A Novel M2M Backbone Network Architecture

Abstract

Network architecture analysis is a curial issue for a large scale Machine-To-Machine (M2M) network. Considering an M2M backbone network which consists of distributed satellite clusters in geosynchronous orbit (GEO), a new distributed satellite cluster network (DSCN) hybrid topology architecture is proposed in this paper. To the best of the authors' knowledge, the conceptions of domains, strong/weak link, hubs, small world, and degree realizability are proposed for the first time in the DSCN based M2M backbone networks. How these features affect the network is given through analysis and simulation. By employing Network Science Theory, a strong constraint DSCN topology is presented. In addition, we compare the DSCN with several typical network topologies. Results show that the proposed hybrid architecture realizes a stunning trade-off between the efficiency and robustness.

1. Introduction

Wireless M2M networks supporting M2M-enabled machine devices are pivotal to the success of M2M. Sensor nodes in wireless M2M networks could be connected by a wide range of wireless network technologies, for example, satellite networks, especially the latest space information networks (SINs). With the developing of satellite transmission technologies, the SIN has been playing a more important role in the M2M backbone network than ever. As one of the trends in the future satellite networks, distributed satellite cluster network (DSCN) recently has drawn more and more attention. Many distributed satellite clusters (DSCs) have been deployed by some demonstrations, such as F6 (Future, Fast, Flexible, Fractionated, Free-Flying) Program, Techsat-21, and 3CSat (Three-Corner Satellite) [1–3]. DSC refers to a number of satellites that distribute on the same or adjacent orbit position. The satellites in one or adjacent DSCs cooperate to achieve a particular mission and intercommunicate with each other through intersatellite links. In general, DSC is also referred to as payload distributed communication satellite system (DCSS), distributed space system (DSS), and fractionated spacecraft clusters (FSCs) [4].

With respect to flexibility and robustness, satellites with traditional configurations, that is, monolithic satellites, are associated with more uncertainty than DSCs. The flexibility and robustness for monolithic satellites can only be improved with novel operations. If a monolithic satellite fails, the feasible method to continue the missions carried on the defunct satellite would be launching a new satellite.

The problems that the monolithic satellite has to face mainly include the following:

• (1)

The increasing transmission requirement of M2M terminals leads to a speedy increasing of payload, which is impossible to be met by a single monolithic satellite platform.

(2)

The orbital slots are limited, especially for GEO.

(3)

The building, deploying, and serving period is too long, such as 15 years, which means that the latest technology cannot be applied in time.

(4)

Increasing complexity of system leads to threats of electromagnetic coupling and movement coupling. The risks of manufacturing and launching also increase; meanwhile, the robustness of the M2M backbone network gets worse.

Since the satellite nodes in DSC are separated physically, DSC is a novel concept that not only provides the ability to repair, replace, upgrade, and add modules at a low cost without experiencing the service blackout, but also mitigates the vulnerability to debris and external interference. The above problems which arose among monolithic satellites can also be eliminated in DSCs.

In previous work regarding DSCs, the 802.11s protocol was introduced to the F6 Program by Michel et al. in [5]. It had shown that multiradio mesh extension provided by 802.11s yields a robust and scalable mesh network, which is suitable for cluster of low earth orbit (LEO) satellites. Yaglioglu proposed a DSC architecture for earth observation missions in [6]. The sizing of the modules within Yaglioglu's architecture was made based on an incremental launch or one module per launch, approach. However, the intersatellite links were not considered. In [7], Orndorff et al. discussed the DSCN architecture for responsive space. A satellite architecture consisting of multiple DSCs in GEO was proposed. The architecture provided standard communications and propulsion services to client satellites flying within the clusters. However, only the star topology was built and analyzed, which could not meet the M2M transmission requirements. More information about DSCN can be found in [8–15].

As shown above, none of previous work provided an efficient solution to design and analysis of DSCN, especially for M2M networks. In this paper, we propose a novel M2M backbone network architecture. The main contributions of our paper are summarized as follows:

• (1)

A new DSCN hybrid topology is proposed. The architecture, which consists of DSCs in GEO, is designed for the backbone transmission of the M2M network.

(2)

The conceptions of domains, strong/weak link, hubs, small world, and degree realizability are introduced to DSCN. How these features affect the network is investigated by logical derivation and Monte Carlo simulation.

(3)

The performance of the proposed DSCN architecture is analyzed in the metrics of standard deviation of degree, natural connectivity, and network efficiency. It can be found that the proposed DSCN hybrid topology outperforms typical topologies significantly.

2. Network Features Analysis on DSCN

In this section, we introduce a typical M2M backbone network based on DSCN and investigate the typical DSC topologies.

2.1. Distributed Satellite Cluster Network

The existing studies show that the vehicles in DSCs can use 2.4 GHz Wi-Fi and 802.11s [16]. However, intersatellite laser links, whose transmission rate ≻10 Gbps, can highly improve the transmission capability among vehicles in DSCs [17]. Normally, the distance between two vehicles varies from 10 km to 100 km. In the case of formation flying, the satellites need to be controlled precisely to keep a specific configuration. However, DSC flying does not require a strict relative position control as long as collision avoidance is ensured [18, 19].

Figure 1 demonstrates a typical M2M backbone network which consists of three DSCs in geostationary satellite orbit. The communication links between user nodes and DSCs are located at microwave band, and the communication link among DSCs or in DSC is laser link. The distance between DSCs is about 9 × 10⁴ km to achieve a worldwide coverage. The M2M-enabled devices of the DSCN include deep space spacecrafts, space-based vehicles, air-based aircrafts, ground-based sensors, and sea-based ships. The service information includes data, voice, image, video, and remote sensing data.

Figure 1

M2M backbone network.

2.2. Typical Topologies Analysis

The typical DSC topologies include line, ring, star, and mesh, as shown in Figure 2.

Figure 2

Typical topologies of DSCs.

2.2.1. Line Topology

Line topology can be modeled as

$$\begin{array}{cc}& G_{\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}=\left\{S,L,f_{\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}\right\},\end{array}$$

(1)

where $S=[s_{\mathrm{1}},s_{\mathrm{2}},\dots ,s_n]$ denote the satellite nodes in line topology DSC, $n=\left|S\right|$ is the number of nodes, $L=[l_{\mathrm{1}},l_{\mathrm{2}},\dots ,l_m]$ denote the intersatellite links, $m=\left|L\right|=\mathrm{s}\mathrm{u}\mathrm{m}(l_i)$ is the number of links, and $f_{\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ denotes an $N\times N$ adjacency matrix which is employed to generate links mapping function of line topology DSC, where N is a specified value of n. $l_i=\mathrm{0}$ represents that there is no intersatellite link between nodes $s_i$ and $s_{i+\mathrm{1}}$ and $l_i=\mathrm{1}$ represents that there is one intersatellite link between nodes $s_i$ and $s_{i+\mathrm{1}}$ . The adjacency matrix is named as Boolean matrix whose entries are “0” or “1.” For example, if $n=\mathrm{4}$ ,

$$\begin{array}{cc}& f_{\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}=\left[l_i:s_i⟷s_{i+\mathrm{1}}\right]=\left[\begin{array}{cccc}\mathrm{0}& \mathrm{1}& \mathrm{0}& \mathrm{0}\\ \mathrm{1}& \mathrm{0}& \mathrm{1}& \mathrm{0}\\ \mathrm{0}& \mathrm{1}& \mathrm{0}& \mathrm{1}\\ \mathrm{0}& \mathrm{0}& \mathrm{1}& \mathrm{0}\end{array}\right],\hspace{1em}i=\mathrm{1,2},\dots ,n.\end{array}$$

(2)

Since the satellite in line topology is easy to adjust attitude and the topology has no central node, line topology DSCs are easy to operate and simple to maintain. However, the disadvantage of line topology is that each node only links with its neighbor. The average path length (APL) ${\mathcal{l}}_{\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ between a pair of vehicles is $O(n/\mathrm{3})$ in (3), where the APL is the average of all valid paths in the network. With the increasing network scale ( $n\gg \mathrm{1}$ ), the information of all nodes will be relayed in the whole network, which will result in low information transmission efficiency and poor robustness. A typical system in line topology is the earth observation mission [6]:

$$\begin{array}{cc}& {\mathcal{l}}_{\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}=\frac{\mathrm{2}\left(n{\sum }_{i=\mathrm{1}}^{n-\mathrm{1}}i-{\sum }_{i=\mathrm{1}}^{n-\mathrm{1}}{i}^{\mathrm{2}}\right)}{n\left(n-\mathrm{1}\right)}~O\left(\frac{n}{\mathrm{3}}\right),\hspace{1em}n\gg \mathrm{1}.\end{array}$$

(3)

2.2.2. Ring Topology

Ring topology can be modeled as

$$\begin{array}{cc}& G_{\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g}}=\left\{S,L,f_{\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g}}\right\},\end{array}$$

(4)

where $f_{\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g}}$ is an $N\times N$ Boolean matrix which is employed to generate links mapping function of ring topology DSC; $f_{\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g}}=[l_i:s_i\leftrightarrow s_{i+\mathrm{1}}]$ , $i=\mathrm{1,2},\dots ,n-\mathrm{1}$ . For example, if $n=\mathrm{4}$ ,

$$\begin{array}{cc}& f_{\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g}}=\left[l_i:s_i⟷s_{i+\mathrm{1}}\right]=\left[\begin{array}{cccc}\mathrm{0}& \mathrm{1}& \mathrm{0}& \mathrm{1}\\ \mathrm{1}& \mathrm{0}& \mathrm{1}& \mathrm{0}\\ \mathrm{0}& \mathrm{1}& \mathrm{0}& \mathrm{1}\\ \mathrm{1}& \mathrm{0}& \mathrm{1}& \mathrm{0}\end{array}\right],\hspace{1em}i=\mathrm{1,2},\mathrm{3,4}.\end{array}$$

(5)

For a ring topology, the data will transmit in two directions through the network. Each node has two neighbors, one of which is receiving end and the other is transmitting end. The advantage of ring topology is that it can achieve better robustness than line topology, since each node is at an equal position in the network. If one node breaks down, the ring can avoid connecting it and forming a new ring network immediately. However, since ring topology has no central node, it is hard to operate and maintain the network. Moreover, the information will be relayed in a multihop link when the network size expands, which will result in low information transmission efficiency and large time delay. The ${\mathcal{l}}_{\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g}}$ between each pair of vehicles is $O(n/\mathrm{4})$ in (6). A typical system in ring topology is the Transformational Satellite Communications System (TSAT) [20]:

$$\begin{array}{cc}& {\mathcal{l}}_{\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g}}=\left\{\begin{array}{cc}\frac{\mathrm{2}{\sum }_{i=\mathrm{1}}^{\left(n/\mathrm{2}\right)-\mathrm{1}}i+\left(n/\mathrm{2}\right)}{n\left(n-\mathrm{1}\right)},\hfill & \mathrm{i}\mathrm{f}\hspace{0.17em}\hspace{0.17em}n\hspace{0.17em}\hspace{0.17em}\mathrm{i}\mathrm{s}\hspace{0.17em}\hspace{0.17em}\mathrm{a}\mathrm{n}\hspace{0.17em}\hspace{0.17em}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}~O\left(\frac{n}{\mathrm{4}}\right);\hfill \\ \frac{\mathrm{2}{\sum }_{i=\mathrm{1}}^{\left(n-\mathrm{1}\right)/\mathrm{2}}i}{n\left(n-\mathrm{1}\right)},\hfill & \mathrm{i}\mathrm{f}\hspace{0.17em}\hspace{0.17em}n\hspace{0.17em}\hspace{0.17em}\mathrm{i}\mathrm{s}\hspace{0.17em}\hspace{0.17em}\mathrm{a}\mathrm{n}\hspace{0.17em}\hspace{0.17em}\mathrm{o}\mathrm{d}\mathrm{d}~O\left(\frac{n}{\mathrm{4}}\right);\hfill \end{array}\right.\hspace{1em}n\gg \mathrm{1}.\end{array}$$

(6)

2.2.3. Star Topology

Star topology can be modeled as

$$\begin{array}{cc}& G_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}}=\left\{S,L,f_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}}\right\},\end{array}$$

(7)

where $f_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}}$ is an $N\times N$ adjacency matrix which is introduced to generate links mapping function of star topology DSC; $f_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}}=[l_i:s_i\leftrightarrow s_{i+\mathrm{1}}]$ , $i=\mathrm{1,2},\dots ,n-\mathrm{1}$ . For example, if $n=\mathrm{4}$ ,

$$\begin{array}{cc}& f_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}}=\left[l_i:s_i⟷s_{i+\mathrm{1}}\right]=\left[\begin{array}{cccc}\mathrm{0}& \mathrm{1}& \mathrm{1}& \mathrm{1}\\ \mathrm{1}& \mathrm{0}& \mathrm{0}& \mathrm{0}\\ \mathrm{1}& \mathrm{0}& \mathrm{0}& \mathrm{0}\\ \mathrm{1}& \mathrm{0}& \mathrm{0}& \mathrm{0}\end{array}\right],\hspace{1em}i=\mathrm{1,2},\mathrm{3,4}.\end{array}$$

(8)

The star topology is a master-slave structure, in which the center satellite plays a role of hub and others surround the hub as clients. Each client node links and communicates with the master node. Any communications among the client nodes must pass through the master node. The star topology is widely used in satellite communication because of its high efficiency and flexibility. The advantage of star topology DSC is that the ${\mathcal{l}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}}$ between each vehicle is $O(\mathrm{2})$ in (9), which means that ${\mathcal{l}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}}$ does not increase with the expanding of the network scale. It can be found that the star topology can achieve high information transmission efficiency and low time delay. If one slave node breaks down, it will have little effect on network performance. However, when the master node fails, the whole DSC will be disintegrated. Moreover, high traffic load in the hub satellite may lead to a significant network jam for a large scale network. A typical system in star topology is the Space-Based Group (SBG) [7]:

$$\begin{array}{cc}& {\mathcal{l}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}}=\frac{\mathrm{2}\left[\left(n-\mathrm{1}\right)+{\left(n-\mathrm{2}\right)}^{\mathrm{2}}\right]}{n\left(n-\mathrm{1}\right)}~O\left(\mathrm{2}\right),\hspace{1em}n\gg \mathrm{1}.\end{array}$$

(9)

2.2.4. Mesh Topology

Mesh topology can be modeled as

$$\begin{array}{cc}& G_{\mathrm{m}\mathrm{e}\mathrm{s}\mathrm{h}}=\left\{S,L,f_{\mathrm{m}\mathrm{e}\mathrm{s}\mathrm{h}}\right\},\end{array}$$

(10)

where $f_{\mathrm{m}\mathrm{e}\mathrm{s}\mathrm{h}}$ is an $N\times N$ Boolean matrix which is defined as mentioned previously; $f_{\mathrm{m}\mathrm{e}\mathrm{s}\mathrm{h}}=[l_i:s_i\leftrightarrow s_{i+\mathrm{1}}]$ , $i=\mathrm{1,2},\dots ,n-\mathrm{1}$ . For example, if $n=\mathrm{4}$ ,

$$\begin{array}{cc}& f_{\mathrm{m}\mathrm{e}\mathrm{s}\mathrm{h}}=\left[l_i:s_i⟷s_{i+\mathrm{1}}\right]=\left[\begin{array}{cccc}\mathrm{0}& \mathrm{1}& \mathrm{1}& \mathrm{1}\\ \mathrm{1}& \mathrm{0}& \mathrm{1}& \mathrm{1}\\ \mathrm{1}& \mathrm{1}& \mathrm{0}& \mathrm{1}\\ \mathrm{1}& \mathrm{1}& \mathrm{1}& \mathrm{0}\end{array}\right],\hspace{1em}i=\mathrm{1,2},\mathrm{3,4}.\end{array}$$

(11)

Mesh topology is a kind of k-rule graph, also known as fully connected topology. In the mesh DSC, there exists link between every pair of nodes. This topology has the maximum number of links; that is,

$$\begin{array}{cc}& m=\left|L\right|=n\frac{\left(n-\mathrm{1}\right)}{\mathrm{2}}.\end{array}$$

(12)

The advantage of mesh topology is its robustness, due to the fact that each node is equal to each other in the network and there is no center node. If one node breaks down, it has almost no effect on network performance. Each pair of vehicles is allowed to communicate directly, so the information is transferred in time and without relay. ${\mathcal{l}}_{\mathrm{m}\mathrm{e}\mathrm{s}\mathrm{h}}$ between each vehicle is $O(\mathrm{1})$ . However, the disadvantages of mesh topology are obvious. The number of links increases rapidly with $O(n^{\mathrm{2}})$ when the network scale expands. Since there are many limitations on satellite antenna and transponder resources, the mesh topology may not be able to achieve in a practical DSC [21].

As shown in Table 1, we sum up the characteristics of typical topologies. The APL is ${\mathcal{l}}_{\mathrm{m}\mathrm{e}\mathrm{s}\mathrm{h}}\prec {\mathcal{l}}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}}\prec {\mathcal{l}}_{\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g}}\prec {\mathcal{l}}_{\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ . The number of links is $m_{\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}\prec m_{\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g}}\prec m_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}}\prec m_{\mathrm{m}\mathrm{e}\mathrm{s}\mathrm{h}}$ . The network efficiency of line and ring is lower than that of star and mesh. The invulnerability of line topology is worse than that of ring and star, and the invulnerability of mesh is the best. However, this does not mean that we recommend the mesh topology to the DSCs. The factors involved are a joint of APL, link number, network efficiency, invulnerability, and so forth.

Table 1

Characteristics of typical topologies.

Topology	$$\mathcal{l}$$	m	Network efficiency	Invulnerability
Line	$$O(n/\mathrm{3})$$	$$O(n)$$	Low	Poor
Ring	$$O(n/\mathrm{4})$$	$$O(n)$$	Low	Better
Star	$$O(\mathrm{2})$$	$$O(n)$$	High	Better
Mesh	$$O(\mathrm{1})$$	$$O(n^{\mathrm{2}})$$	High	Best

It is worth pointing out that the previous four typical topologies are widely used in DSCs for a single-task purpose, such as F6, SBG, and Techsat-21. They are the foundation of DSCN for multitask, which will be discussed in this paper.

2.3. The Challenges of DSCN Topology Design

Highly efficient and strongly reliable networking technologies reduce the failure risk of DSCN. However, there are some tough challenges in the design of DSCN topology, which should be carefully considered.

• (1)

The relative movement of satellites may lead to link failure, which has negative effect on the DSC topology. For example, Techsat-21, whose formation is made up by three identical satellites in LEO near circular orbit, flies in various configurations with relative distance ranges from 100 m to 5 km [14]. The constellation of Techsat-21 cannot keep relatively fixed topology.

(2)

Perturbation and orbit transfer insertion error make orbital drift between the actual position of satellite and designed orbit. The relative position variation of satellites is quite intense and uncertain.

(3)

The reconfiguration of DSC for a specific task and satellite node failure may also lead to network topology changing.

The DSCN architecture is complex. It is hard to take all factors into consideration when designing a large-scale DSCN architecture. However, the performance of DSCN is affected by its network structure in nature.

Unlike traditional internet or wireless sensor network, the typical topologies above cannot meet the challenges of DSCN. In this paper, we focus on links of DSCN and propose a DSCN hybrid topology in the next section. The proposed architecture has the advantages of high connectivity, short APL, and homogeneous degree distribution, which is practical for satellite vehicles.

3. DSCN Topology Design

DSCN topology design is a complicated issue including many uncertain factors such as technology, requirement, and policy. In this section, we introduce Network Science Theory [22] into DSCN architecture design and try to take the factors above into account as many as we can.

The DSCN topology can be modeled as

$$\begin{array}{cc}& G\left(t\right)=\left\{S\left(t\right),L\left(t\right),f\left(t\right):J\left(t\right)\right\},\end{array}$$

(13)

where $S=[s_{\mathrm{1}},s_{\mathrm{2}},\dots ,s_n]$ are the satellite nodes in DSCN and $n=\left|S\right|$ is the number of satellite nodes. S can also be expressed as $S=[S_{c\mathrm{1}},S_{c\mathrm{2}},\dots ,S_{ck}]$ , where $k=\left|S_c\right|$ is the number of DSCs and $S_c$ is a DSC. $L=[l_{\mathrm{1}},l_{\mathrm{2}},\dots ,l_m]$ is the intersatellite links and $m=\left|L\right|=\mathrm{s}\mathrm{u}\mathrm{m}(l_i)$ is the number of links. It can be found that the L can also be expressed as $L=[L_{c\mathrm{1}},L_{c\mathrm{2}},\dots ,L_{ck},L_c]$ , where $L_{ck}$ is the number of links in a DSC and $L_c$ is the links between DSCs. f is an $N\times N$ adjacency matrix which is introduced to generate links mapping function of DSCN topology. $l_i=\mathrm{0}$ represents that there is no intersatellite link between $s_i$ and $s_{i+\mathrm{1}}$ and $l_i=\mathrm{1}$ means that there is one intersatellite link between $s_i$ and $s_{i+\mathrm{1}}$ . J denotes a function that the satellite nodes and intersatellite links change with time. t denotes time slot.

In the rest of this section, three performance metrics of network will be introduced and used to evaluate the DSCN performance.

3.1. Standard Deviation of Degree

Standard deviation of degree σ is a quantitative measure of DSCN's heterogeneous characteristic [23]:

$$\begin{array}{cc}& \sigma =\sqrt{\frac{\mathrm{1}}{n}{{\displaystyle \sum }}_i{\left(d_i-〈k〉\right)}^2},\end{array}$$

(14)

where $d_i$ is the number of links for satellite node $s_i$ and $〈k〉=m/n$ is the average number of links for each node in DSCN. The larger σ means the less homogeneous of DSCN.

3.2. Natural Connectivity

Natural connectivity $\stackrel{-}{\lambda }$ is a quantitative measure of DSCN's invulnerability performance or network robustness. The information transmission path in DSCN can be expressed as $w=\{l_{\mathrm{0}}{s}_{\mathrm{1}},l_{\mathrm{1}}{s}_{\mathrm{2}},l_{\mathrm{2}}{s}_{\mathrm{3}},\dots ,l_k{s}_k\hspace{0.17em}|\hspace{0.17em}{l}_i\in L,s_i\in S\}$ , where k is the length of information transmission path. The term $n_{ij}^k$ is used for statistics of w and the link redundancy W can be calculated by (15). The larger W, the better invulnerability performance and network robustness:

$$\begin{array}{cc}& W={\displaystyle \sum }_{i=\mathrm{1}}^n\hspace{0.17em}{\displaystyle \sum }_{j=\mathrm{1}}^n\hspace{0.17em}{\displaystyle \sum }_{k=\mathrm{0}}^{\infty }{n}_{ij}^k.\end{array}$$

(15)

Since $n_{ij}^k$ is difficult to calculate directly, the equivalent statistics is $W^{\prime }={\sum }_{i=\mathrm{1}}^n{e}^{{\lambda }_i}$ , which has been introduced in [24]. In this paper, we define natural connectivity $\stackrel{-}{\lambda }$ as

$$\begin{array}{cc}& \stackrel{-}{\lambda }=\ln \left(\frac{\mathrm{1}}{n}{\displaystyle \sum }_{i=\mathrm{1}}^N{e}^{{\lambda }_i}\right),\end{array}$$

(16)

where ${\lambda }_i$ is the characteristic root of G adjacency matrix. In this paper, the invulnerability performance of the network is evaluated by $\stackrel{-}{\lambda }$ .

3.3. Network Efficiency

Network efficiency ε has been mentioned in Table 1. The network efficiency tries to quantitatively depict the information transmission performance of DSCN, which is a key metric of DSCN topology design progress.

The high DSCN topology efficiency means that the network has the shortest APL for users' information transmission. Thus, the important factor to determine the efficiency should be the APL in (17), where $\min (w_{ij})$ denotes the shortest path w of $s_i\leftrightarrow s_j$ :

$$\begin{array}{cc}& L=\frac{\mathrm{1}}{n\left(n-\mathrm{1}\right)}{\displaystyle \sum }_{i\ne j}\mathrm{m}\mathrm{i}\mathrm{n}\left(w_{ij}\right).\end{array}$$

(17)

However, if there exist isolated nodes in the network, $\mathrm{m}\mathrm{i}\mathrm{n}(w_{ij})$ will be $\to \infty$ and L will be divergent. To avoid this state, we define the network efficiency ε as the sum of the reciprocal of $\mathrm{m}\mathrm{i}\mathrm{n}(w_{ij})$ , in (18). It can be found that ε is a trade-off between the APL and hop count of nodes [25]:

$$\begin{array}{cc}& \epsilon =\frac{\mathrm{1}}{n\left(n-\mathrm{1}\right)}{\displaystyle \sum }_{i\ne j}\hspace{0.17em}\frac{\mathrm{1}}{\min \left(w_{ij}\right)}.\end{array}$$

(18)

4. Demonstration and Analysis

In this section, we take a DSCN as an example, which has the characteristics of domains, strong/weak links, hubs, small worlds, degree realizability, multitask, self-organization, and so forth, as shown in Figure 3. These simulations were carried out using the NS2 simulator. All of the simulations were run 100 times and the average was given. The three DSCs in GEO are networking together to achieve a global seamless coverage.

Figure 3

The three DSCs in GEO are networking together to achieve a global seamless coverage.

Each DSC is referred to as a domain. In each domain, the satellite nodes connect together through dense intersatellite laser links, which is referred to as strong links in the following, and are denoted by “1” in Figure 3. The DSCN can be composed of line topology, ring topology, star topology, mesh topology, or even other atypical topologies depending on mission requirements. Since the distances between DSCs are far (c. 8.83 × 10⁴ km), the inter-DSC links need high power laser and are difficult to realize in applications. Instead, the point-to-multipoint intersatellite laser communication can be used by enlarging the beam divergence angle [26], for example, $s_{\mathrm{12}}\leftrightarrow s_{\mathrm{8}}$ and $s_{\mathrm{12}}\leftrightarrow s_{\mathrm{9}}$ in Figure 3. The distance between nodes in DSC is much closed (c. 10 to 100 km) in fact. Many inter-DSC links, denoted by “2” in Figure 3 and referred to as weak links in follows, are needed. Since the features of long distance between DSCs and near distance inner DSC, each DSC can be equivalent to a big virtual satellite, that is, domain or hub in Figure 3.

Assuming that the satellite nodes are static in a short time, the DSCN in Figure 3 can be represented by

$$\begin{array}{cc}& G=\left\{S,L,f:J\right\},\end{array}$$

(19)

where $S=[D_{\mathrm{1}},D_{\mathrm{2}},\dots ,D_i,\dots ,D_K]$ , $D_i$ denotes the domain i, and $D_i=[s_{i,\mathrm{1}},s_{i,\mathrm{2}},\dots ,s_{i,k}]$ . K and k are the number of DSCs and the number of satellites, respectively. In Figure 3, $D_{\mathrm{1}}=[s_{\mathrm{1,1}},s_{\mathrm{1,2}},\dots ,s_{\mathrm{1,5}}]$ , $D_{\mathrm{2}}=[s_{\mathrm{2,6}},s_{\mathrm{2,7}},\dots ,s_{\mathrm{2,11}}]$ , $D_{\mathrm{3}}=[s_{\mathrm{3,12}},s_{\mathrm{3,13}},\dots ,s_{\mathrm{3,15}}]$ , and $L=[l_{\mathrm{1}},l_{\mathrm{2}},\dots ,l_{\mathrm{28}}]$ are the intersatellite links. Links in domain 1 are $\{l_{\mathrm{1}},l_{\mathrm{2}},\dots ,l_{\mathrm{6}}\}$ , links in domain 2 are $\{l_{\mathrm{7}},l_{\mathrm{8}},\dots ,l_{\mathrm{16}}\}$ , and links in domain 3 are $\{s_{\mathrm{3,12}},s_{\mathrm{3,13}},\dots ,s_{\mathrm{3,15}}\}$ . Links between domain 1 and domain 2 are $\{l_{\mathrm{24}},l_{\mathrm{25}}\}$ , links between domain 2 and domain 3 are $\{l_{\mathrm{26}},l_{\mathrm{27}}\}$ , and link between domain 3 and domain 1 is $l_{\mathrm{28}}$ . $f=\{f_{D_1},f_{D_2},f_{D_3},f_{{}_{\text{inter\_DSCs}}}\}$ are defined in

$$\begin{array}{cc}& f_{D_1}=\left[\begin{array}{ccccc}\mathrm{0}& \mathrm{1}& \mathrm{0}& \mathrm{0}& \mathrm{1}\\ \mathrm{1}& \mathrm{0}& \mathrm{1}& \mathrm{0}& \mathrm{1}\\ \mathrm{0}& \mathrm{1}& \mathrm{0}& \mathrm{1}& \mathrm{0}\\ \mathrm{0}& \mathrm{0}& \mathrm{1}& \mathrm{0}& \mathrm{1}\\ \mathrm{1}& \mathrm{1}& \mathrm{0}& \mathrm{1}& \mathrm{0}\end{array}\right],\\ f_{D_2}=\left[\begin{array}{cccccc}\mathrm{0}& \mathrm{1}& \mathrm{0}& \mathrm{1}& \mathrm{0}& \mathrm{1}\\ \mathrm{1}& \mathrm{0}& \mathrm{1}& \mathrm{0}& \mathrm{1}& \mathrm{0}\\ \mathrm{0}& \mathrm{1}& \mathrm{0}& \mathrm{1}& \mathrm{0}& \mathrm{1}\\ \mathrm{1}& \mathrm{0}& \mathrm{1}& \mathrm{0}& \mathrm{1}& \mathrm{0}\\ \mathrm{0}& \mathrm{1}& \mathrm{0}& \mathrm{1}& \mathrm{0}& \mathrm{1}\\ \mathrm{1}& \mathrm{0}& \mathrm{1}& \mathrm{0}& \mathrm{1}& \mathrm{0}\end{array}\right],\\ f_{D_3}=\left[\begin{array}{cccc}\mathrm{0}& \mathrm{1}& \mathrm{1}& \mathrm{1}\\ \mathrm{1}& \mathrm{0}& \mathrm{1}& \mathrm{1}\\ \mathrm{1}& \mathrm{1}& \mathrm{0}& \mathrm{1}\\ \mathrm{1}& \mathrm{1}& \mathrm{1}& \mathrm{0}\end{array}\right],\\ f_{\text{inter-DSCs}}=\left[\begin{array}{ccc}\mathrm{0}& \mathrm{2}& \mathrm{1}\\ \mathrm{2}& \mathrm{0}& \mathrm{2}\\ \mathrm{1}& \mathrm{2}& \mathrm{0}\end{array}\right].\end{array}$$

(20)

Since the dynamic change of nodes in GEO DSCs is not considered, we set $J=\mathrm{0}$ in this paper.

4.1. Domain

The domain refers to features that the nodes in DSC have high information-interaction frequency, high transmission capacity, and low time delay. The satellite nodes are in tightly coupled relationship and have a reliable connectivity. The advantages of domain are the fact that the network is modularized and P&P (plug and play). During the construction of DSCN, the gradual development and flexible networking can be implemented. During the network development stage, the change of each domain impacts little on the others. Thus, each DSC can evolve independently.

4.2. Strong/Weak Links

Since the transmission delay in the domain is low and the connectivity is reliable, intersatellite links in DSC are defined as strong links. If we connect all the DSCs pair wisely as mesh, there will be too many strong links to realize. The current technique does not allow so many intersatellite laser links, especially for the antenna-limited satellites. For inter-DSC links, the transmission delay is long and the connectivity is poor. Thus, the links between domains are defined as weak links [27] in DSCN.

Since the weak link is the shortcut to connect two domains faraway, the weak links are the key connection of the DSCN, which is more important than strong links. The weak link determines network efficiency ε fundamentally. When the weak link fails, ε will decrease remarkably, as shown in Figure 4. Actually, due to the existence of weak links, the path length of nodes in DSCN is greatly reduced. The information just needs less hop number to arrive at the sink nodes. This feature is referred to as the small world effect in this paper. In our demonstration, Algorithm 1 is proposed to evaluate the affect difference between strong/weak links.

Figure 4

Strong/weak link failures effect on ε.

It can be found in Figure 4 that ε will decrease remarkably when the weak link fails. We can conclude that the weak links are the key connections of the net, which are more important than strong links.

4.3. Hubs and Small World

The hub is the node with strong processing ability and large number of links, especially weak links. In traditional satellite network, one satellite nodes cannot afford so many links due to limited factors, such as antennas, power, and satellite payload. However, the number of inter-DSC links is much larger than that of conventional satellite system using laser links, since the DSC can establish many links based on its distributed antennas. Moreover, the DSC also has the strong processing ability based on its distributed pool of processor and storage. The DSCs can be treated as the hub of the DSCN.

Small world means that although the DSCN has many nodes and the distance is rather long, the information just needs a few hops to reach the sinks. There could be no direct link between one node and most of the rest nodes, but the existence of hubs builds a small word. The existence of weak link and small world avoids the disintegration of DSCN.

4.4. Degree Realizability

Comparing with World Wide Web (WWW) which is typically scale-free with power law $h(k)=k^{-r}$ [28], we assume that the satellite node is degree uniform, and DSC node is similar scale-free. The features of scale-free play a great role in complex network. However, scale-free may not be suitable for DSCN.

Sequences of Degree Distribution. The degree is the number of links for one node. For DSCN, we use (21) to represent the degree of $S=[s_{\mathrm{1}},s_{\mathrm{2}},\dots ,s_{\mathrm{15}}]$ , where g is the lossy information compression for G in (13):

$$\begin{array}{cc}& g=\left[d_{\mathrm{1}},d_{\mathrm{2}},\dots ,d_{\mathrm{15}}\right],\end{array}$$

(21)

where $d_i$ denotes the number of links for node $s_i$ . Normalizing the lossy information vector g, the sequences of degree distribution $g^{\prime }$ can be expressed as

$$\begin{array}{cc}& g^{\prime }=\left[h_{\mathrm{1}},h_{\mathrm{2}},\dots ,h_{\mathrm{m}\mathrm{a}\mathrm{x}\_d}\right],\end{array}$$

(22)

where $h_{\mathrm{1}}$ is the proportion of nodes whose degree is 1, $h_{\mathrm{2}}$ is the proportion of nodes whose degree is 2, and $h_{\mathrm{m}\mathrm{a}\mathrm{x}\_d}$ is the proportion of nodes which have the largest degree in the DSCN. Similar to the probability density function (PDF) in Probability Theory, the sum of elements in $g^{\prime }$ is 1. In order to depict different satellite topology clearly, we evaluate the sequences of degree distribution of typical topologies and DSCN, as shown in Figures 5 and 6.

Figure 5

Sequences of degree distribution of typical topologies.

Figure 6

Sequences of degree distribution of DSCN.

Algorithm 1.

Strong/weak link failures effect on ε.

Step  1. Initialize algorithm; compute the shortest paths of whole satellite clusters network

$$\begin{array}{cc}& \min \left(w_{ij}\right)=\left\{s_i⟷s_j\hspace{0.17em}|\hspace{0.17em}{s}_i,s_j\in S\right\}\\ {\epsilon }_{\mathrm{0}}=\frac{\mathrm{1}}{n\left(n-\mathrm{1}\right)}{\displaystyle \sum }_{i\ne j}\hspace{0.17em}\frac{\mathrm{1}}{\min \left(w_{ij}\right)}.\end{array}$$

(23)

Step  2. While the number of strong links failure $k\prec$ inter-DSC links number do wipe off the corresponding paths $C_n^k$ involved, compute shortest paths

$$\begin{array}{cc}& \mathrm{m}\mathrm{i}\mathrm{n}\left(w_{ij}\right)=\left\{s_i⟷s_j\hspace{0.17em}|\hspace{0.17em}{s}_i,s_j\in S,\hspace{0.17em}\hspace{0.17em}\stackrel{-}{L}=L-\left(l_{\mathrm{1}},l_{\mathrm{2}},\dots ,l_k\right)\right\},\\ \mathrm{m}\mathrm{i}\mathrm{n}{\left(w_{ij}\right)}_k=\frac{\mathrm{s}\mathrm{u}\mathrm{m}\left(C_n^k\min \left(w_{ij}\right)\right)}{C_n^k},\\ {\epsilon }_{sk}=\frac{\mathrm{1}}{n\left(n-\mathrm{1}\right)}{\displaystyle \sum }_{i\ne j}\hspace{0.17em}\frac{\mathrm{1}}{\mathrm{m}\mathrm{i}\mathrm{n}{\left(w_{ij}\right)}_k},\\ \stackrel{-}{L}=L-\left(l_{\mathrm{1}},l_{\mathrm{2}},\dots ,l_k\right),\\ \hspace{1em}k=k+\mathrm{1},\end{array}$$

(24)

end while

Step  3. While the number of weak links failure $k<\mathrm{\hspace{0.17em}\hspace{0.17em}}n$ -inter-DSC links number do wipe off the corresponding paths $C_n^k$ involved, compute shortest paths

$$\begin{array}{cc}& \mathrm{m}\mathrm{i}\mathrm{n}\left(w_{ij}\right)=\left\{s_i⟷s_j\hspace{0.17em}|\hspace{0.17em}{s}_i,s_j\in S,\hspace{0.17em}\hspace{0.17em}\stackrel{-}{L}=L-\left(l_{\mathrm{1}},l_{\mathrm{2}},\dots ,l_k\right)\right\},\\ \mathrm{m}\mathrm{i}\mathrm{n}{\left(w_{ij}\right)}_k=\frac{\mathrm{s}\mathrm{u}\mathrm{m}\left(C_n^k\mathrm{m}\mathrm{i}\mathrm{n}\left(w_{ij}\right)\right)}{C_n^k},\\ {\epsilon }_{wk}=\frac{\mathrm{1}}{n\left(n-\mathrm{1}\right)}{\displaystyle \sum }_{i\ne j}\hspace{0.17em}\frac{\mathrm{1}}{\mathrm{m}\mathrm{i}\mathrm{n}{\left(w_{ij}\right)}_k},\\ \stackrel{-}{L}=L-\left(l_{\mathrm{1}},l_{\mathrm{2}},\dots ,l_k\right),\\ \hspace{1em}k=k+\mathrm{1},\end{array}$$

(25)

end while

Figure 5(a) is $g^{\prime }$ of line topology. It can be found that the degree is more than 80% at 2, which means that the satellite nodes have two links. Small number of links may add limits to the transmission possibilities of satellite vehicles. Figure 5(b) shows that $g^{\prime }$ of ring topology is 100% at 2. In Figure 5(c), $g^{\prime }$ of star topology is 93% at 1. In Figure 5(d), $g^{\prime }$ of mesh topology is 100% at 15. It can be readily found that $g^{\prime }$ is rather uneven. When the network scale increases constantly, the problem will be more severe due to nonhomogeneous of $g^{\prime }$ . Comparing with Figure 5, the degree of DSCN in Figure 6 is more homogeneous. The degrees of most satellite nodes are centralized at 3 and 4. The degree of few nodes is larger than 5, which means that the links can be fit for engineering realization. This phenomenon is referred to as degree realizability in this paper. It is obvious that a power law behavior may not be seen in a small cluster of satellites. This conclusion still holds true for a large number of DSCN statistical results.

4.5. Multitask and Self-Organization

Since the DSCN is a space based comprehensive M2M backbone network, the ability of DSCN shall meet the multitask requirements for all kinds of M2M terminals. The proposed architecture of the DSCN consists of domains, which allow each domain to work relatively independently and cooperatively at the same time, that is, multitask ability. For many distributed satellite missions, the system is single-task at one moment.

Similar to the intelligent mobile nodes in ad hoc networks, the satellites in DSCN can be self-organized when the mission is changed. If one node is damaged, other nodes will reject this node and reconfigure intelligently to maintain the original functions.

4.6. Performance Comparison

The standard deviation of degree σ, natural connectivity $\stackrel{-}{\lambda }$ , and network efficiency ε measure the performance of DSCN from different viewpoints, respectively. From Table 2, we can find that the standard deviation of degree is ${\sigma }_{\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g}}={\sigma }_{\mathrm{m}\mathrm{e}\mathrm{s}\mathrm{h}}\prec {\sigma }_{\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}\prec {\sigma }_{\mathrm{D}\mathrm{S}\mathrm{C}\mathrm{N}}\prec {\sigma }_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}}$ , the natural connectivity is ${\stackrel{-}{\lambda }}_{\mathrm{m}\mathrm{e}\mathrm{s}\mathrm{h}}\succ {\stackrel{-}{\lambda }}_{\mathrm{D}\mathrm{S}\mathrm{C}\mathrm{N}}\succ {\stackrel{-}{\lambda }}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}}\succ {\stackrel{-}{\lambda }}_{\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g}}\succ {\stackrel{-}{\lambda }}_{\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ , and network efficiency is ${\epsilon }_{\mathrm{m}\mathrm{e}\mathrm{s}\mathrm{h}}\succ {\epsilon }_{\mathrm{D}\mathrm{S}\mathrm{C}\mathrm{N}}\succ {\epsilon }_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}}\succ {\epsilon }_{\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g}}\succ {\epsilon }_{\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$ . ${\sigma }_{\mathrm{D}\mathrm{S}\mathrm{C}\mathrm{N}}$ suggests that the DSCN is not a flat structure network, which has hubs in the network. ${\stackrel{-}{\lambda }}_{\mathrm{D}\mathrm{S}\mathrm{C}\mathrm{N}}$ and ${\epsilon }_{\mathrm{D}\mathrm{S}\mathrm{C}\mathrm{N}}$ are larger than others except for mesh. The mesh network has zero σ, the highest $\stackrel{-}{\lambda }=11.29$ , and $\epsilon =0.94$ , comparing with line topology, ring topology, star topology, and DSCN. It means that the mesh network is a flat, centerless structure and has strong invulnerability and best information transmission performance. However, the mesh is an ideal network topology. As the number of satellite nodes is increasing, the network will be unrealizable.

Table 2

Performance comparison of network parameters ( $N=\mathrm{15}$ ).

Topology	σ	$$\stackrel{-}{\lambda }$$	ε
Line	0.34	0.78	0.31
Ring	0	0.82	0.35
Star	3.24	1.30	0.53
Mesh	0	11.29	0.94
DSCN	0.72	1.66	0.54

As shown in Table 2, the DSCN hybrid topology designed has the low $\sigma =0.72$ , high $\stackrel{-}{\lambda }=1.66$ , and $\epsilon =0.54$ . It can be found that the hybrid topology is a trade-off between the complexity and performance. It can be concluded that the DSCN hybrid topology is better than typical topologies in view of implementation.

5. Conclusion

A DSCN hybrid topology has been studied under the Network Science Theory. It has been proved that the weak link is the shortcut to connect two domains faraway. Moreover, the homogeneous degree of DSCN means that the architecture can be practically realized. Performance comparison has been given to demonstrate the superiority of the proposed topology. Results show that the hybrid topology can achieve a good trade-off between the efficiency and invulnerability performance comparing with the conventional topologies.