Design and Evaluation of Dynamic Topology for Mega Constellation Networks

Abstract

Due to numerous Low Earth Orbit (LEO) satellites, urgent analysis of many temporary inter-satellite links (ISLs) is necessary for mega constellation networks. Therefore, introducing a dynamic link in topology design is crucial for increasing constellation redundancy and improving routing options. This study presents one class of static topology of satellites (STLS) and two types of dynamic topology of satellites (DTLS). Firstly, a call model based on global population density distribution is determined using world population density by provincial administrative divisions. Then, using a common simulation platform, the Dijkstra algorithm obtains random paths between 10,000 pairs of urban ground stations, adopting a time slice division strategy. Finally, 3 indexes are obtained within 66-time slices: average call distance, number of hops, and total time delay. Results show that DTLS1 reduces these indexes by 3.58%, 3.72%, and 3.57%, respectively, compared with DTLS2 under the same conditions, indicating that DTLS1 has the best network performance, transmitting traffic quickly in any direction through the reverse track, thereby verifying the related hypothesis.

1. Introduction

With the breakthrough of new technologies related to satellite communications, the promotion of the 5G era, and the development of smart cities, more than 10 domestic and foreign companies have proposed to build large satellite constellations, such as Globalstar, Iridium, and other new LEO constellations. However, there is no international standard for the number of giant constellations, and it is challenging to coordinate and manage a mega constellation system only from the national level.

Generally, the emerging LEO mega-constellation program aims to provide broadband internet access services to users worldwide through hundreds to tens of thousands of LEO satellites. This program features comprehensive coverage, low latency, high resistance to destruction, and airspace integration, making it ideal for ubiquitous connectivity [1]. All aspects of our daily life are closely related to satellite communications. In the future, a star-ground-converged heterogeneous network will integrate wireless networks, the Internet, local area networks, cellular networks, and more to enhance collaboration between different networks [2].

The topology of a satellite constellation network refers to the connectivity relationships among the satellite nodes in the constellation, including mutual visibility, azimuth, elevation, inter-satellite distance length, and distance variation rate [3]. Variations in satellite topology often affect performance metrics such as ISL connectivity, communication terminal utilization, average end-to-end delay, average inter-satellite proximity distance, and the number of hops for packet forwarding [4]. In addition, the destructiveness of the satellite network itself is also closely related to the topology configuration. Therefore, a reasonable network topology directly affects the routing communication, quality of service, and system complexity of the constellation.

The high number of satellites in a mega constellation and their rapid and perpetual movement results in a complex satellite topology that requires immediate analysis, optimization, and evaluation. This paper employs the topological configuration as a basis and introduces dynamic links to investigate optimal network performance. Furthermore, we evaluate and compare the simulation results of the designed constellation network topology in three areas, highlighting the contributions of our research:

• Based on the complexity of the number of satellites and the periodic and predictable nature of their movements within mega constellations, a virtual topology is constructed using equidistant time slicing to enable dynamic simulation and management of the topology;
• After introducing dynamic links, two different combinations were adopted for the three fixed links, and based on the dynamic link selection algorithm, connection thresholds were set for each satellite to obtain the corresponding dynamic topology during each time slice;
• A joint simulation platform established a call model based on global population density to perform network performance simulations and compare the designed static topology, two dynamic topologies, and a benchmark topology. The evaluation was focused on the performance of different topology networks in three aspects: average call distance, number of hops for packet forwarding, and total time delay.

As shown in Section 2.1, two types of existing satellite network topologies are static and dynamic. Previous work has focused chiefly on the fixed mesh topology, but this type of topology could be more flexible and can limit network performance. To fully leverage a satellite’s operation and obtain the variation law of topology during the operational cycle for optimal performance, it is imperative to optimize satellite topology [5]. A well-designed satellite network topology can reduce link switching caused by the high-speed operation of LEO satellites and maximize the use of limited link bandwidth to meet user requirements. As such, developing an efficient ISL allocation algorithm is a critical task in satellite network planning technology and the main contribution of this paper.

The remainder of this paper is structured as follows. Section 2 presents an overview of static and dynamic satellite network topology. Section 3 describes the time slice division strategy, the way static links are combined, and the dynamic link selection algorithm. Section 4 provides a detailed description of the basic methodology of the simulation, the step-by-step process, and the parameters to be set. Section 5 reveals the simulation results using the proposed strategy. Finally, this work is concluded in Section 6.

2. Related Works

The satellite network topology consists of ISLs whose structure indicates the satellites’ location information and interrelationships in orbit. In this section, we will compare the characteristics of static topologies of domestic and foreign satellite networks, introduce two main types of typical dynamic link assignment strategies, and summarize their shortcomings based on this current work.

2.1. Static Satellite Network Topology

In general, typical static topologies of satellite networks cover star, ring, tree, and mesh topologies [6]. The study of satellite network topology analysis not only helps improve the constellation’s overall performance but also plays a key role in performance evaluation. In recent years, scholars at home and abroad have been continuously studying and improving the structure of satellite network topology in depth [7].

Table 1. Topology characteristics.

Topology Type	Advantages	Disadvantages
Star topology [8]	Simple structure, easy to improve	Inability to achieve full coverage and heavy burden on central nodes
Ring topology	Stable communications in the coverage area	Low communication efficiency and poor scalability
Tree topology	Small diameter and efficient routing	Root nodes are heavily burdened and prone to congestion
Mesh topology [9]	High reliability, high redundancy, low latency, many links	High cost, difficult to control and inefficient

illustrates a comprehensive comparison of the four types of typical topologies commonly used and an analysis of their strengths and weaknesses.

2.2. Dynamic Satellite Network Topology

The typical dynamic link assignment policies are summarized as the following two policies. The first is generated based on the shortest distance strategy, while the second is based on the longest visible time strategy [10].

1.

Based on the shortest distance strategy.

The central concept of the link selection strategy based on the shortest distance is that the source satellite selects the nearest target when choosing a satellite to establish an ISL. As the satellites constantly move at high speeds, the distance between each node must be continuously calculated, and their visibility analyzed to ensure link connectivity. When the source satellite detects a closer node, it adjusts the connection and establishes a new link with the nearest satellite.

2.

Based on the maximum visible time strategy.

According to the core idea of the link selection strategy derived from the longest visual time, the source satellite will give preference to the target with which it has the longest visual time when selecting satellites to establish an ISL. Once the link is established between the two satellites, the connectivity continues until the target satellite is out of the visual range of the source satellite, and the other satellite with the longest visual time is then reselected after the interruption.

Noakes et al. [11] proposed a link assignment algorithm suitable for dynamic satellite networks, which optimizes the overall network topology connectivity. The algorithm enables rapid decision making on whether to establish or terminate links based on the time-varying state of the network. However, the algorithm is relatively complex and may not be feasible for prominent constellations. Qi et al. [12] reviewed the dynamic routing algorithm based on virtual nodes and proposed using a low-complexity probability routing algorithm (LCPR) to solve the problem of selecting the next hop when the satellite receives the packet. By obtaining the location information of the source node and target node, the optimal path is obtained by using the distributed computing method, but the LCPR algorithm is only applicable to the polar orbit in the LEO satellite network. Alhussein et al. [13] adopted a connection-oriented link allocation strategy aimed at reducing the vast network overhead caused by frequent routing table updates. Although this method can balance the network traffic, the network performance will be significantly reduced when the network topology loses its regularity.

In another paper, Dai et al. [14] developed an intelligent optimization algorithm that analyzes the dynamic network topology to determine the quality of experience of various regions and provide orbital parameters for satellite constellation configuration. However, the assumed demand distribution is static and overly idealized, which does not accurately reflect real-world user demand. Marbel et al. [15] developed a cost-effective, dynamic network for computing and proposed a heuristic algorithm to calculate link assignments for interstellar optical communication networks. However, the proposed method is limited to interstellar laser links and does not address scalability issues in prominent constellations.

Despite extensive research and analysis by numerous scholars on the design and optimization of satellite network topologies, most simulations encounter various issues. These challenges include insufficient satellites incorporated in testing, high algorithm complexity, overlooking the periodicity and regularity of prominent constellations, and proposed optimization algorithms that do not apply to mega-satellite networks.

Previous work cannot balance the shortcomings mentioned above while improving the overall performance of the constellation network. Therefore, it is necessary to combine the characteristics of numerous temporary dynamic links in the constellation and propose a new link allocation strategy. This strategy should calculate and filter satellites that meet the conditions for link establishment, as well as select the optimal topological configuration, to minimize the total time delay of space communication and improve the transmission efficiency of the links.

3. Problem Analysis

This section presents a time slice division principle based on the number of satellites per orbit, followed by two fixed-link combinations. Finally, a dynamic non-adjacent orbital plane link (NOPL) selection strategy is proposed, which establishes dynamic links based on the regularity of inter-satellite distances without exceeding four connections per satellite, ensuring that the link length is shorter than the shortest adjacent orbit link length. By calculating the dynamic satellite connectivity in the first two time slots, the dynamic links for the remaining time slices can be determined. A dynamic link selection algorithm is designed with the combined time slices and dynamic link selection strategy, resulting in two dynamic topologies.

3.1. Time Slice Division Principle

Due to the substantial heterogeneity of the mega constellation network, frequent link breakage and reconstruction of the topology, and the variability of the ISL distance, it is necessary to continuously improve and optimize the dynamic topology of the constellation to obtain a network with better communication performance index. Assuming a Walker constellation with 24 orbits and 66 satellites per orbit, the calculation of the nearest non-adjacent orbiting satellite at different moments requires a total of $5742\times \left(24-3\right)\times 66$ calculations for a single satellite in the constellation. If the nearest satellite is searched in the network of the entire constellation, the number of calculations will be as high as $5742\times \left(24-3\right)\times 66\times 1584$.

Therefore, without dividing the time slice, the complexity of the algorithm will be high due to the large data magnitude, which is not suitable for use in mega constellation networks with a large number of nodes, and the irregularity of the topology will also significantly increase the difficulty of prediction for links, which is not conducive to the development of network routing algorithms. Meanwhile, the maximum connectivity of each satellite in the constellation is four. The traditional strategy of building a link based on the shortest distance has not yet taken into account the specified maximum connectivity, which will make the topology less resistant to destruction if the link is disconnected after exceeding the range [11].

The mega constellation is a network of satellites with a constantly changing topology, periodic and predictable satellite movements, and a regular constellation topology so that the time slices can be divided into equal intervals by constructing a virtual topology, thus ultimately achieving dynamic topology management [16].

The Walker constellation assumed in this paper has an operation period equal to 5742 s, and 1584 satellites need to be launched and deployed in the first phase. Suppose only the dynamic links established in the first 33 time slices need to be calculated. In that case, this reduces the computational effort to a great extent and facilitates the further use of routing algorithms to filter dynamic links and generate and analyze regular topologies [17].

Based on the variation in interstellar distance, a time slice division method is constructed using the number of satellites per orbit, corresponding to Figure 1. According to the theory of satellite numbering within the constellation [18], definitions are established for the orbits and inner satellites of the Walker constellation. The named satellite nodes are denoted as $S(i,j)$, representing the satellite $j$ within the orbital plane $i$, where $i$ ranges from 1 to 24, and $j$ ranges from 1 to 66. $T_n$ represents the time slice $n$; since there are 66 satellites in each orbit, this implies that $n\in [1,66]$. The core idea is summarized in the following figure.

For example, consider $S(2,x)$, representing the satellite $x$ in the $O{P}_2$. Assuming that in the $T_1$, the satellite closest to $S(2,x)$ is $S(y,z)$, representing the satellite z on the $O{P}_y$. Both satellites comply with the numbering principle, i.e., $x\in [1,66]$, $y\in [1,24]$, and $z\in [1,66]$. The nearest satellite to $S(2,x-(n-1))$ in the $T_n$ is $S(y,z-(n-1))$ when $x-(n-1)\ge 0\mathrm{and}z-(n-1)\ge 0$; the nearest satellite to $S(2,x-(n-1))$ is $S(y,z-(n-1)+66)$ when $x-(n-1)\ge 0\mathrm{and}z-(n-1)<0$; the nearest satellite to $S(2,x-(n-1)+66)$ is $S(y,z-(n-1))$ when $x-(n-1)<0\mathrm{and}z-(n-1)<0$; and the nearest satellite to $S(2,x-(n-1)+66)$ is $S(y,z-(n-1)+66)$ when $x-(n-1)<0\mathrm{and}z-(n-1)<0$.

Therefore, as long as the initial satellite in any orbit is calculated in the first time slice from the nearest satellite node in the whole network, the link connectivity of the remaining 65 satellites can be directly derived, thus reducing computational effort and improving computing performance.

3.2. Combination of Three Fixed Links

Satellites can establish ISLs with other satellites in the same orbital plane (OP) or different OPs in a mega constellation. In order to take into account the east–west connectivity of the satellites, a uniform connection rule is defined: when $1\le i\le 24$, the odd-numbered satellites in each orbit connect to the satellite with the shortest distance from the adjacent orbit on the left, allowing hop-by-hop transmission along the orbital direction; the even-numbered satellites are only connected to the shortest distance satellite in the right adjacent orbit and complete hop-by-hop transmission along the orbit in the opposite direction. This ensures that two adjacent satellites in the same orbit are a pair, avoiding duplicate connections and that the two closest satellites in adjacent orbits are connected [19]. Since there is only one link between the different satellites, if the connection of the adjacent orbital links between $O{P}_1$ and $O{P}_{23}$ is specified, the satellite connections on $O{P}_{24}$ can be predicted directly [20].

Before the introduction of dynamic links, two combinations are designed for the remaining three fixed links. Figure 2a mainly consists of one adjacent OP ISL (AOPL) and two intra-OP links, while Figure 2b consists of two AOPLs and one intra-OP link.

• The connection method of intra-OP ISLs plus one AOPL enables the links within each orbit to connect with the preceding and following neighboring satellites at any given time, allowing for hop-by-hop transmission in either direction along the orbit. In the network topology, the AOPLs on the right side provide data transmission from west to east, while the AOPLs on the left provide the opposite direction [21].
• The connection method of one intra-OP ISL plus two AOPLs ensures that the links between the two orbits are always connected to the nearest adjacent satellite nodes at any given time, allowing for hop-by-hop data transmission in the east–west direction. As the adjacent satellite nodes on the same orbit are relatively stationary, permanent links of equal length exist for both forward and backward directions [22].

The above is a combination of fixed links. Even though the stability of the satellite network topology is relatively maintained to a certain extent, it is difficult to completely break through the limitations of the static topology by relying solely on fixed links. Therefore, this paper introduces a dynamic link in addition to the above description of fixed links, which helps to enhance the flexibility of the mega constellation further.

3.3. Dynamic Link Selection Algorithm

An arbitrary initial satellite $S(i,j)$ is selected in the first step, and the link relationships connected within the first two time slices are analyzed. Secondly, a time slice division strategy is used based on the number of satellites per orbit. Only temporary dynamic links exist in non-adjacent orbits. According to the variation of inter-satellite distance in different time slices, the first 33 time slices are selected to study how the remaining 65 satellites in the same orbit achieve data transmission through dynamic links. Thirdly, through a comprehensive dynamic link selection strategy, all corresponding dynamic links of all satellites in orbit are introduced. Finally, twenty-one orbits not adjacent to the orbit are selected, and the dynamic links of the remaining satellites are calculated according to the condition constraints of maximum connectivity of four and dynamic links one-to-one correspondence, respectively [23].

In order to obtain dynamic links for all satellites across 66 time slices, the process mentioned above is repeated in a continuous cycle. To optimize the topological configuration of the mega constellation based on the concept of dynamic link design, a specific selection algorithm’s pseudo-code is presented in Algorithm 1.

In the pseudocode, $T$ represents the selection of a time slice in the cycle. At a given moment, $R_1$ and $R_2$ represent the distances from satellites $S_1$ and $S_2$ to the center of the Earth, respectively. The angle $\theta$ formed between the satellites and the center of the Earth is determined using the satellite orbit parameters. At the same time, the instantaneous ISL distances of $S_1$ and $S_2$ are calculated based on the geocentric angle $\theta$ [24].

Algorithm 1 Pseudocode for the dynamic link selection

Input: Connectivity threshold C_M←4 for each satellite, initial satellite $S_1$       $S\leftarrow \left\{\left\{1,\left\{S(1,1),\cdots ,S(24,66)\right\}\right\},\cdots ,\left\{66,\left\{S(1,1),\cdots ,S(24,66)\right\}\right\}\right\}$       $C\leftarrow \left\{1,\left\{3,\cdots ,3\right\},\cdots ,\left\{66,\left\{3,\cdots ,3\right\}\right\}\right\}$// specify the connection degree at the initial time Output: Set of satellite link results for each time slice LISL_SET 1:  ISL_SET ←$\left\{\right\}$, TempMap ←$\left\{\right\}$, entry ←$\left\{\right\}$ 2:   for  t ← 1  to  2  // first calculate connectivity in the first two time slices of $S_1$ 3:     SNN ← selectNonNer$(S_1,S)$ // take the set of satellites in non-adjacent orbits to $S_1$ 4:       for i ← 1 to 66, j ← 1 to 24, SNN ← $S(i,j)$ 5:        d ←$d_{12}=\sqrt{R_1^2+R_2^2-2\times R_1\times R_2\times \cos \theta }$// calculate the ISL distance between $S_1$ and $S_2$ 6:          TempMap.add$(S_2,d)$   // the address key is satellite and the value is $d_{12}$ 7:       end 8:       SortByDistance(TempMap)   // sorted by call distance from smallest to largest 9:         For entry IN TempMap   // define entry as address key 10:           IF C (T, entry) > C_M Then 11:              S(T).remove(entry) 12:       Else 13:              LISL_SET.add((T,S1),entry) // t time slice $S_1$ and entry.key satellite establish link 14:              C(T,S1) ←4; C(T,entry) ←4 15:    Next entry 16:    Next T 17:    For K ← 3 to 66  // dynamic links for the remaining time slices of $S_1$ are inferred from the dynamic link pattern 18:         ISL_SET ← DLSRGenerater(S1,LISL_SET,K) 19:    Next K 20:    For P←3 to 23   // all dynamic links based on combined dynamic link selection strategy and track change pattern 21:        ISL_SET ← DLSRAndCATS(ISL_SET,C,S,P) 22:    Next P

The advantage of the designed dynamic link selection algorithm is that once the non-adjacent orbit satellites connected to each satellite in the first two time slices are calculated, the algorithm can directly determine the dynamic links established by all satellites in that orbit at any time slice. The links established by the corresponding non-adjacent orbit satellites in the remaining time slices can also be obtained accordingly, completing the link connections of all satellites in different time slices during the cycle. Moreover, the resulting network topology is relatively regular, facilitating future routing research.

In addition, compared with the static topology consisting of four fixed links, the introduction of dynamic links provides more path options and shorter inter-satellite distances, resulting in smaller communication delays. Additionally, traffic can be quickly transmitted in various directions, significantly reducing the number of routing hops during inter-satellite communications. Therefore, the network performance is better in a large-scale constellation with many hops.

4. Modeling System Approach

The satellite communication network serves as a facility that operates around the clock to receive calls. Incoming calls are regarded as customers awaiting service, and their wait times adhere to a specific distribution. To capture the call process, diverse topological arrangements of the network are created and implemented. Statistical analysis is subsequently performed to evaluate the network’s capacity to handle and dispatch calls, thus enabling appropriate conclusions to be drawn regarding the queuing service process.

4.1. Call Model Based on Global Population Density

In the model utilized in this paper, low-earth orbit satellite networks that provide communication services are analyzed as loss systems. When a new service request is made, there will be no idle channels in the entire satellite communication network, and a window will inevitably be available to provide service. The service system does not need to wait. If there is no available window for service, the request will be blocked and recorded as a failed call.

The global population data as of 2020 is about 7.970 billion, the per capita broadband demand is about 10 Mbps, and the total transmission rate demand is about 796.96 Tbps. Figure 3 shows the global population density by provincial administrative divisions, with population deciles ranging from 5 to 45 per square kilometer. The more economically developed continents are mainly North America, Asia, and Europe. The level of population density and economic development varies from region to region, and this characteristic will undoubtedly affect the division of communication business volume.

The global population distribution shows that most people are concentrated in the lower latitudes of the northern hemisphere, accounting for 80% of the total global population. Therefore, it is possible to predict the business volume demand in each location from the global population density. It is observed that the regions are divided according to the latitude and longitude of the site where the application service request is sent, mainly subdivided into South America, Australia, the Eurasian plate, etc. Eurasia has the highest demand for call services, accounting for over 40% of the total, followed by North America, accounting for 30% of the total, and each of the remaining segments accounts for 10%.

4.2. General Framework of the Simulation

In order to gain a deeper understanding of the communication performance of the satellite network, a unified maximum service time strategy simulation was adopted to simulate the call test between the earth station and the satellite, minimizing the number of link switches in the process from the earth station to the satellite. The general flow of the simulation is shown in Figure 4, and the specific steps are as follows:

• The ground stations A to B send service requests sequentially in the calling order, and the corresponding satellite with the longest service time within the visual range is selected by combining the Time strategy, in which the satellite node connected to ground station A is called source satellite C and the satellite node connected to ground station B is called target satellite D;
• ISLs are constructed according to different connection strategies, resulting in different topologies for the entire mega constellation network;
• After setting the time slice size, the link connections of satellites in each time slice are recorded in the matrix K of ISLs, and the shortest path P from C to D in the LEO satellite network is obtained by Dijkstra’s algorithm, with a static network topology table generated in different time slices;
• Analyze the resource allocation of the remaining channels of all satellites in the shortest path P. If the remaining channels are not zero, access to the current call is allowed while the total number of channels in the path is subtracted by one. If there are no remaining free channels, the call is blocked directly at the current moment, and the result is recorded as a call failure;
• Continue to access new call requests and repeat the above process until there are no new ones.

When a new call request is generated and accessed, the existing call queue needs to be updated, and two main influencing factors need to be taken into account. Firstly, when implementing dynamic switching of ISLs in particular time slices, it should be ensured that the calls to be switched are made in continuous time Y and that the shortest path P from C to D also changes continuously within time Y. Secondly, as the satellite is operating at high speed, the angle between the ground base station and the satellite needs to be kept within the minimum elevation angle criteria. If the minimum elevation angle is exceeded, it is necessary to re-judge whether the ISL needs to be switched.

4.3. Simulation Parameter Settings

It is assumed that there are 10,000 pairs of ground stations obeying the global traffic model that are randomly distributed among the nodes in each time slice, and each call covers the 4 critical parameters of the latitude and longitude location of the sender and receiver, respectively. Regarding the specific distribution of calls, the two ground stations obey a global service volume distribution model between them.

• The distribution of calls in the continuous time from sending to receiving shows a negative exponential distribution.
• The time of arrival of calls at the receiving end obeys an independent Poisson distribution with the parameter $\lambda$.
• The density of call service requests is adjusted by changing the value of the parameter $\lambda$.

The first deployment phase of the joint simulation targeting the Walker constellation is primarily configured, as shown in

Table 2. Parameters of the Walker constellation of 1584 satellites.

Satellite Parameters	Value
Models	walker1584
Track height	550 km
Number of track planes	66
Number of satellites in orbit	24
Track inclination	53°
Operating cycle	95.7 min
Timepiece size	87 s
Number of channels per satellite	300
Minimum elevation angle of the ground station to access the satellite	40°

. The entire simulation cycle is set to 5742 s with a step size of approximately 87 s, allowing for the subdivision of 1 cycle into 66 equally spaced time slots of identical length.

The shortest call distance path of the interplanetary link is obtained by the Dijkstra algorithm. At the beginning of each time slice, 10,000 pairs of city pairs obeying the service volume distribution model are randomly selected to send communication calls from the ground station.

The performance indicators such as call distance, total time delay, and the number of hops of packet forwarding are compared under different topologies to analyze the advantages and disadvantages of different topological configurations comprehensively. Among them, the 3D visualized physical topology constructed in the selected 1584 simulations is shown in Figure 5.

Manhattan network (MHD) defines a mesh connection distinguished by high stability, low latency, and strong resistance to damage. Among the static topologies discussed in Section 2.1, the mesh topology is most commonly utilized in the static structure of LEO satellite constellations. For instance, the OneWeb constellation’s fixed topology adopts a mesh configuration, making MHD more representative.

In summary, the MHD is selected as the static benchmark topology, and the distance-based strategy and the longest visible time strategy as the dynamic benchmark topology, which are compared with the static topology and the two dynamic topologies designed in this paper to derive the topology with the best network performance and to verify the superior version.

Table 3. Topology classification and description.

Type	Network Topology	Description
Baseline topology	MHD	Manhattan Network defines the mesh connection method
	Distance	Dynamic allocation strategy based on shortest distance
	Time	Dynamic allocation strategy based on maximum visibility time
The optimized topology designed in this paper	STLS	2 intra-OP links plus 2 AOPLs
	DTLS1	2 intra-OP links plus 1 AOPL plus 1 dynamic link
	DLTS2	1 intra-OP link plus 2 AOPLs plus 1 dynamic link

shows the topologies used for the simulation validation and briefly describes them.

5. Performance Evaluation

After establishing a global population density-based call model and configuring simulation parameters for the giant constellation network, we can derive three key network performance metrics—average call distance of transmitted packets, number of packet-forwarding hops, and total delay across 66 time slices. These data points will be analyzed to assess the performance of the designed topology.

5.1. Average Call Distance of Transmitted Packets

Figure 6 shows the average call distances of packets transmitted between 10,000 randomly selected pairs of earth stations in 6 topologies at the beginning of each different time slice.

The dynamic topology generated by the Time strategy has the longest average call distance. Comparing the static topology generated by STLS and MHD policies, STLS has a shorter average call distance while the MHD strategy generates a longer distance for the topology. When comparing the dynamic topology with the static topology, the DTLS1 strategy reduces the average call distance by 7.26%, and the DTLS2 strategy reduces the average call distance by 3.81% compared to the STLS strategy if STLS is used as a benchmark. In the STLS strategy, the distance variation is minor, indicating a more stable link, while all three dynamic policies require reconnection of the link with the switch of the time slice, so the distance variation is more significant.

Comparing several dynamic topologies, the DTLS1 strategy proposed in this paper is superior to all other strategies except for the Distance strategy. When using the Time strategy as a baseline, DTLS1 reduces the distance by 35.97% compared to it, while DTLS2 reduces the distance by 33.59%; when using the Distance strategy as a baseline, DTLS1 increases the distance by 20.28% compared to it, while DTLS2 increases distance by 24.75%.

The simulation results demonstrate that for the 2 combinations of DTLS1 and DTLS2, it is evident that the DTLS1 strategy reduces the average distance by 3.58% compared to the DTLS2 strategy. As the average call distance of data transmission packets decreases, network performance improves. Therefore, the DTLS1 strategy performs better.

5.2. Number of Hops for Packet Forwarding

Figure 7 shows the number of packet hops forwarded between 10,000 pairs of randomly selected ground stations in 6 topologies at the beginning of each time slice.

The hop count of STLS is about 3.82% less than that of MHD. Since STLS connects all satellites in the same and adjacent orbits, many hops are required for relaying if the randomly selected ground stations are far away. Still, the MHD network requires more hops than STLS to transmit packets to the location of the destination satellite.

The comparative analysis shows that DTLS1 has 6.32% fewer hops compared to Distance and 36.72% fewer hops compared to Time strategy; meanwhile, DTLS2 has 2.70% fewer hops compared to Distance and 34.27% fewer hops compared to Time. The significant variation in the topology obtained according to the dynamic connection strategy is still mainly caused by the uncertainty in the distance between the randomly selected ground stations tested.

Among the topologies mentioned in this paper, STLS, DTLS1, and DTLS2, when compared with STLS as the baseline, DTLS1 has reduced hop count by 30.87%, and DTLS2 has reduced hop count by 28.19%. Furthermore, the hop count of DTLS1 is lower than DTLS2 by approximately 3.72%. The data shows that STLS1 dynamic topology has the least average hop count. Since a lower hop count leads to better network performance, the designed DTLS1 in this paper is superior in this metric.

5.3. Total Time Delay

Figure 8 illustrates the total delay, consisting of propagation delay and processing delay, between 10,000 randomly selected pairs of ground stations in 6 topologies at the beginning of each different time slice.

As shown in the figure, the variation of both is slight, and the overall trend is relatively flat. The delay of STLS is significantly lower than that of MHD, with a reduction of about 12.24% due to the shorter call distance of STLS and the lower number of relay hops.

The algorithm used in this paper goes through the dynamic link selection strategy, which can directly launch the connected ISLs according to the changing pattern of time slices, significantly reducing the computation time; therefore, the overall latency of the dynamic strategy is lower than both STLS and MHD.

When comparing the four dynamic topologies, Time has the highest latency and the smoothest variation. In contrast, Distance has the second highest latency and the jitteriest variation because both strategies need to calculate the distances of the remaining satellites when selecting the available satellites, which takes longer to determine.

The total time delay of the 2 strategies constructed in this paper is significantly reduced, with DTLS1 being 51.15% and DTLS2 49.34% lower compared to Time, and DTLS1 being 30.67% and DTLS2 being 28.10% lower compared to Distance. Thus, DTLS1 has more downward propagation and processing delay, by approximately 3.57%, compared to DTLS2.

6. Conclusions

This paper first adopts a time slice division strategy based on the number of satellites per orbit according to the characteristics of the LEO mega constellation and takes 66 time slices for simulation. Then, based on the divided population density, a call model based on global service capacity distribution is determined, and two optimized dynamic topology strategies, DTLS1 and DTLS2, are designed using the dynamic link selection algorithm to compare with the static topology STLS and the three benchmark topologies of Time, Distance, and MHD. The Dijkstra algorithm is used to obtain random paths between any 10,000 pairs of urban ground stations. The average call distance, packet-forwarding hops, and total delay of transmitted packets within 66 time slices are obtained and compared to verify the effectiveness of the dynamic topology algorithm adopted in this paper and the degree of improvement of the satellite network performance.

The simulation results indicate that incorporating dynamic links in the inter-satellite topology reduces the average call distance and effectively decreases the total time delay and the number of hops during data transmission. Among various topologies, the DTLS1 topology, which comprises two intra-OP ISLs and one AOPL, exhibits optimal comprehensive performance while ensuring a maximum connection degree of four for each satellite. Additionally, it can rapidly transmit traffic in any direction through the reverse orbit.