0018-9545 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TVT.2020.3007263, IEEE
Transactions on Vehicular Technology
1
Resource Cube: Multi-Virtual Resource
Management for Integrated Satellite-Terrestrial
Industrial IoT Networks
Danyang Chen
∗
, Chungang Yang
∗
, Peng Gong
†
, Lizhong Chang
∗
, Junqi Shao
∗
, Qiang Ni
‡
, Alagan
Anpalagan
§
, Mohsen Guizani
¶
Abstract—Industrial Internet of Things (IIoT) has found
wider research, and satellite-terrestrial network (STN) can
provide large-scale seamless connections for IIoT. With virtu-
alization, we design resource cube to describe the integration
and state of multi-dimensional virtual resources. To achieve
higher resource utilization and smarter connections, we
design a matching considered preferences (MCPR) algorithm
to match IIoT nodes with service sides. The matching design
considers the resource cube (MCRC) algorithm based on
MCPR algorithm to lower the total system delay. In addition,
in order to simplify the analysis of resource management, we
adopt a layered architecture and multiple M/M/1 queuing
models. We analyze the resource utilization and the total
system delay for three different combinations of arrival
rate and service rate of each resource cube. With MCRC
algorithm, the utilization of resources is slightly reduced,
while the total system delay is greatly reduced compared
with MCPR algorithm.
Index Terms—Internet of Things, multi-virtual resource
management, satellite-terrestrial network, virtualization
Copyright (c) 2015 IEEE. Personal use of this material is permit-
ted. However, permission to use this material for any other purpos-
es must be obtained from the IEEE by sending a request to pubs-
permissions@ieee.org.
∗
D. Chen, C. Yang, L. Chang, and J. Shao are
with the State Key Laboratory on Integrated Services
Networks, Xidian University, Xi’an, 710071 China (e-
mails: Cdanyang_chen@163.com; chgyang2010@163.com;
lzchang.66@foxmail.com; ruya0905@163.com); and C. Yang is also
supported by National Mobile Communications Research Laboratory,
Southeast University.
†
P. Gong is with Beijing Institute of Technology, Beijing, 100081,
China (email: penggong@bit.edu.cn).
‡
Q. Ni is with School of Computing and Communications, Lancaster
University, Lancaster, UK. (email: q.ni@lancaster.ac.uk).
§
A. Anpalagan is with the Department of Electrical and Com-
puter Engineering, Ryerson University, Toronto, ON, Canada (email:
alagan@ee.ryerson.ca).
¶
M. Guizani is with Electrical and Computer Engineering Depart-
ment University of Idaho, Idaho, USA. (email: mguizani@ieee.org).
This work was supported in part by the National Science Foun-
dation of China (61871454); by the open research fund of Nation-
al Mobile Communications Research Laboratory, Southeast University
(No. 2019D10); by the Fundamental Research Funds for the Central
Universities (JB190119); by the National Science Foundation of China
under Grants 61671062; by the CETC Key Laboratory of Data Link
Technology (CLDL-20182308). Prof. P. Gong’s work was supported
in part by the National Key Research and Development Program of
China under Grant 2018YFC0823003 and the National Natural Science
Foundation of China under Grant 61671062.
I. INTRODUCTION
With the development of the next generation networks
and the Industry 4.0, there will be multiple traffic types
of Internet applications under different network scenarios,
leading to different requirements and different represen-
tative applications. For example, Machine Type Com-
munication represented by the IoT, whose purpose is to
realize the connectivity of all things around us. Enhanced
mobile broadband pursues the ultimate communication
experience between people, which requires large traffic,
wide frequency band and high frequency utilization [1].
Self-driving cars are a representative application of Ultra
Reliable Low Latency Communications, which requires
low latency and reliable connectivity [2]. Among these
new and diverse network scenarios and applications, the
Industrial IoT (IIoT) plays an important role with the
development of Industry 4.0.
Predicted by Cisco, there will be 50 billion devices
connected to the Internet by 2020 [3]. Furthermore, the
continuous development of the IIoT puts forward higher
requirements for network service capability. First of all,
with the rise of emerging applications, the IIoT has pro-
posed a broader need for network coverage, even beyond
the terrestrial network coverage. Meanwhile, a large num-
ber of IIoT applications increase the demand for network
resources, and the terrestrial network is difficult to provide
network resources that meet all IIoT requirements in some
cases. As a result, single terrestrial networks can hardly
meet requirements of multi-emerging IIoT applications.
Since the satellite networks are characterized by large
coverage and high delay, and the terrestrial networks are
characterized by small coverage and low delay, joint-
ly considering the terrestrial networks and the satellite
networks, i.e., the integrated satellite-terrestrial network
(STN), is the future development trend of network. Be-
sides, different satellites have different features. For in-
stance, low earth orbit (LEO) satellites have lower la-
tency with lower pass over time [4]. Medium earth orbit
(MEO) satellites and geostationary orbit (GEO) satellites
are characterized by broader coverage but longer delay
[5]. Therefore, the combination of multi-layer satellites
and the terrestrial networks can provide different services
Authorized licensed use limited to: Lancaster University. Downloaded on July 08,2020 at 07:30:06 UTC from IEEE Xplore. Restrictions apply.
0018-9545 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TVT.2020.3007263, IEEE
Transactions on Vehicular Technology
2
according to different needs. And it can provide more
flexible and better services for IIoT applications. Because
the satellite networks and the terrestrial networks have
different characteristics, they can complement each other.
Meanwhile, the integration of resources of the satellite
networks and the terrestrial networks can bring more
benefits and achieve more efficient and rational resource
utilization. More importantly, the STN can accomplish
tasks that are difficult to accomplish in a single network.
In the meantime, using the STN to provide services
for IIoT applications has become a tendency in industry
and academia [6]–[11]. As mentioned in [6], an integrated
satellite-terrestrial network can support IoT with virtu-
alization. In [7], the authors demonstrate the advantage
of using the LEO satellites to provide services for IoT
applications, and point out that the LEO satellites can
play an irreplaceable role in the development of the IoT.
Using the STN to support applications of the Internet of
remote things is presented in [8] with important issues
about applications using heterogeneous networks and the
promising enormous advantages. The development of the
STN can bring much more benefits for IIoT applications.
Besides, different characteristics of the terrestrial and the
satellite networks mean that they cannot simply be mixed
together. In order to simplify the process, the hierarchical
architecture [12] [13] is adopted to provide services for
broader coverage of IIoT applications.
Meanwhile, in order to manage multi-dimensional re-
sources in the STN, we adopt the virtualization technol-
ogy. There have also been some studies on the use of
virtualization in the STN [14]–[26]. Among those studies,
authors in [14]–[16] studies the architecture of the STN.
Authors in [14] consider a satellite-terrestrial architecture
with software defined features, and analyze key perfor-
mances between its resource management schemes. And
authors in [15] studies using software defined network
(SDN) in the design of architecture in multi-layered STN.
Authors in [16] propose an integrated architecture based
on SDN for managing cache resources. In addition to
studies of architecture, there are some studies about re-
sources management in the STN. Authors in [18] analyze
three dynamic resource request strategies in the satellite
networks based on queue volume and arrival rate. A cloud-
based integrated satellite-terrestrial network is proposed
in [20], considering a scenario that the terrestrial and the
satellite networks share the same frequency band. Authors
in [22] conclude the work related to the space informa-
tion network using SDN/NFV, and propose a three-tier
integrated space satellite framework based on the previous
work. They propose two heuristic algorithms to provide
fine-grained QoS assurance for multiple users. And there
also researches about the satellite gateway placement.
Authors in [23] studies the optimal configuration of satel-
lite gateway in the STN. And in [24], authors further
studies the optimal configuration of STN network satellite
gateway under the condition of latency minimization with
reliability guarantee. Hence, using virtualization to mix
the terrestrial and the satellite networks and the joint
management of multi-dimensional resources are important
trends. Meanwhile, in order to allocate resources flexibly
and improve resource utilization, we consider using the
technology of virtualization to implement the orchestra-
tion of computation, communication and storage resources
in STN. Those existing researches is mainly about the
management of one or two kinds of resources, multi-
dimensional resources are not considered.
In order to achieve efficient management of multi-
dimensional resources based on IIoT applications in the
STN, we have designed a utility function that maximizes
resource utilization within pre-defined time delay. Since
there are heterogeneous networks in STN, we choose
matching game to determine the network node that pro-
vides services for IIoT applications. As the number of
IIoT nodes increases, the network scale also becomes very
large. Meanwhile, efficient resource allocation schemes
usually require global information from the network which
is difficult to obtain as the network scale increases. While
Markov approximation can solve the problem that the
optimization problem is difficult to deal with due to
the complexity of network scale and the lack of glob-
al information. Hence we adopt the mean of matching
with Markov approximation and Markov chain [27]–[31].
Among the existing work, authors in [28] summarize
some game theories used in resource management of IoT
systems. In addition, authors in [29] use Markov chain
as an auxiliary with game theory to analyze resource
management in the satellite networks.
The contributions of this paper are as follows:
• We design resource cubes to depict the combination
of virtual communication, computation and storage
resources and implement a simple description of re-
source state transfer based on the concept of resource
cubes.
• According to the quantity of resource cubes, we set
virtual resource controllers to adjust service sides
matched by part of IIoT nodes intelligently. By
adjusting the matching results of these IIoT nodes,
unnecessary queuing delay can be avoided.
• For getting the steady-state probability involved in
using Markov approximation, we use a new method
based on Markov chain.
The remainder of this paper is organized as follows.
We describe the system architecture in section II. Section
III describes resource cubes we designed. In Section IV,
we describe matching games between IIoT nodes and
network service sides, and then in Section V use Markov
chain and Markov approximation to deal with the resource
utilization maximization problem. And Section VI and VII
give simulation results, analysis and conclusions of the
whole paper respectively.
Authorized licensed use limited to: Lancaster University. Downloaded on July 08,2020 at 07:30:06 UTC from IEEE Xplore. Restrictions apply.
0018-9545 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TVT.2020.3007263, IEEE
Transactions on Vehicular Technology
3
Satellite
Network
GEO
LEO
MEO
Cache
devices
Terrestrial
Network
Micro Base Station
Small Base Station
Sever
Cache Devices
Terrestrial
Network
IIoT
Nodes
VRC 2VRC 1 VRC n
Virtual
Resource
Controller
...
Fig. 1. The transoceanic logistics in the integrated satellite-terrestrial network
II. SYSTEM ARCHITECTURE
The application scenario considered is transoceanic
logistics, and the architecture is illustrated in Fig. 1.
It contains IIoT nodes in transoceanic logistics, virtual
resource controller (VRC), the terrestrial networks (TN)
and the satellite networks (SN). The satellite networks
consist of the LEO, the MEO and the GEO satellites.
And based on the idea of SDN, LEO is responsible for
data forwarding as the data side in the satellite network,
while MEO and GEO play roles as SDN controllers in
much circumstances, but they can also undertake data for-
warding tasks according to the requirements of IIoT node
when necessary. In order to obtain better performances,
the whole architecture adopts a hierarchical architecture.
To be simple, we put SN and TN together as service sides.
In this system, sensors are responsible for collecting
data from IIoT nodes, VRCs are responsible for selecting
service sides for IIoT nodes according to the requirements
of IIoT nodes and the number of different types of
resources owned by service sides. And VRCs are also
responsible for establishing the connection between IIoT
node and base stations or satellites. Each terrestrial or
satellite node contains computation, storage and commu-
nication resources. Different terrestrial or satellite nodes
have different resource configurations, i.e., the amount
of different types of resources are different in different
terrestrial or satellite nodes. In each VRC, we use the
M/M/1 queuing model to analyze resource utilization and
system service delay at different arrival rate λ and service
rate µ.
The detailed work process is depicted as follows.
• Since the application scenario under consideration
is transoceanic logistics, the distribution of IIoT
nodes will be particularly extensive. In the case of
broad range of distribution, IIoT nodes may exceed
the coverage of the terrestrial networks. Due to the
broader coverage of the satellite networks, when IIoT
nodes are located at sea or remote areas that outside
the coverage of the terrestrial networks, the satellite
networks can maintain the service and provide a
seamless connection service for IIoT nodes in the
transoceanic logistics.
• After sensors in IIoT nodes collect information in-
cluding delay, amount of data to be transmitted, and
the preference of resources types, etc., the infor-
mation is uploaded to VRC. For IIoT nodes have
different types of traffic requirements, and they are
distributed in different places, VRC is responsible
for determining the different requirements of differ-
ent IIoT nodes and for determining the number of
computation, storage and communication resources
for IIoT nodes based on the information.
• After the information uploaded to VRC, VRC deter-
mines the number of resource cubes required based
on the received information. Then it matches IIoT
nodes with service sides based on MCPR algorithm.
And according to different requirements of resources,
VRC chooses different service sides to provide ser-
vice for different IIoT nodes.
• After determining the service side of IIoT node, the
total amount of resources required by all IIoT nodes
served by each TN or SN is also determined. In this
case, resources of some TN or SN are insufficient
while resources of some TN or SN are remaining. If
resources of TN or SN cannot meet requirements of
IIoT nodes it served, it will bring about unnecessary
waiting delay. Therefore, we design an algorithm, M-
CRC algorithm, to adjust matching results under the
consideration of resource cubes. And the adjustment
is also accomplished by VRC.
For obtaining higher resource utilization and smarter
connections, we consider the preference of IIoT nodes for
resource tpes in the designed matching algorithm: MCPR
algorithm.
Authorized licensed use limited to: Lancaster University. Downloaded on July 08,2020 at 07:30:06 UTC from IEEE Xplore. Restrictions apply.
0018-9545 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TVT.2020.3007263, IEEE
Transactions on Vehicular Technology
4
As mentioned above, VRC plays an important role in
the whole process. Like a link, VRC matches IIoT nodes
and network service sides when IIoT nodes and service
sides are not in contact.
TABLE I
SYMBOL COMPARISON
Symbol Definition
U The set of IIoT nodes
u
j
IIoT node
U
j
The task of node u
j
o
j
The total delay
l
j
The amount of data
Γ
j
The resource requirements of node u
j
a
j
The allocation of different resources
q
j
Queuing delay
t
j
Propagation delay
f
j
Computing delay
l
nj
The distance between u
j
and service side
ψ = (g, a) One kind of network resource configuration
L
ut
j
, L
tu
n
, L
su
m
Preference Lists
III. RESOURCE CUBE AND PROBLEM FORMULATION
For ease of understanding, the main symbol definitions
used are listed in table I. We use U
j
= {o
j
, l
j
, Γ
j
} to
describe the task of node u
j
needs to accomplish. Among
these definitions, o
j
is the total delay, l
j
is the amount
of data to be processed, and Γ
j
is a vector consisting of
the requirements of u
j
for three kinds of resources, i.e.
Γ
j
=
Γ
cm
j
, Γ
cp
j
, Γ
st
j
.
For the nth terrestrial node, we use t
st
n
t
cp
n
and t
cm
n
to denote the storage resource, the computation resource,
and the communication resource, respectively. While for
the nth satellite node, we use s
st
n
s
cp
n
and s
cm
n
to denote
the storage resource, the computation resource, and the
communication resource, respectively.
It is well known that transoceanic logistics in the IIoT
is characterized by massive connections, and data volume
of each connection is very small. Therefore, in order to
realize flexible allocation of multi-dimensional resources,
we design the resource cube, as shown in Fig. 2. The unit
resource cube is composed of one portion communica-
tion resource, one portion computation resource and one
portion of storage resource.
Considering the characteristics of transoceanic logistics
in the IIoT, we can easily get that the amount of data
of each IIoT node is small. Then the physical resources
contained in the portions of various resources are defined
as follows: one portion of communication resources refers
to 1kbit/s bandwidth, denoted as b; one portion of com-
putation resource refers to one CPU cycle per second,
which one CPU cycle per second can deal with 1kbits
data, denoted as c; and one portion of storage resource
refers to storage space of 1kbits data, denoted as s.
With the resource cube definition in Fig. 2, we use a
vector a
j
to describe the allocation of different resources.
For a
j
=
a
b
j
, a
c
j
, a
s
j
, where a
b
j
, a
c
j
and a
s
j
are the
Computation
Resource
Communication
Resou rce
Storage
Resou rce
Fig. 2. The sample of the resource cube
amount of communication, computation and storage re-
sources contained in a
j
that allocated to the IIoT node u
j
respectively. After given the number of different resources
allocated to the IIoT node u
j
, the ability of resource cubes
allocated to the IIoT node u
j
is determined accordingly.
In this paper, we adopt service delay to evaluate the
QoS. For node u
j
, ∀u
j
∈ U, service delay is denoted
as o
j
= q
j
+ t
j
+ f
j
, where U represents the set of
IIoT nodes, q
j
is queuing delay, t
j
is propagation delay,
and f
j
is computing delay. Assuming that the workload
of each IIoT node u
j
obeys the Poisson arrival process,
based on the M/M/1 queuing model and the allocated
resource cube, queuing delay when serving the node u
j
is q
j
=
λ
a
b
j
µ
1
µ−
λ
a
b
j
. We define the distance between the
IIoT node u
j
and the TN t
n
as l
t
nj
, and similarly, the
distance between the IIoT node u
j
and the SN s
m
as l
s
mj
.
To simplify, we use l
nj
to denote the distance between the
IIoT node u
j
and service side. Therefore, the propagation
delay t
j
usually obeys t
j
= θl
nj
; θ is a scalar representing
the weight factor. Assuming that processing l
j
data needs
c CPU cycles, then we can get that f
j
=
l
j
a
c
j
c
. Then service
delay of u
j
can be expressed as
o
j
= q
j
+ t
j
+ f
j
=
λ
a
b
j
µ
1
µ −
λ
a
b
j
+ θl
nj
+
l
j
a
c
j
c
.
(1)
The constraint of delay can be written as
C1 : o
j
≤ o
thr
, (2)
where o
thr
is the predefined threshold of service delay.
To meet the requirements of Γ
r
j
and allocate resources
easily, and ensure pulling the job off, resource cubes
allocated to IIoT node u
j
needs to meet the following
constraint:
C2 : a
b
j
b + a
c
j
c + a
s
j
s ≥ Γ
cm
j
+ Γ
cp
j
+ Γ
st
j
a
b
j
= a
c
j
k a
b
j
= a
s
j
k a
c
j
= a
s
j
a
b
j
b + a
c
j
c + a
s
j
s ≥ l
j
,
(3)
i.e., the sum of resources allocated to the IIoT node u
j
should be greater than the sum of required resources, and
the number of any two resources allocated to it is equal
considering the convenience of the allocation of resource
Authorized licensed use limited to: Lancaster University. Downloaded on July 08,2020 at 07:30:06 UTC from IEEE Xplore. Restrictions apply.
0018-9545 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TVT.2020.3007263, IEEE
Transactions on Vehicular Technology
5
cube. And the number of resource cubes allocated is an
integer.
According to the constraint C1, in order to satisfy the
physical meaning of q
j
, value of a
b
j
needs to satisfy that
a
b
j
>
λ
j
µ
, therefore, we can get an initial value of a
b
j
. As
long as we make sure that this basic condition is met, the
amount of resources allocated to the IIoT node u
j
can
be adjusted without exceeding the amount of resources of
its service side. For example, if Γ
j
=
Γ
cm
j
, Γ
cp
j
, Γ
st
j
=
{2, 2, 4} while the initial value of a
b
j
is 3, and the storage
resource of service side is insufficient, then the allocation
can be a
j
= {a
b
j
, a
c
j
, a
s
j
} = {3, 3, 2}. This is just one
example, and the final resource allocation is determined
according to matching results and resource constraints.
Under constraints C1 and C2, it can be concluded that
it is unnecessary to allocate resources according to the
amount of various resources required by the IIoT node
u
j
absolutely. As long as the total amount of resources
allocated exceeds the total amount of resources required
by the IIoT node u
j
, and the task processing requirements
can be met under the condition of delay tolerance o
thr
.
This means that if the number of resources required by
users conflicts with the number of resources existing in the
network, i.e., when the number of certain type of resource
in the network is insufficient, other types of resources can
be used to replace it under certain conditions. Let give a
special example to clarify the replacement:
o
1
j
=
λ
a
b,1
j
µ
1
µ −
λ
a
b,1
j
+ θl
nj
+
l
j
a
c,1
j
c
=
λ
a
b,2
j
µ
1
µ −
λ
a
b,2
j
+ θl
nj
+
l
j
a
c,2
j
c
= o
2
j
,
(4)
where a
b,1
j
and a
c,1
j
, a
b,2
j
and a
c,2
j
represents the different
amount of communication and computation resources
contained in two different resource cubes a
1
j
and a
2
j
.
As a result, there may be several possible ways of
allocating that meets constraints C1 and C2. Therefore,
how to choose the most appropriate way from multiple
resource allocation ways is the problem that needs to be
dealt with. The resource allocation we choose takes into
account both the resource requirements of the IIoT node
u
j
, i.e. Γ
j
, and and the number of resources on the service
side (TN or SN). For ease of resource allocation, the value
of a
b
j
, a
c
j
, and a
s
j
start at one and increase by one.
We can get the constraint of resource cubes as follows:
C3 :
X
j∈U
a
b
j
b ≤
X
n∈T
t
cm
n
+
X
m∈S
s
cm
m
X
j∈U
a
c
j
c ≤
X
n∈T
t
cp
n
+
X
m∈S
s
cp
m
X
j∈U
a
s
j
s ≤
X
n∈T
t
st
n
+
X
m∈S
s
st
m
,
(5)
i.e., the total number of resource cubes assigned to IIoT
nodes cannot exceed the total amount of resources of the
terrestrial and the satellite networks.
Constraint C3 can be divided into two parts based on
services provided by different networks, as shown below.
If IIoT nodes are served by the satellite networks, which
are denoted as U
S
, then constraint C3 can be simplified
as
C3
S
:
X
j∈U
S
a
b,S
j
b ≤
X
m∈S
s
cm
m
X
j∈U
S
a
c,S
j
c ≤
X
m∈S
s
cp
m
X
j∈U
S
a
s,S
j
s ≤
X
m∈S
s
st
m
.
Similarly, if it is served by the terrestrial networks,
constraint C3 can be simplified as
C3
T
:
X
j∈U
T
a
b,T
j
b ≤
X
n∈T
t
cm
n
X
j∈U
T
a
c,T
j
c ≤
X
n∈T
t
cp
n
X
j∈U
T
a
s,T
j
s ≤
X
n∈T
t
st
n
,
where U
T
is used to denote IIoT nodes served by the
terrestrial networks.
We use x
t
jn
and x
s
jm
as the indicator to describe
whether IIoT nodes is connected to TN t
n
or SN s
m
,
and the value of this indicator is 1 when connected. We
can get the constraint C3 as:
C3 :
X
n∈T
x
t
jn
+
X
m∈S
x
s
jm
= 1, ∀j ∈ J.
In order to simplify, we set g =
P
n∈T
x
t
jn
, then
P
m∈S
x
s
jm
= 1 −g. Therefore, we can get that g is a binary
variable: g ∈ {0, 1}. Then C3 can be converted to
C3 : g ∈ {0, 1} . (6)
The ultimate goal is to achieve the highest resource
utilization while meeting requirements U
j
(o
thr
, l
j
), there-
fore, we define the utility function as:
R(g, a
j
) =
X
n∈N
T
,m∈M
S
X
j∈U
h
gF
N
T
j
+ (1 − g)F
M
S
j
i
,
(7)
where F
N
T
j
and F
M
S
j
are the utilization of resource cubes
of the terrestrial and the satellite networks respectively,
i.e.,
F
N
T
j
=
a
b
j
b + a
c
j
c + a
s
j
t
cp
n
+ t
cm
n
+ t
st
n
F
M
S
j
=
a
b
j
b + a
c
j
c + a
s
j
s
s
cp
m
+ s
cm
m
+ s
st
m
.
(8)
Authorized licensed use limited to: Lancaster University. Downloaded on July 08,2020 at 07:30:06 UTC from IEEE Xplore. Restrictions apply.