computer Engineering Department
as well as the Computer Science Department, University of Houston, Houston,
TX, USA. His research interests include wireless resource allocation and man-
agement, wireless communications and networking, game theory, big data
analysis, security, and smart grid.
Dr. Han received an NSF Career Award in 2010, the Fred W. Ellersick
Prize of the IEEE Communication Society in 2011, the EURASIP Best Paper
Award for the Journal on Advances in Signal Processing in 2015, the IEEE
Leonard G. Abraham Prize in the field of Communications Systems (Best
Paper Award in IEEE JSAC) in 2016, and several Best Paper Awards in
IEEE conferences. He is also the winner of the 2021 IEEE Kiyo Tomiyasu
Award, for outstanding early to mid-career contributions to technologies hold-
ing the promise of innovative applications, with the following citation: “for
contributions to game theory and distributed management of autonomous com-
munication networks.” He has been a 1% highly cited researcher since 2017,
according to Web of Science. He was an IEEE Communications Society
Distinguished Lecturer from 2015 to 2018, and has been an AAAS Fellow
since 2019, and an ACM Distinguished Member since 2019.
