Research Article | Open Access

Zipeng Ye, Qingrui Zhou, "Performance Evaluation Indicators of Space Dynamic Networks under Broadcast Mechanism", *Space: Science & Technology*, vol. 2021, Article ID 9826517, 11 pages, 2021. https://doi.org/10.34133/2021/9826517

# Performance Evaluation Indicators of Space Dynamic Networks under Broadcast Mechanism

#### Abstract

Large-scale heterogeneous constellations will be the major forms of future space-based systems, and the implementation of numerous derived applications depends mainly on intersatellite communication. The nodes representing heterogeneous satellites will form the networks with rapidly changing topology. However, few researches have been carried out for such networks. This paper studies the broadcast mechanism for space dynamic networks and establishes centralized and distributed routing framework. And then, performance evaluation indicators are proposed to evaluate both the connectivity of dynamic networks and the effectiveness of routing algorithms. Finally, we examine the performance of multigroup networks and verify the rationality of corresponding indicators. We also explore the impact of information survival time which directly affects the delivery ratio and, if unfortunately, may waste the communication resources. Empirical conclusion about the survival time is given in the final part. We believe the performance indicators and the routing algorithms proposed in this paper are great help to future space-based system and both the broadcast mechanism designing.

#### 1. Introduction

With the development of space technology, the cost of deploying low-earth orbit (LEO) spacecrafts is rapidly decreasing. In recent years, a series of LEO satellite cluster programs have been proposed by several institutes [1–3]. The most representative one is the Blackjack Pit Boss program proposed by Defense Advanced Research Projects Agency (DARPA). Through communicating at the commercial data transmission layer and combining with onboard data processing software, it can realize various strategic missions such as target identifying, tracking, surveilling, area reconnoitering, and all-weather multidomain resource detecting without the involvement of human. Data sharing by effective communication mechanism is a prerequisite for these cluster programs to accomplish data fusion, autonomous decision-making, and collaboration. Therefore, it is necessary to make a profound study on the network structure and communication mechanism of satellite cluster.

The delay/disruption tolerant network (DTN) model proposed by Intel and NASA has been widely used for space networks [4, 5]. The Consultative Committee for Space Data Systems (CCSDS) has also built a DTN working group to promote the standardization of DTN technology. DTN adopts “store-wait-forward” routing mechanism, that is, an intermediate node stores information temporarily, waits for the establishment of a communication link with the next hop node, and then forwards the information. By repeating this mechanism, information is transmitted from the source node to the destination node.

The most well-known routing algorithm for the DTN model is the epidemic algorithm [6]. It can reach the highest delivery ratio in the shortest period without any prior knowledge assistance. However, epidemic algorithm leads to a severe wasting of resources. An improved and universal method called PRoPHET can efficiently cut down the overhead by some constrains [7], that is, nodes deliver messages through the similarity which decided by the history, i.e., the implement of the PRoPHET algorithm requires prior knowledge. There are other routing algorithms proposed in [8–11], both of whom are flooding-based and can achieve trade-off through dropping or reducing policies. Indeed, all these algorithms can realize high delivery ratio and low average delay if the resources are unlimited.

Based on the predictability of space networks, Merugu and Zegura and Fischer et al. have studied the routing framework, routing algorithms, and the effective solutions to unexpected situation [12, 13]. Their main works include designing both the space-time graph and the optimal transmission routing table from the source node to the destination node. Such space-time graph-based algorithms are channel resources friendly, yet they have high computational complexity. Similar space-time graph-based algorithms can be referred to [14–17]. Yan et al. and Wang et al. have evaluated these typical DTN routing algorithms and designed an onboard routing algorithm [18, 19]. Based on the transmission delay, delivery ratio, they have given some suggestions for future space DTN research.

Scholars have conducted extensive research on space DTN, and most of these focus on end-to-end information transmission. Future LEO satellite clusters, such like Blackjack program, are more dependent on information sharing among all satellites, so as to achieve efficient data fusion, autonomous decision-making, and collaboration. However, there is still a lack of research on space dynamic networks under this broadcasting mechanism. This paper is aimed at proposing some metrics that can effectively evaluate the network performance and routing algorithm performance under broadcasting mechanism and providing valuable ideas for subsequent research.

#### 2. Model

Static network has simpler model, with more complete research in theory and engineering implementations. The dynamic network is totally different since the dynamic network is with sequence and irreversibility. For example, if node is connecting with node and is connecting to , then there is a link between and . However, in dynamic network, if the connection between and occurs after and , then we cannot assert that there is a link between and .

Dynamic networks are usually divided into two forms: lossless form and lossy form. The lossless form records all the connection status, while lossy form divides timespan into several segments, regards every segment as a static network, and finally connects all segments to form a complete network. The lossless form needs to record every moment that connection relationship has changed, which requires a large amount of storage. Therefore, the lossy form can be used to model a dynamic network [12, 13]. Considering a quaternion, where represents the two nodes, respectively, and denotes the moment connection occurring and denotes the duration of the connection. For a segment , if satisfies one of the following conditions,

Meeting any of the above conditions means that there is always a part of time in the whole connecting duration that is within the specified segment . Then, an edge is created between the nodes, and all such edges form the set of edges . Let the snapshot of segment be . Then, we can model the dynamic network as , where represents the total timespan, , and is the set of all snapshots. Accumulating each small segment can obtain the entire networks.

As shown in Figure 1, there exist four nodes , and the subgraphs of Figure 1 are snapshots . At time , if node needs to transmit information to target node , there are two routing methods: (1) information is transmitted from node to node at time and then transmitted from node to node at , and this “store-wait-forward” routing way belongs to the DTN method; (2) node waits until to establish a complete path with node , and this routing method is often used for ad hoc networks. Obviously, the complete path between the source and the destination may not always appear, so the DTN routing method can not only realize the information delivery in a shorter time, but also improve the delivery ratio [20–22].

#### 3. Routing in Space Networks under Broadcasting Mechanism

Traditional research focuses on end-to-end communication (unicast) problems [23–25], and its routing algorithms and routing metrics are based on the quality of end-to-end communication. Nowadays, there are also some studies for multicast problems [26–28], but the difference between “unicast” and “multicast” mainly lies in the improvement of routing algorithms but not evaluation metrics. Traditional routing algorithms show some inspirations to the broadcast mechanism, while the evaluation metrics are obviously no longer applicable. This section will propose some frameworks for centralized and distributed routing algorithms under broadcast mechanisms.

##### 3.1. Centralized Routing Algorithm Framework

The fundamental reason why space networks can achieve centralized routing is that they are predictable. And we can directly design the optimal transmission routing table by predicting the future contacting graph. The centralized routing under the broadcast mechanism has the following features: (1)A connection-oriented transmission protocol is usually used, i.e., when two nodes satisfy the connection conditions, they are considered as linked, and all the links are equal. For example, node establishes a connection with node , and at the same time node establishes a connection with node , the two links are equal in the calculation of the optimal path, regardless of which node is closer to node . This is because usually the waiting time for nodes to establish a link is much longer than the information propagation time, so the path distance can be ignored(2)Create evolutionary contacting graphs based on model characteristics. Since the source node has to design the optimal path for broadcasting to all other nodes, it needs to maintain a series of evolutionary graphs from current to the future. There are 2 elements need to be considered while designing contacting graphs: (a)The time interval between adjacent graphs(b)The total number of required graphs, which can reflect the information survival time (time-to-live, TTL)

These two elements directly affect the storage and computation, and a feasible optimization method is to discard the connection whose duration is shorter than a certain threshold and then select the remaining shortest duration time as the graph interval time. The threshold must be greater than the sum of the message sending delay and propagation delay. The selection method for the number of graphs, i.e., the TTL, is usually related to the network connectivity performance, which will be analyzed in detail later.

After above steps, let the distance between nodes be the moment that they connect. The contacting graph of Figure 1 is shown in Figure 2.

After obtaining contacting graph as shown in Figure 2, the optimal routing problem can be treated as optimal path problem. (3)Select an optimal path algorithm, usually the shortest path algorithm can be used, such as the Dijkstra algorithm [29]. But our case is a little different from classical problem since there is a time sequency limitation. Fortunately, the Dijkstra algorithm can always find one shortest path from source node to any others with forward property [30] (i.e., easily satisfying the time sequency requirement with a little modification), and the detail of the improved Dijkstra algorithm for the shortest-path problem in above evolving graphs is discussed in [19]

##### 3.2. Distributed Routing Algorithm Framework

The epidemic algorithm based on the flooding mechanism is an efficient distributed routing algorithm for broadcast [31, 32]. Each time two nodes establish connections, they exchange the list of messages IDs and transmit the messages that the opposite does not have by comparing the list. Obviously, the epidemic model can achieve the fastest message transmission to all nodes, but when the number of nodes is large, connections will be established constantly, thus generating redundant list exchanges and consuming more energy. One solution is to reduce the transmission times by setting a reasonable message survival time TTL and deleting expired messages [9].

In addition, employing a priori knowledge of the network can also get better results [33–36], which include the routing algorithms based on the structure of network communities. This algorithm uses different routing mechanism for intercommunity and intracommunity, to achieve better routing results. The use of this method first requires reliable community detection, and for the problem of distributed community detection in dynamic networks, this paper proposes a method that is simple to implement by only three steps: (1)Set all spacecraft as a single-node community and set the similarity between nodes to 0(2)Calculate the similarity between nodes(3)Compare the similarity with the threshold and then update the community ID according to the comparison

The similarity between node and node at time is updated by the following: where the decay coefficient satisfies .

If node and node are always connected, the similarity is

And it satisfies the following:

If node and node are not connected at moment , the similarity is

And it satisfies the following:

Therefore, let the threshold be

This threshold ensures that members within the same community remain connected when the update time is reached, and update and determine the community ID synchronously. The update strategy is as follows: (1)If , then group the nodes and into the same community(2)If , then divide the nodes and into different communities(3)When nodes and are in the same community and nodes and are in the same community, then group the nodes and into the same community through simple communication

In our experiment, community detection is performed for 115 satellites in orbit, and the community structure at some point is shown as Figure 3.

After the distributed community detection, a community structure which is highly connected intracommunity can be obtained. Based on this, a distributed routing framework can be designed as shown in Figure 4.

In Figure 4, are the IDs of each community, and the specific process of the algorithm is as follows:
(1)*Intercommunities*. Using the epidemic model, the list records the community IDs which have obtained the corresponding message, and when nodes meet, only part of the list is exchanged (opposite is not recorded in this part), and through it to build a delivering request. The opposite accepts (opposite has not received these messages so far) or rejects (opposite has already received these messages but the requester is still unknown, e.g., “” sends message to “,” and then, “A” sends it to “.” Through the list, “” knows that “” has the message yet “” does not know that “” already has it. “” plays the role of “requester,” and “” is the “opposite” who rejects the requirement) it according to the conditions and updates the list after the delivery is completed. For example, when any two nodes in community and community meet again after the list in Figure 4 updated, no exchange request is made to because exists in all lists of community . Similarly, exists in all lists of community , so no exchange request is made to .(2)*Intracommunity*. Due to the strong connectivity, it is possible to quickly generate a static graph of the community and design an optimal routing policy without redundancy.

In the distributed routing algorithm, nodes do not need to maintain a large amount of contacting graph or design a routing table in advance. It not only saves computational resources, but also has stronger robustness.

#### 4. Performance Evaluation

At present, there are few studies on the broadcasting mechanism of space networks with rapidly changing topology. It is necessary to carry out the evaluation mechanism for both network itself and routing algorithm. To this end, we aim to provide theoretical support for the design of future space-based system and both the routing algorithms.

##### 4.1. Average Delivery Ratio

The average delivery ratio is defined as the average ratio of nodes that receive randomly generated messages within TTL. And it can reflect the connectivity of the entire network. It can be calculated as follows: where is the total number of messages, is the number of nodes, and is obtained by the following:

Ignoring the sending and propagation delay, we can define the instantaneous connectivity of the network as follows:

##### 4.2. *Average Transmission Time*

The average transmission time can reflect the degree of network connectivity and is defined as the average time that expended for delivering messages to other nodes within the message survival time TTL. To describe the performance more concretely, we use relative average transmission time and absolute average transmission time, respectively.

###### 4.2.1. Relative Average Transmission Time

The relative average transmission time can be defined as follows: where is obtained by the following: where is the time delay of th message delivered to node .

###### 4.2.2. Absolute Average Transmission Time

The absolute average transmission time can be defined as follows: where is obtained by the following:

##### 4.3. Average Times of RREQ Initiated

To evaluate the efficiency of the routing algorithm, the metric of the average times of RREQ initiated is proposed. Since the routing goal of the space network is to transmit messages to all nodes, then the total amount of messages that need to be transmitted is equal for both the flooding algorithm and the optimal routing algorithm. The difference between them lies in the number of connection establishment and the times of routing requires initiated. The flooding algorithm needs to initiate a flood of routing requests, while the optimal routing algorithm only needs to initiate times routing requests. Obviously, it is possible to reduce energy consumption by designing efficient routing algorithms that reduce the times of RREQ initiated.

We define the average times of RREQ initiated as follows: where is the total number of messages, is the number of nodes, is the average delivery ratio, and is the times of RREQ initiated between node and node .

##### 4.4. Ratio of Congested Node

The ratio of congested nodes can reflect the engineering feasibility of the routing algorithm. If the node transmission capacity is not considered, the designed routing algorithm may excessively use a specific node in a short period of time, which leads to node overload as well as data loss. Therefore, designing the routing algorithm by considering the congestion of nodes will enhance the reliability of the algorithm in practical engineering.

We define it as the ratio of nodes that arise congestion events when messages are broadcast to the entire network: where is defined as follows: and where is the ratio of the messages need to be transmitted by node to the maximum transmission capacity of node and is the capability threshold, where is related to both the total number of messages, the message generation interval, and the routing algorithm.

#### 5. Simulation and Analysis

Combined with the orbit of space-based systems, we implement simulation to verify the rationality of the metrics that we proposed for evaluating the performance of dynamic network and the broadcasting mechanism. The simulation uses the actual orbital data of infrared and electrodetection satellites in orbit. The communication conditions are set as Figure 5.

Two satellites can realize communicate when they meet the following conditions (approximately estimated according to Iridium constellation [37, 38]): (a) the distance between them is less than 4000 km; (b) the height of communication link is always larger than 100 km to the ground.

##### 5.1. Performance Comparison of Different Space Networks

We have selected 10 satellites randomly among all satellites to generate a satellite network, and the network is expanded based on add new satellites. All five groups of the networks are shown in Figure 6.

The simulation generates 500 messages randomly in multiple moments, respectively, and sets the TTL to 3000 seconds. To compare the performance of different network structure, we both use epidemic routing algorithm for these networks. Figure 7 shows the average delivery ratio of networks in Figure 6.

The connectivity performance of the network tends to increase as the number of satellites in the network increases and the average delivery ratio keeps increasing at the same TTL. The absolute average transmission time for the networks in Figure 6 is shown in Figure 8.

The relative average transmission time for the networks in Figure 6 is shown in Figure 9.

The calculation of absolute transmission time is independent from the delivery ratio and only considers the time spent on the actual delivered messages, so it needs to be used together with the average delivery ratio when measuring the network performance. The calculation of relative transmission time considers the undelivered messages and configures their time as TTL, so the relative transmission time also reflects the delivery ratio to a certain extent.

The average delivery ratio of the network reflects the connectivity of the network, and the average transmission time reflects the degree of connectivity, so that the performance of the network can be reliably evaluated using these two metrics.

##### 5.2. Centralized vs. Distributed Routing Algorithm

The simulation randomly selects a 50,000-second timespan and generates messages at random nodes and random moments. Then, we use the centralized and distributed routing algorithms proposed previously for message routing. In the centralized algorithm, the interval of adjacent contacting graphs is 300 seconds, and 10 future graphs are maintained by each node.

The delivery ratio of the five group networks in Figure 6 under the two algorithms is shown in Figure 10.

The delivery ratio of the distributed algorithm is almost equal to the centralized algorithm. The relative average transmission time of the five groups of networks in Figure 6 under the two algorithms is shown in Figure 11.

The centralized algorithm has a slightly shorter transmission time than the distributed algorithm. The average times of RREQ initiated for the five groups of networks in Figure 6 under the two algorithms are shown in Figure 12. And the total number of messages is equal.

Under the centralized algorithm, each message is transmitted according to its own routing table, so the average times of RREQ initiated are always 1, independent of whether it is successfully delivered or not and both independent of the density of message. Under the distributed algorithm, when the message is dense, the transmission confirmation of multiple messages can be completed simultaneously in one route request; when the message is sparse, the transmission confirmation of multiple messages cannot be completed simultaneously. Due to the flooding mechanism for messages delivering intercommunity, and the route request cannot be completed for multiple messages at the same time, the average times of RREQ initiated gradually rise when the messages are sparse. And the higher the number of nodes in the network, the larger the average times of RREQ initiated will be.

##### 5.3. Message TTL Setting

The message survival time TTL directly affects the message delivery ratio. Setting the TTL too small will lead to low delivery ratio, and too large will lead to communication resource wasting since some routing algorithms (e.g., epidemic algorithm) will keep initiating routing requests. Therefore, this subsection conducts a simulation on the TTL and proposes some suggestions.

Six groups of networks with different connectivity performance are generated and simulated, and messages are generated at random nodes and random moments. We use the epidemic algorithm for message routing, and the variation of delivery ratio with different TTL is shown in Figure 13.

As the TTL increases, the delivery ratio gradually increases to 1. And when the TTL is 0, it returns the instantaneous connectivity defined in the previous section, and the larger the , the smaller the TTL required for a demanding delivery ratio. This section is aimed at calculating the specific TTL value by only. To this end, it is necessary to fit the delivery ratio curve with respect to both and TTL. The ratio curve is fitted as follows: where denotes the delivery ratio. Figure 14 shows the fitted and real curves.

By obtaining the instantaneous connectivity in advance through ground simulation and setting the required delivery ratio to 0.99, the required TTL can be calculated by follows:

The star at Figure 14 is the TTL time required for 99% delivery ratio calculated according to the above formula.

#### 6. Conclusions

In this paper, the space network under the broadcasting mechanism is studied. Firstly, we have given definition and analysis of the dynamic network model. Then, the space routing algorithm framework under broadcast mechanism is introduced, which includes centralized routing algorithm based on the model predictability and distributed algorithm based on community structure.

Moreover, the performance evaluation indicators of network and routing algorithm are proposed, including average delivery ratio, average transmission time, average times of RREQ, and the ratio of congested nodes. Simulation is conducted for several groups of space networks, respectively, and the evaluation indicators can effectively distinguish the good and bad network structure. Results show the reasonableness of the evaluation metrics.

And then, we implement simulation and analysis of centralized and distributed routing algorithms. Finally, the setting of message survival time TTL, which affects the message delivery ratio, is studied, and the setting suggestion of TTL is given.

The simulation of congestion is not given in this paper because the definition of congestion is related to the actual capability of node and the actual data size. Furthermore, the parameters of such indicator need to be set for specific problems; thus, it is not analyzed experimentally in this paper. However, the node congestion is a case that must be considered in practical engineering, so that the routing algorithm can be optimized by the congestion status.

This paper presents some problems and feasible research directions in related fields. It may help to build the framework for the research of information sharing in dynamic space-based networks.

#### Data Availability

The data used to support the findings of this study are available from the author upon reasonable request.

#### Conflicts of Interest

The authors declare that they have no conflicts of interest.

#### Authors’ Contributions

Qingrui Zhou contributed to the conception of the study and performed the analysis with constructive discussions. Zipeng Ye performed the experiment and analyzed the results . The writing of the manuscript was done by Zhou and Ye together.

#### Acknowledgments

This research was supported by the National Key R&D Program of China under Grant 2018YFA0703800.

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#### Copyright

Copyright © 2021 Zipeng Ye and Qingrui Zhou. Exclusive Licensee Beijing Institute of Technology Press. Distributed under a Creative Commons Attribution License (CC BY 4.0).