Cooperative Caching and Resource Allocation in Integrated Satellite–Terrestrial Networks

Abstract

Due to the rapid development of low earth orbit satellite constellations, e.g., Starlink, OneWeb, etc., integrated satellite-terrestrial networks have been viewed as a promising paradigm to globally provide satellite internet services for users. However, when the contents from ground data centers are provided for users by satellite networks, there will be high capital expenditures in terms of communication delay and bandwidth usage. To this end, in this paper, a cooperative-caching and resource-allocation problem is investigated in integrated satellite–terrestrial networks. Popular contents, which are cached on satellites and ground data centers, can be accessed via inter-satellite and satellite–terrestrial networks in a cooperative way. The optimization problem is formulated to jointly minimize the deployment costs of storage resource usage and network bandwidth consumption. A cooperative caching and resource allocation (CCRA) algorithm based on a neighborhood search is proposed to address the problem. The simulation results demonstrate that the proposed CCRA algorithm outperforms Greedy and BFS in reducing the deployment costs.

1. Introduction

With the development of wireless communication technologies, terrestrial networks with edge caching can provide internet services, e.g., multimedia services, web services, and application services, etc., for terminal users to improve the user service experience and the network running utility. Additionally, cache contents as close to users as possible are accessed to reduce the costs of data transmission delay and network bandwidth consumption [1,2]. Note that content caching servers are usually located on edge nodes in terrestrial networks. However, more than 80% land and 95% sea areas have not been covered by terrestrial networks due to high capital expenditures and harsh geographical environments [3], and only 67% of the global population can access the internet [4]. In that case, content services cannot be provided for remote terminal users, which are not in the coverage of terrestrial networks, e.g., oceans, deserts, and mountainous areas. As a supplement to terrestrial networks, large-scale low Earth orbit (LEO) satellite constellations, such as Starlink and OneWeb, can provide the global services of wireless communication and internet access for terminal users [5,6]. Therefore, LEO satellite constellations are viewed as important parts of the beyond fifth-generation (B5G) communication systems and the sixth-generation (6G) communication systems, which are integrated by satellite and terrestrial networks [7,8].

For conventional satellite networks with just data routing and forwarding, terminal users need to access internet services from the ground by satellite networks, which can result in high service latency and large network load [9,10,11]. Considering the characteristics of global seamless coverage and low transmission latency for LEO satellite networks, satellite edge caching, as viewed as a new paradigm, can provide edge caching services for terminal users, where caching servers are placed on LEO satellites. However, there are strictly limited on-board resources for satellite networks, which cannot meet with the service requirements of users when a large number of terminal users arrive [12,13]. By combining the advantages of terrestrial and satellite networks, cooperative content caching in integrated satellite–terrestrial networks has been a promising approach to provide content services for terminal users on-demand in a flexible and efficient way [14,15]. It should be noted that, different from terrestrial networks with relatively unchanged topologies and sufficient resources, the topologies of satellite networks with strictly limited on-board resources can also be time-varying [16]. Accordingly, it is a challenging issue to make the feasible strategies of cooperative caching and resource allocation in integrated satellite–terrestrial networks.

Extensive research focuses on the issues of cooperative caching and resource allocation in integrated satellite–terrestrial networks [17,18]. Some existing related works without inter-satellite communication are preliminarily studied based on the consideration of simplifying the problem complexity [19,20], where the performance cannot be guaranteed due to the lack of inter-satellite cooperative caching. Furthermore, the inter-satellite communication capabilities for LEO satellite networks are considered to provide cooperative caching services for terminal users. The problems are also formulated to optimize the objectives, e.g., cache hit-rate [21], content access delay [22], net-gains [23], etc. However, little of the existing related work discusses the joint optimization problem of data routing, network bandwidth, and on-board storage resources for cooperative caching in integrated satellite–terrestrial networks. Moreover, as the number of satellites increases, the dimensional information concerning the spatial state will correspondingly increase, which can also bring a difficulty in the global resource management [24]. Therefore, the cooperative caching architectures of integrated satellite–terrestrial networks should also be investigated to reduce the system complexity of resource management and improve the real-time decision-making.

In this paper, a cooperative caching and resource allocation problem in integrated satellite–terrestrial networks is discussed, where the inter-satellite and satellite–terrestrial cooperative caching is introduced to manage the satellite–terrestrial network resources in a more flexible and effective way. Each terminal user can retrieve the cache content just from the access satellite, the neighbors, or the ground data center to simplify the system complexity. Different content popularity and geographical distribution of terminal users are also considered for the system model. Then, the problem is formulated under multiple physical constraints, and the aim is to jointly minimize the total deployment costs of storage resource usage and network bandwidth consumption. To reduce the computation complexity while improving the real-time decision making, a cooperative caching and resource allocation (CCRA) algorithm is proposed by introducing a neighborhood search approach, where the content service can be provided for each user in the neighboring sub-network of the access satellite. Finally, the simulation experiments are conducted to evaluate the performance of the proposed CCRA algorithm in different application scenarios, as well as compared with the existing approaches of Greedy and breath-first search (BFS). The results show that the proposed CCRA algorithm outperforms Greedy and BFS in reducing the total deployment costs of storage resource usage and network bandwidth consumption. The main contributions in this paper can be summarized as follows.

• A system model is studied by introducing a neighboring sub-network approach in integrated satellite–terrestrial networks, where the inter-satellite and satellite–terrestrial cooperative caching is considered.
• The problem is formulated under multiple physical constraints, the aim is to jointly minimize the deployment costs of storage resource usage and network bandwidth consumption.
• The CCRA algorithm is proposed based on a neighborhood search to find the feasible strategy in an acceptable running time. The performance is also evaluated by different experiments.

The remaining parts of this paper are provided as follows. Section 2 reviews the related work concerning cooperative caching. Section 3 discusses the system model. Section 4 formulates the optimization problem. Section 5 proposes the CCRA algorithm to address the problem. Section 6 evaluates the performance of the proposed CCRA algorithm. Finally, the conclusion is provided in Section 7.

2. Related Work

This section reviews the related work of cooperative caching in terrestrial networks, satellite networks, and satellite–terrestrial networks, respectively.

2.1. Cooperative Caching in Terrestrial Networks

For terrestrial networks which are content-centric, cooperative edge caching can effectively alleviate the heavy burden in bandwidth consumption and service latency, where popular contents are cached and forwarded at the edge of networks [25,26,27]. Specifically, a heterogeneous information network-based content caching is discussed to reduce the network load while improving the quality of service in [28], and a content caching placement approach is also proposed to maximize the cache hit-rate in [29]. Furthermore, a cooperative edge caching approach is investigated to optimize the content placement and cluster size in large-scale user-centric mobile networks in [30]. In addition, a mobility-aware edge caching strategy is also implemented to improve the content hit-rate in the internet of vehicles [31].

However, different from terrestrial networks, there are time-varying topologies and restricted onboard resources in satellite networks, which can bring a difficulty for cooperative caching.

2.2. Cooperative Caching in Satellite Networks

Considering the characteristics of LEO satellite networks, several research works are focused on providing global content services for terminal users in satellite networks [32,33]. For example, an effective load balancing scheme based on cache resource allocation is investigated [34], and a hybrid caching placement strategy is discussed to improve the quality of service [35]. Furthermore, a joint optimization problem is studied to minimize the total service delay of users [36], and a collaborative caching approach for content sharing among neighboring satellites is investigated to maximize the storage resource utilization [37].

Note that the content service provisioning cannot meet with the service requirements for large number of users as the strictly limited on-board resources of satellite networks.

2.3. Cooperative Caching in Satellite–Terrestrial Networks

Satellite–terrestrial networks with cooperative caching can enhance the performance of user service experience and network running utility [38,39]. Initially, a two-layer content caching and delivery approach is proposed to minimize the satellite bandwidth consumption [40], a caching placement optimization problem is investigated to maximize the quality of experience [41], and a coding-based collaborative caching scheme is also studied to jointly optimize the strategy of caching placement and power allocation [42]. However, the above existing works just discuss the problems in satellite–terrestrial networks without inter-satellite communication, which can result in performance degradation.

Then, satellite–terrestrial networks with inter-satellite communication are further investigated for cooperative caching, where a cooperative multi-layer edge caching approach for base stations, satellites, and gateways is proposed to minimize the content service delay of users [43], and a simple yet effective cooperative content retrieval scheme is studied to reduce the traffic load [44]. Moreover, a content popularity-aware caching placement approach is discussed to improve the cache hit-rate and content service delay [45]. Note that the joint optimization problems of data routing, network bandwidth, and storage resources are not fully considered. To this end, this paper comprehensively considers all of the routing path, storage and bandwidth resource allocation, and caching placement and proposes a neighborhood search approach to address the problem effectively.

3. System Model

This section introduces the proposed system model, including an integrated satellite–terrestrial network, users, contents, and a cooperative caching and resource allocation model.

3.1. Integrated Satellite–Terrestrial Network

An integrated satellite–terrestrial network is considered to discuss the cooperative caching and resource allocation problem, where the integrated satellite–terrestrial network can consist of LEO satellites, a ground station, and a cloud center, as shown in Figure 1. Each LEO satellite has an edge server with certain storage resources and can provide edge caching services with particular contents for terminal users, different LEO satellites are connected by inter-satellite links (ISLs) to route the data in a cooperative way. A cloud center on the ground with sufficient storage resources can provide remote content services with all contents for terminal users. A ground station is responsible for resource management, strategy selection, and caching placement in the integrated satellite–terrestrial network, where the cloud center can communicate with the ground station by terrestrial networks and satellite satellites. Note that the detailed network implementation is beyond the scope of our work and will be neglected in this paper, such as channel design, network protocol, and information interaction.

The integrated satellite–terrestrial network is composed of a satellite network $G(V,E)$ and a cloud center $dc$, where V and E are indicated as the set of satellites and the set of ISLs. Satellite network $G(V,E)$ is built based on a central satellite and h hops, where the central satellite will be predetermined and unchanged over time when the network is established. For each satellite v, $v\in V$, there are two ISLs from the in-orbit adjacent satellites and two ISLs from the inter-orbit adjacent satellites [21], and the available storage resources are indicated as $C_v$. For each link e, $e\in E$, the available bandwidth resources and the transmission delay can be indicated as $B_e$ and $t_e$, where the time of transmitting and receiving the content for each satellite can be neglected in order to simplify the system complexity. Considering the limited available resources of satellites, satellite v can just provide content services for the maximum number $D_v^{max}$ of users. The sets of input degrees and output degrees for satellite v can be indicated as $E_v^{in}$ and $E_v^{out}$, respectively. Furthermore, it is assumed that the available storage and satellite–terrestrial bandwidth resources for cloud center $dc$ are sufficient, and the cloud center is also in the coverage of access satellite $v_{dc,a}$, where the distance between cloud center $dc$ and access satellite $v_{dc,a}$ is indicated as $k_{dc}$.

Considering that the operation costs will correspondingly increase as the number of satellites increases, a large LEO satellite network can be divided into multiple small satellite networks by a network partitioning approach. Several ground stations are distributed to manage the small network resources and provide content services in parallel. In that case, the centralized satellite-terrestrial network framework proposed in this paper can be also extended to a distributed satellite–terrestrial network framework to decrease the operation costs.

3.2. Users and Contents

The set of users is indicated as U with M users, and all users are randomly located in the coverage of satellite network $G(V,E)$ and can only communicate with their access satellites directly. Satellite v for user u will be indicated as the access satellite $v_{u,a}$ when user u accesses the network by satellite v. The link bandwidth resources between user u and access satellite $v_{u,a}$ are denoted as $b{w}_u$. For the satellite–terrestrial link between user u and access satellite $v_{u,a}$, the transmission power, the channel gain, and the noise power can be indicated as $p_{u,tr}$, $g_{u,c}$, and $p_{u,n}$, and the distance is indicated as $k_u$. The velocity of data transmission is also indicated as c in the wireless communication environment.

Furthermore, the set of available content is denoted as W, and the number is also indicated as Q. For each content w, $w\in W$, the data size and the content popularity are indicated as $s_w$ and $p_w$. Note that the greater the content popularity is, the higher the access opportunity for terminal users will be. In addition, the maximum service delay of retrieving content w for user u is indicated as $t_{u,w}^{max}$.

3.3. Cooperative Caching and Resource Allocation

Different from terrestrial networks, similar to the existing related work in [9,44], the cooperative caching and resource allocation problem is discussed to reduce the problem complexity in a quasi-static scenario. Specifically, a time-varying satellite network is divided into several segments by a division approach based on time slots, where the network topology remains unchanged within each time slot but can vary over different time slots. Furthermore, it is assumed that the caching service strategies are unchanged, and the service requirements can be also guaranteed during the service periods.

The procedure of cooperative caching and resource allocation in dynamic environment can be illustrated as follows. Initially, the ground station can abstract, manage and orchestrate all the available physical resources of an integrated satellite–terrestrial network by introducing software-defined network and network virtualization technology [24,42]. Then, in order to describe the proposed system model more clearly, it is assumed that all of the information concerning the content services of new users can be accessed through the integrated satellite–terrestrial network via their access satellites at the beginning of each time slot, and the strategies can be made and deployed during the current time slot. However, considering the dynamic movement of satellites, the caching content on satellites will be replaced over different time slots. In that case, a maximum threshold time for the onboard cache contents not being accessed can be pre-set. The cache contents on satellites will be released, and the occupied storage resources will be reallocated for new contents after the time is more than the maximum threshold.

However, different strategies of cooperative caching and resource allocation can have a significant impact on network bandwidth consumption and storage resource usage. Therefore, from the perspective of network operators, the problem is formulated to minimize the weighted sum of storage resource usage and network bandwidth consumption while content services should be provided for users as much as possible.

An example of a cooperative-content service in an integrated satellite–terrestrial network is shown for different users in Figure 2, where there are 7 users $\left\{u_1,u_2,\cdots ,u_7\right\}$, 6 satellites $\left\{v_1,v_2,\cdots ,v_6\right\}$, 6 contents $\left\{w_1,w_2,\cdots ,w_6\right\}$, and one cloud center $dc$, the users are randomly located in the coverage of the satellites, and the access satellite for cloud center $dc$ is viewed as $v_5$. In the beginning, the ground station can sense the information concerning user service requirements in real-time and then make the joint strategies of cooperative caching and resource allocation based on network running states and user service requirements. All of the current contents are deployed on the cloud center, and just parts of the contents can be placed on satellites due to the limited onboard storage resources. In that case, users can retrieve the required contents from the integrated satellite–terrestrial network by the obtained joint strategies. Specifically, user $u_1$ can retrieve the caching content $w_2$ from the access satellite $v_1$. As the access satellite $v_4$ for user $u_2$ can not deploy the required content $w_1$, user $u_2$ will retrieve the content $w_1$ from satellite $v_1$ by the path $v_1\to v_4$. Similarly, user $u_3$ retrieves the required content $w_4$ from satellite $v_3$ by the path $v_3\to v_2$, and user $u_7$ retrieves the required content $w_5$ from cloud center $dc$ by the path $dc\to v_5\to v_6$.

4. Problem Formulation

In this section, the joint optimization problem is formulated to minimize the weighted sum of storage resource usage and network bandwidth consumption, and then, the problem analysis is provided.

4.1. Cooperative Caching and Resource Allocation Problem

The formulated problem can be viewed as two subproblems of storage resource usage and network bandwidth consumption with multiple constraints. To better describe the formulated problem, more variables are provided as follows.

Firstly, binary decision variable $x_{u,w}$ indicates whether user u retrieves content w, and $x_{u,w}=1$ indicates that user u retrieves content w, otherwise $x_{u,w}=0$. Binary decision variable $y_{w,v}$ indicates whether content w is deployed on satellite v, and $y_{w,v}=1$ indicates that content w is deployed on satellite v, otherwise $y_{w,v}=0$.

Considering the different geographical distribution of users and the restriction of access services on each satellite, the same content w can be deployed on multiple satellites. Therefore, binary decision variable $z_{u,v}^w$ indicates whether user u can retrieve content w on satellite v, $z_{u,v}^w=1$ indicates that user u can retrieve content w on satellite v, otherwise $z_{u,v}^w=0$.

Furthermore, when users retrieve contents from the integrated satellite–terrestrial network, a path composed of multiple ISLs will be used to route the data. In that case, binary decision variable $q_{u,e}^w$ indicates whether user u retrieves content w by link e, and $q_{u,e}^w=1$ indicates that user u retrieves content w by link e, otherwise $q_{u,e}^w=0$.

Additionally, binary decision variable $a_{u,dc}$ indicates whether user u retrieves content w from cloud center $dc$, $a_{u,dc}=1$ indicates that user u retrieves content w from cloud center $dc$, otherwise $a_{u,dc}=0$.

The main symbols for the formulated problem are summarized in

Table 1. List of SYMBOLS.

Name	Description of Symbols
Satellite–terrestrial Network
$G(V,E)$	Satellite network with satellites V and links E.
$dc$	Cloud center.
h	Number of network hops.
$C_v$	Available storage resources for satellite v.
$v,e$	The v-th satellite and the e-th link.
$B_e$	Available bandwidth resources for link e.
$t_e$	Transmission delay for link e.
$D_v^{max}$	Maximum number of users provided content services for satellite v.
$E_v^{in},E_v^{out}$	Sets of input and output degrees for satellite v.
$v_{dc,a}$	Access satellite of cloud center $dc$.
$k_{dc}$	Distance between cloud center $dc$ and the access satellite.
Users and Contents
$U,M$	Set of users and the number of users.
$u,v_{u,a}$	The u-th user and the access satellite.
$b{w}_u$	Bandwidth between user u and the access satellite.
$g_{u,c}$	Channel gain of retrieving the content for user u.
$p_{u,n}$	Noise power of retrieving the content for user u.
$p_{u,tr}$	Transmission power of retrieving the content for user u.
$k_u$	Distance between user u and the access satellite.
c	Velocity of data transmission.
$W,Q$	Set of contents and the number of contents.
w	The w-th content.
$s_w,p_w$	Data size and popularity for content w.
$t_{u,w}^{max}$	Maximum service delay of retrieving the content for user u.
Decision Variables
$x_{u,w}$	$x_{u,w}=1$ if user u retrieves content w.
$y_{w,v}$	$y_{w,v}=1$ if content w is deployed on satellite v.
$z_{u,v}^w$	$z_{u,v}^w=1$ if user u retrieves content w on satellite v.
$q_{u,e}^w$	$q_{u,e}^w=1$ if user u retrieves content w by link e.
$a_{u,dc}$	$a_{u,dc}=1$ if user u retrieves content w from cloud center $dc$.
Variables
${\varphi }_U$	Objective function of content services for all users.
${\lambda }_{u,w}^{stor}$	Cost factor of storage resource usage for user u.
${\lambda }_{u,w}^{bw}$	Cost factor of network bandwidth consumption for user u.
$j_{v,v_{dc,a}}$	$j_{v,v_{dc,a}}=1$ indicates satellite v can be viewed as satellite $v_{dc,a}$.

.

4.1.1. Caching Model

When satellite network $G(V,E)$ provides edge caching services for users, each satellite can deploy parts of all the contents as the onboard storage resources are limited. Furthermore, the content placed on a satellite can be accessed by different users, where a content sharing approach can be used to decrease the onboard storage resource usage. Therefore, in order to describe the formulated caching problem more clearly, the onboard storage resource usage for users can be viewed in two scenarios of first and non-first content services. In the first content service scenario, content w on satellite v is firstly accessed by user u, then the storage resources deploying content w on satellite v are viewed as the storage resource usage for the content service of user u. In the non-first content service scenario, content w on satellite v is not firstly accessed by user u, then the storage resources deploying content w on satellite v are viewed as zero for the content service of user u. Therefore, the onboard storage resource usage for the content service of user u can be indicated as

$${\phi }_{u,w}^{stor}=\left\{\begin{array}{cc}{x}_{u,w}·(1-a_{u,dc})·{\displaystyle \sum _{v\in V}}{y}_{w,v}·z_{u,v}^w·s_w,& \mathrm{First}\mathrm{service},\\ 0,& \mathrm{Non-first}\mathrm{service}.\end{array}\right.$$

(1)

4.1.2. Bandwidth Consumption Model

When content services are provided for users by satellite network $G(V,E)$, the satellite network bandwidth resources, as well as the wireless communication channels between users and their access satellites, will be used to transmit the data. In the wireless communication environment between user u and access satellite $v_{u,a}$, the transmission rate for retrieving content w can be given as

$$b_{u,w}^{wire}={bw}_u·{lg}_2·\left(1+\frac{p_{u,tr}·g_{u,c}}{p_{u,n}}\right).$$

(2)

The current available network bandwidth resources of retrieving content w for user u in satellite network $G(V,E)$ can be given as

$$b_{u,w}^{isl}=\underset{e\in E,q_{u,e}^w\ne 0}{min}{B}_e.$$

(3)

Note that the actual data rate for retrieving contents can be influenced by the available network bandwidth resources and the wireless communication environment. It can be considered that the data rate for retrieving the content is the minimum value of the current available network bandwidth resources and the wireless transmission rate. Therefore, the actual data rate of retrieving content w for user u can be indicated as

$$b_{u,w}=min(b_{u,w}^{wire},b_{u,w}^{isl}).$$

(4)

Then, the network bandwidth consumption of retrieving content w for user u can be indicated as

$${\phi }_{u,w}^{bw}=x_{u,w}·\sum _{e\in E}{q}_{u,e}^w·b_{u,w}.$$

(5)

4.1.3. Communication Model

For the content service of user u, the service delay can be composed of the transmission time between user u and access satellite $v_{u,a}$, the routing time for ISLs, the transmission time between cloud center $dc$ and access satellite $v_{dc,a}$, and the sending time of data. The sending time of content w for user u can be given as

$$t_{u,w}^{snd}=\frac{x_{u,w}·s_w}{b_{u,w}},$$

(6)

the total transmission time of satellite–terrestrial links, i.e., user u and access satellite $v_{u,a}$ and cloud center $dc$ and access satellite $v_{dc,a}$, for the content service of user u can be given as

$$t_{u,w}^{tr}=\frac{x_{u,w}·k_u}{c}+\frac{x_{u,w}·a_{u,dc}·k_{dc}}{c}.$$

(7)

The routing time between different ISLs for the content service of user u can be indicated as

$$t_{u,w}^{isl}=x_{u,w}·\sum _{e\in E}{q}_{u,e}^w·t_e.$$

(8)

Then, the total service delay time of retrieving content w for user u can be given as:

$$t_{u,w}=t_{u,w}^{snd}+t_{u,w}^{tr}+t_{u,w}^{isl}.$$

(9)

4.1.4. Problem Description

When the cost factors of storage resource usage and network bandwidth consumption for the content service of user u are indicated as ${\lambda }_{u,w}^{stor}$ and ${\lambda }_{u,w}^{bw}$, the objective function for all users can be given as

$${\varphi }_U=\frac{{\displaystyle \sum _{u\in U}}({\lambda }_{u,w}^{stor}·{\phi }_{u,w}^{stor}+{\lambda }_{u,w}^{bw}·{\phi }_{u,w}^{bw})}{{\displaystyle \sum _{u\in U}}{x}_{u,w}}·\frac{M}{{\displaystyle \sum _{u\in U}}{x}_{u,w}}.$$

(10)

There are multiple physical constraints to be considered for cooperative caching and resource allocation. When the satellite network provides content services for users, user u can retrieve the required content w from one and only satellite, which can be given as

$$\sum _{v\in V}{y}_{w,v}·z_{u,v}^w=x_{u,w}·(1-a_{u,dc}).$$

(11)

It is guaranteed that the required storage resources of deploying contents should not be greater than the current available onboard resources, which can be indicated as

$$\sum _{w\in W}{y}_{w,v}·s_w\le C_v,vs.\in V.$$

(12)

It is also guaranteed that the required network bandwidth resources for each link can not be more than the current available bandwidth resources. The network bandwidth resource constraint can be indicated as

$$\sum _{u\in U}{x}_{u,w}·q_{u,e}^w·b_{u,w}\le B_e,e\in E.$$

(13)

It is also guaranteed that the content service delay for each user should not be more than the maximum acceptable service delay, which can be indicated as:

$$t_{u,w}\le t_{u,w}^{max},u\in U,w\in W.$$

(14)

Furthermore, the number of users provided content services for each satellite should not be more than the maximum value $D_v^{max}$, which can be given as

$$\sum _{u\in U}{x}_{u,w}·(1-a_{u,dc})·y_{w,v}·z_{u,v}^w\le D_v^{max},vs.\in V.$$

(15)

Moreover, when content service are provided by satellite network $G(V,E)$ for one user, a path will be used to route the data. In that case, the number of input and output degrees for each satellite can not be greater than 1. Therefore, the constraint of input and output degrees can be indicated as

$$\left\{\begin{array}{c}{\displaystyle \sum _{e\in E_v^{in}}}{q}_{u,e}^w\le x_{u,w},v\in V,u\in U,w\in W,\hfill \\ {\displaystyle \sum _{e\in E_v^{out}}}{q}_{u,e}^w\le x_{u,w},v\in V,u\in U,w\in W.\hfill \end{array}\right.$$

(16)

It is also guaranteed that the number of input and output degrees can usually be equal for each satellite. Note that a satellite providing content service for one user is viewed as the source, and the access satellite is viewed as the destination. Therefore, the number of output degrees for the destination, as well as the number of input degrees for the source, is viewed as 0. The binary auxiliary variable $j_{v,v_{dc,a}}=1$ indicates that the satellite v can be viewed as the access satellite $v_{dc,a}$ of cloud center $dc$, otherwise $j_{v,v_{dc,a}}=0$, and then, the path selection constraint for user u and content w can be given as

$$\left\{\begin{array}{c}{\tau }_v=z_{u,v}^w·(1-a_{u,dc})+j_{v,v_{dc,a}}·a_{u,dc},v\ne v_{u,a},\hfill \\ {\tau }_v=(z_{u,v}^w-1)·(1-a_{u,dc})+(j_{v,v_{dc,a}}-1)·a_{u,dc},vs.=v_{u,a},\hfill \end{array}\right.$$

(17)

where ${\tau }_v$ is indicated as

$${\tau }_v=x_{u,w}·(\sum _{e\in E_v^{out}}{q}_{u,e}^w-\sum _{e\in E_v^{in}}{q}_{u,e}^w).$$

(18)

As in the above discussion, the joint optimization problem of cooperative caching and resource allocation with multiple physical constraints in (11)–(17) can be given as

$$\begin{array}{cc}\hfill min& {\varphi }_U,\hfill \\ \hfill s.t.& \left(11\right)–\left(17\right).\hfill \end{array}$$

(19)

4.2. Problem Analysis

For the formulated problem, each satellite for users is viewed as a plant, the current available storage resources are indicated as the plant capacity, and the retrieved contents on satellites are indicated as goods with identified demands. Then, the used storage resources can be viewed as the operation costs of plants, and the network bandwidth consumption of retrieving the contents for users can also be indicated as the transportation costs. Therefore, the aim of the formulated problem can be considered to minimize the total costs of operation costs and transportation costs. In that case, a capacitated plant location problem with single source constraints [46], which is viewed as NP-hard, can be reduced to the formulated problem, where an exponential computation complexity is considered for solving the optimal solution.

5. Proposed Algorithm

Considering that the formulated problem is viewed as NP-hard, it can bring difficulty in obtaining the optimal solution. Therefore, several intelligent optimization algorithms, e.g., Stackelberg game [34], genetic algorithm [40], and mayfly algorithm [42], have been widely introduced to tackle the optimization problems by searching for feasible solutions in an acceptable running time. However, when contents can be cached on all the satellites on-demand, the system complexity will correspondingly increase as the number of satellites increases. Furthermore, in order to improve the service experience, users should retrieve the required contents from the access satellites or their neighbors as much as possible. Therefore, similar to the existing related work in [24,37], the CCRA algorithm based on neighborhood search is proposed to obtain a feasible solution. The detailed description of the proposed CCRA algorithm is provided as follows.

For the satellite network $G(V,E)$, the neighboring sub-network $G(V_{v,sub},E_{v,sub})$ for each satellite v can be firstly built based on the number $h_{sub}$ of hops and the service requirements of users. Each satellite is viewed as an intelligent agent with environment-aware, autonomous, and social behavior, which can be responsible for resource management, content caching, and accessing services autonomously in the neighboring sub-network. When there are insufficient available storage resources or restricted service provisioning in the sub-network, users will retrieve the required contents from the cloud center via the satellite network $G(V,E)$ in a cooperative way.

Furthermore, the onboard storage resource utilization can be improved by the content sharing technology, where different users with the same service requirement can access the same content deployed on a satellite. Considering that the cache contents with higher popularity are more easily accessed for users, the average storage costs for each user will decrease. In that case, it is considered that all the users for each satellite can be sorted by the popularity of accessed contents in descending order. Then, the strategies for users can be made, deployed, and executed one-by-one.

Specifically, for the content service of each user, a neighborhood search approach is used to obtain the feasible strategy of content placement and routing path by traversing both satellites and links in the neighboring sub-network. The access satellite for each user is viewed as the only root candidate in the initial layer, where the root candidate will be firstly searched to obtain a feasible strategy under multiple constraints. When the root candidate is searched, the neighboring satellites of the root candidate will be viewed as the new candidates in the next layer. Note that one satellite with the required content in the sub-network may provide the content service for the current user, then the storage resource usage for the content service of the user can be viewed as 0 according to Equation (1). Therefore, in order to obtain the feasible strategy with minimum deployment costs, whether or not a feasible strategy is obtained in the current layer, the new candidates in the next layer will continue to be searched until the current number of hops is equal to $h_{sub}$ in the sub-network.

When there are insufficient storage resources, restricted content services, or the access satellite of cloud center $dc$ covered in the sub-network, the content services may be provided by the cloud center. Then, L shortest paths $P_{u,dc}^L$ between the access satellite of user u and cloud center $dc$ can be traversed to obtain the feasible routing path in descending order.

An example of content service provisioning by the neighborhood search is illustrated in Figure 3. In the beginning, the neighboring sub-networks of satellite $v_0$ for $h_{sub}=1$ and $h_{sub}=2$ are established and represented with green and red lines, respectively. Then, a neighborhood search approach is used to obtain the feasible strategy for content service in the neighboring sub-network with $h_{sub}=2$. Specifically, for one user, the root candidate in the initial layer, i.e., the access satellite $v_0$, is firstly searched, but a feasible strategy of content service cannot be provided due to the insufficient storage resources. Then, the candidates $\{v_1,v_2,v_3,v_4\}$ in the next layer will be traversed and two feasible strategies can be obtained, i.e., strategy 1 and strategy 2. For strategy 1, satellite $v_1$ has sufficient storage resources to deploy the required content and the content can be transmitted by routing path $v_1\to v_0$ to the user. That is, the deployment costs can be composed of onboard storage resource usage and network bandwidth consumption. For strategy 2, as the required content was deployed on satellite $v_4$, the content service can be just provided by routing path $v_4\to v_0$, where the deployment costs can be only from the network bandwidth consumption. Furthermore, the candidates $\{v_5,v_6,\cdots ,v_{12}\}$ in the third layer will continue to be searched and strategy 3 can be obtained, where the required content was also deployed on satellite $v_8$ and the content service can be just provided by routing path $v_8\to v_3\to v_0$. Therefore, considering that the bandwidth consumption of strategy 3 is more than that of strategy 2, strategy 3 will be viewed as the feasible strategy with minimum deployment costs.

In a dynamic environment, for each time slot, the ground station can autonomously perceive the changes in the surroundings and then make the strategies for new users one-by-one. The cache contents on satellites will be released to reduce the storage resource usage when the idle time is more than the threshold time. However, in practical application scenarios, considering the real-time of content services, the content services are provided based on the content caching strategies generated in the previous time slot, and then, the performance can be improved based on the current service requirements.

The procedure of the proposed CCRA algorithm for one time slot is shown in Algorithm 1, where the input parameters include users U and sub-network hops $h_{sub}$, and the output parameters are the feasible strategies $S_U^{*}$ for all the users. In the beginning, the state information can be updated, e.g., network operation, resource utilization, and content caching. Then, the new accessed users $U_v$ for each satellite v are sorted by content popularity in descending order, and the feasible strategy with minimum deployment costs will be searched for each user.

Algorithm 1 Proposed CCRA Algorithm.

Input: Users U, sub-network hops $h_{sub}$;

Output: $S_U^{*}$;

1: Initialize: Update the information of network state;   2: for each $v\in V$ do   3:    Sort all users by content popularity in descending order;   4:    for each $u\in U_v$ do   5:      $s_u=⌀,A_{layer}\leftarrow \{v_{u,a},path=⌀\}$;   6:      while $A_{layer}\ne ⌀$ do   7:         ${\overline{A}}_{layer}=⌀$;   8:         for each $a\in A_{layer}$ do   9:           if the required content is deployed then 10:              if Equations (12)–(15) are satisfied then 11:                $s_u\leftarrow \{a,True,True\}$; 12:              end if 13:           else 14:              if Equations (13)–(15) are satisfied then 15:                $s_u\leftarrow \{a,True,False\}$; 16:              end if 17:           end if 18:           if the current hops are less than $h_{sub}$ then 19:              ${\overline{A}}_{layer}\leftarrow$ the available neighbors and paths; 20:           end if 21:         end for 22:         $A_{layer}\leftarrow {\overline{A}}_{layer}$; 23:      end while 24:      if $s_u=⌀$ or satellite $v_{dc,a}\in V_{v,sub}$ then 25:         for each $path\in P_{u,dc}^L$ do 26:           if the bandwidth resources are satisfied then 27:              $s_u\leftarrow \{path,False,False\}$ and break; 28:           end if 29:         end for 30:      end if 31:      $s_u^{*}\leftarrow min{s}_u$ calculated by Equation (19) and provide content service by $s_u^{*}$; 32:      Update the information of network state again; 33:    end for 34: end for 35: return $S_U^{*}=\left\{s_u^{*}|u\in U\right\}$;

For each user u, in the beginning, the strategy set can be indicated as $s_u=⌀$, the information concerning the root candidate, i.e., access satellite $v_{u,a}$, in the initial layer can be indicated as $A_{layer}\leftarrow \{v_{u,a},path=⌀\}$, and an auxiliary set is also indicated as ${\overline{A}}_{layer}=⌀$ to describe the procedure of the proposed algorithm more clearly. Then, all the candidates in $A_{layer}$ will be searched to obtain the feasible strategies, where there are two possible scenarios for each candidate a to be considered. In the case of the required content deployed on the current satellite, a feasible strategy $\{a,True,True\}$ will be obtained when the constraints in Equations (13)–(15) are satisfied. Strategy $\{a,True,True\}$ indicates that the required content was deployed on the current satellite and the content service can be provided by the path from the candidate a. Furthermore, in the case of the required content not deployed on the current satellite, when both of the available onboard storage and network bandwidth resources, as well as the constraints of service delay and service provisioning, are satisfied, the other feasible strategy $\{a,True,False\}$ can be just obtained. Strategy $\{a,True,False\}$ indicates that the current satellite with sufficient storage resources can cache and provide the required content by the path from the candidate a. Then, if the current hops are less than $h_{sub}$, the available neighbors and paths for the current candidate will be updated into ${\overline{A}}_{layer}$. When all the candidates in $A_{layer}$ are searched, it will be viewed as $A_{layer}\leftarrow {\overline{A}}_{layer}$. The process of neighborhood search will be terminated when $A_{layer}=⌀$.

When $s_u=⌀$ or the access satellite $v_{dc,a}$ is one of the satellites in the current neighboring sub-network, the L shortest paths $P_{u,dc}^L$ will be traversed to obtain a feasible strategy $\{path,False,False\}$ if the network bandwidth resources are satisfied for the $path$, where $\{path,False,False\}$ indicates that the required content can be retrieved by the $path$ from cloud center $dc$. Furthermore, the feasible strategy with minimum deployment costs from $s_u$ can be viewed as the optimal strategy $s_u^{*}$, that is, $s_u^{*}\leftarrow min{s}_u$.

For each time slot, M users can access the integrated satellite–terrestrial network and require the content services. According to the proposed CCRA algorithm based on neighborhood search, there are $V_{v,sub}$ satellites and $E_{v,sub}$ ISLs, as well as L shortest paths $P_{u,dc}^L$, to be searched for each user in the worst scenario. Therefore, the computation complexity of the proposed CCRA algorithm can be viewed as $O\left(M\right(|V_{v,sub}|+|E_{v,sub}|+L))$.

6. Performance Evaluation

In this section, the simulation parameters are firstly provided. Then, the experiments are conducted to evaluate the performance of the proposed CCRA algorithm.

6.1. Simulation Parameters

Initially, a Walker constellation [47] with six orbits and 11 satellites per orbit, as well as an altitude of 780 km, is built by Systems Tool Kit (STK) [48], SGP4 [49], and Networkx [50]. Then, satellite network $G(V,E)$ can be established when the fifth satellite on the fourth orbit for the Walker constellation is viewed as the central satellite and the number of network hops is indicated as $h=2$, where the initial storage resources for each satellite are 1000 Mbits, the initial bandwidth resources for each ISL are 1000 Mbps, and the maximum number of users provided with content services for each satellite is 30. Furthermore, cloud center $dc$ is in the coverage of the fifth satellite on the sixth orbit, the number of paths between cloud center $dc$ and access satellite $v_{dc,a}$ is indicated as 4. In addition, the number of hops for each neighboring sub-network is viewed as $h_{sub}=1$.

Furthermore, it is assumed that users are randomly located within the coverage of satellites. For the wireless communication channel between a user and the access satellite, the bandwidth resources are [2, 4] MHz, and the transmission power, the channel gain, and the noise power are 3 W, $-200$ dB, and $-174$ dbm, respectively. Additionally, the velocity of data transmission is $3\times {10}^8$ m/s. For each content, the data size and the content popularity can be generated from [100, 500] Mbits and [1, 10], respectively. It is also assumed that the service delay of retrieving the content for each user can be less than the maximum service delay, and the cost factors of storage resource usage and network bandwidth consumption are indicated as 0.4 and 0.6.

Table 2. Simulation parameters setting.

Integrated Satellite–Terrestrial Network
Name	Network Hops	Storage Resources	Bandwidth Resources	Sub-network Hops	Serviced Users	Shortest Paths
Value	2	1000 Mbits	1000 Mbps	1	30	4
Wireless Communication Channels between Users and Access Satellites and Contents
Name	Bandwidth Resources	Transmission Power	Channel Gain	Noise Power	Data Size	Content Popularity
Value	[2, 4] MHz	3 W	−200 dB	−174 dbm	[100, 500] Mbits	[1, 10]

provides the main simulation parameters, which are viewed as the default parameters if not specified. The simulation platform is built by a commodity computer with i5-1135G7 CPU, 16 GB, Windows 10, and Python language. The average results are provided after the experiments run for 100 times.

6.2. Performance Comparison for Three Different Scenarios

Initially, it is assumed that all users are in the coverage of several particular satellites due to the different geographical distribution of users, where the number of access satellites for users is indicated as $N_a$. For the simulation parameters in Table 2, the experiments are conducted to evaluate the performance of content service in three different scenarios of cooperative caching, edge caching, and cloud center, where $Q=5$, $N_a=4$, and $M=\{200,210,\cdots ,300\}$. In the case of the cloud center, the content services of users are just provided by a cloud center, where the contents can be routed by a satellite network from the cloud center to users. For edge caching, a satellite network with edge caching can provide edge content services for users. Furthermore, for cooperative caching, as proposed in this paper, the content services of users can be provided by an integrated satellite–terrestrial network in a cooperative way. The performance comparison for content service in the three different scenarios, as shown in Figure 4, can be provided for each user service in terms of storage resource usage, network bandwidth consumption, and total deployment costs.

The average storage costs of each user service in the three scenarios are shown in Figure 4a. For the cloud center, all the content services of users are provided by a cloud center, and the satellite network is just responsible for data routing. Therefore, the onboard storage costs for different users are viewed as 0. For edge caching, considering that the content services of users are provided just by a satellite network with edge caching, more content services can be provided for users as the number of contents deployed on satellites increases. Furthermore, for cooperative caching, the cooperative content services of users can be provided by an integrated satellite–terrestrial network, where a cloud center on the ground can provide content services by the satellite network for users considering the restricted edge service provisioning. Therefore, the average storage costs of each user service for Edge Caching are more than that of cooperative caching. The average storage costs of each user service for cooperative caching can reduce by $30.37\%$ compared with edge caching.

The average bandwidth costs of each user service in the three scenarios are shown in Figure 4b, where it can be found that the average bandwidth costs are the largest for the cloud center, followed by cooperative caching, and then edge caching. This is due to the fact that the content services for all users in the cloud center and several users in cooperative caching can be provided by a cloud center. However, the other users in cooperative caching and all users in edge caching will be provided content services by a satellite network with edge caching. Note that the cloud-based content service can bring an increase in network bandwidth consumption compared with the edge-based content service. On average, the bandwidth costs of each user service for cooperative caching can reduce by $83.9\%$ for the cloud center and just increase by $32.36\%$ for edge caching.

Furthermore, the average total deployment costs of each user service are provided in Figure 4c, where the total deployment costs are composed of storage resource usage and network bandwidth consumption based on a weighted sum approach, as shown in Equation (10). It can be found in Figure 4a,b that there are different influences for the three scenarios on storage costs and bandwidth costs. However, the total deployment costs of each user service for cooperative caching are less than that of cloud center and edge caching, where the total deployment costs of each user service for edge caching are also less than that of cloud center. Compared with cloud center and edge caching, the average total deployment costs of each user service for cooperative caching can reduce by $56.3\%$ and $15.79\%$, which also demonstrates that cooperative caching can outperform both of cloud center and edge caching in decreasing the total deployment costs.

Moreover, the performance evaluation for normalized costs in three different scenarios is also provided in Figure 5, where the weighted factors for storage resource usage and network bandwidth consumption are indicated as 0.3 and 0.7. Similar to the results in Figure 4, for cooperative caching, the normalized storage costs of each user service are less than that of edge caching, and the normalized bandwidth costs of each user service are between that of the cloud center and edge caching. However, the normalized total costs of each user service for cooperative caching are less than that of the cloud center and edge caching.

6.3. Performance Comparison with Three Different Algorithms

The experiments are also conducted to evaluate the performance of the proposed CCRA algorithm for the content service compared with two baselines of Greedy and BFS. For Greedy [51], the joint strategy of cooperative caching and resource allocation for the formulated problem can be obtained by searching the neighboring sub-network in a greedy way, where the searching process will be terminated until the first feasible strategy is found. However, for BFS [52], the joint strategy of cooperative caching and resource allocation is searched by BFS based on multi-priority, where all the candidates in one search layer are sorted by content caching, storage resource usage, and service delay in descending order. According to the simulation parameters in Table 2, and $Q=5$, $N_a=4$, $M=\{200,210,\cdots ,300\}$, the experiment results of each user service are provided for CCRA, Greedy, and BFS in Figure 6, including storage costs, bandwidth costs, and total deployment costs.

Figure 6a illustrates the average storage costs of each user service for CCRA, Greedy, and BFS. For Greedy, the cooperative caching services of users are provided by a greedy way, that is, the first available satellite with sufficient storage resources may be used to cache the required content if the required content of one user has not been deployed on the traversed satellites. In that case, the storage costs of each user service can be increased. However, for BFS, the content sharing approach will be given priority for content service to improve the utilization of storage resources when the candidates in one search layer are traversed to obtain the strategy, which can reduce the storage costs as much as possible. Furthermore, for CCRA, the content sharing approach can be given priority for all the satellites in the neighboring sub-network. Therefore, the average storage costs of each user service are the largest for Greedy, followed by BFS, and then CCRA. Note that more users can be provided content services by the content sharing approach as the number of accessed users increases, which will correspondingly reduce the storage costs of each user service, as shown in Figure 6a. On average, the storage costs of each user service for CCRA can reduce by $25.96\%$ for Greedy and $20.61\%$ for BFS.

Figure 6b shows the average bandwidth costs of each user service for CCRA, Greedy, and BFS, where it can also be found that the average bandwidth costs of each user service for Greedy and BFS are close and slightly more than that of CCRA. Specifically, the average bandwidth costs of each user service for CCRA, Greedy, and BFS are 7.32 Mbps, 7.57 Mbps, and 7.5 Mbps, respectively. On average, compared with Greedy and BFS, the bandwidth costs of each user service for CCRA can reduce by $3.3\%$ and $2.34\%$.

Furthermore, Figure 6c describes the average total deployment costs of each user service for CCRA, Greedy, and BFS. Considering that Greedy can provide content services for users in a greedy way, it cannot be guaranteed that content services for users are provided by the content sharing approach as much as possible, which can bring the largest total deployment costs of each user service. For BFS, the content sharing approach can be given priority for all the candidates in one search layer but cannot be guaranteed for all the candidates between different search layers. Therefore, the average total deployment costs of each user service are less than that of Greedy. For CCRA, it can be guaranteed that the content sharing approach is given priority for all the satellites in the neighboring sub-network, which is shown in Figure 3. Therefore, the average total deployment costs of each user service for CCRA are less than that of Greedy and BFS. Specifically, the average total deployment costs of each user service for CCRA can reduce by $18.71\%$ for Greedy and $14.53\%$ for BFS, respectively.

To further evaluate the performance of the proposed CCRA algorithm, the experiments are conducted for $M=\{200,220,\cdots ,300\}$, $Q=\{5,10\}$, and $N_a=\{4,8\}$, as well as the simulation parameters in Table 2. The simulation results for CCRA, Greedy, and BFS in different simulation environments are provided in

Table 3. Performance comparison for CCRA, Greedy, and BFS in different simulation environments.

M	Q	Storage Costs per User (Mbits)						Bandwidth Costs per User (Mbps)						Total Deployment Costs per User
		Greedy		BFS		CCRA		Greedy		BFS		CCRA		Greedy		BFS		CCRA
		${\mathit{N}}_{\mathit{a}}=\mathbf{4}$	${\mathit{N}}_{\mathit{a}}=\mathbf{8}$	${\mathit{N}}_{\mathit{a}}=\mathbf{4}$	${\mathit{N}}_{\mathit{a}}=\mathbf{8}$	${\mathit{N}}_{\mathit{a}}=\mathbf{4}$	${\mathit{N}}_{\mathit{a}}=\mathbf{8}$	${\mathit{N}}_{\mathit{a}}=\mathbf{4}$	${\mathit{N}}_{\mathit{a}}=\mathbf{8}$	${\mathit{N}}_{\mathit{a}}=\mathbf{4}$	${\mathit{N}}_{\mathit{a}}=\mathbf{8}$	${\mathit{N}}_{\mathit{a}}=\mathbf{4}$	${\mathit{N}}_{\mathit{a}}=\mathbf{8}$	${\mathit{N}}_{\mathit{a}}=4$	${\mathit{N}}_{\mathit{a}}=\mathbf{8}$	${\mathit{N}}_{\mathit{a}}=\mathbf{4}$	${\mathit{N}}_{\mathit{a}}=\mathbf{8}$	${\mathit{N}}_{\mathit{a}}=\mathbf{4}$	${\mathit{N}}_{\mathit{a}}=\mathbf{8}$
200	5	27.43	36.62	26.11	34.65	22.19	32.03	5.47	2.74	5.63	2.62	5.39	3.26	14.26	16.29	13.82	15.43	12.11	14.77
	10	34.10	45.19	33.20	43.21	31.74	42.16	7.32	6.07	7.21	5.95	6.38	5.63	18.03	21.72	17.61	20.85	16.52	20.24
220	5	27.08	33.29	25.70	31.59	21.54	29.62	6.08	2.59	6.15	2.57	5.88	2.93	14.48	14.87	13.97	14.18	12.14	13.60
	10	29.79	41.14	28.95	39.53	27.29	38.14	7.29	6.16	7.39	6.19	6.82	5.83	16.29	20.15	16.02	19.53	15.01	18.75
240	5	24.84	32.63	22.86	31.17	18.40	28.98	7.19	3.08	7.24	3.09	7.02	3.24	14.25	14.90	13.49	14.32	11.57	13.53
	10	28.47	38.16	27.68	36.46	26.18	35.74	8.89	6.25	8.56	6.20	7.97	5.69	16.72	19.01	16.21	18.31	15.25	17.71
260	5	22.58	29.86	21.16	28.78	16.20	25.82	8.15	3.47	7.85	3.43	7.79	3.57	13.93	14.02	13.18	13.57	11.16	12.47
	10	25.90	35.59	25.21	35.01	22.92	33.84	9.17	6.62	9.01	6.42	8.48	6.01	15.86	18.21	15.49	17.86	14.25	17.14
280	5	22.41	29.62	20.48	28.36	15.43	25.41	8.68	4.04	8.40	4.02	8.30	4.08	14.17	14.27	13.23	13.76	11.15	12.61
	10	24.02	33.99	23.25	33.04	20.85	32.22	9.46	7.28	9.40	7.04	8.73	6.76	15.29	17.97	14.94	17.45	13.57	16.94
300	5	21.35	27.22	19.22	26.26	13.79	22.75	9.45	4.31	9.38	4.44	9.37	4.56	14.21	13.48	13.32	13.17	11.14	11.84
	10	24.69	31.67	23.37	30.86	20.93	30.06	10.41	7.53	10.24	7.13	9.78	6.63	16.12	17.19	15.50	16.62	14.24	16.00

, which includes the average results of storage costs, bandwidth costs, and total deployment costs for each user service.

From Table 3, it can be found that the average storage costs of each user service for CCRA are also less than that of Greedy and BFS in all the cases. For example, compared with Greedy and BFS, CCRA can reduce the average storage costs of each user service by $13.53\%$ and $10.28\%$ for the case of $M=260,Q=5,N_a=8$, as well as $4.91\%$ and $3.34\%$ for the case of $M=260,Q=10,N_a=8$. Note that more contents can be deployed on satellites to provide different content services for users as the number of contents increases. Therefore, the average storage costs of each user service can be correspondingly increased. Furthermore, it can be found that the average bandwidth costs of each user service for CCRA may be more than that of Greedy and BFS in several cases, such as $M=260,Q=5,N_a=8$ and $M=300,Q=5,N_a=8$. The reason is that the contents can be deployed on more satellites to provide content services for users as the number $N_a$ of access satellites increases. Considering that the content sharing approach can be given priority for all the satellites in the neighboring sub-network, the network bandwidth consumption will be increased when content services for users are provided by the satellites that are far from the access satellite. However, for all the cases, the average total deployment costs of each user service for CCRA are less than that of Greedy and BFS. Specifically, for the case of $M=260,Q=5,N_a=8$, the average total deployment costs of each user service for CCRA can reduce by $11.05\%$ for Greedy and $8.1\%$ for BFS. In addition, for the case of $M=260,Q=10,N_a=8$, CCRA can also reduce the average total deployment costs of each user service by $5.87\%$ for Greedy and $4.03\%$ for BFS.

7. Conclusions

In this paper, the cooperative content services in an integrated satellite–terrestrial network are studied, where the inter-satellite and satellite–terrestrial cooperative caching is considered. The optimization problem is formulated to minimize the total deployment costs of each user service, which is viewed as the weighted sum of storage resource usage and network bandwidth consumption. The CCRA algorithm based on a neighborhood search is proposed to find a feasible strategy, as well as simplifying the system complexity.

The experiments are conducted for three different scenarios of content services, where it can be shown that the content services based on cooperative caching can outperform the content services based on edge caching and the cloud. Furthermore, the performance is evaluated for three different algorithms of CCRA, Greedy, and BFS, where the performance for CCRA is better than that of Greedy and BFS. Additionally, considering that the content services for users may be provided by the satellites that are far from the access satellite as the content sharing approach is given priority for all the satellite in a neighboring sub-network, the average bandwidth costs of each user service for CCRA may be more than that of Greedy and BFS. However, it is shown from the performance evaluation that the proposed CCRA algorithm is effective and efficient in providing the cooperative content services for users in an integrated satellite–terrestrial network.