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Link-State Aware Hybrid Routing in the Terrestrial–Satellite Integrated Network^{ †}

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## Abstract

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## 1. Introduction

- Link-state aware hybrid routing: Although existing works have already studied the communication link planning according to the network topology information, the intermittent and dynamic nature of the TSE–satellite link selection is still missing. In our work, we propose a link-state aware hybrid routing scheme for data transmission in the dynamic TSIN. The design is under a practical communication scenario that the link connections in satellites and resources are time-varying. By deriving the delay of both inter-satellite and TSE–satellite links, we formulate a hybrid routing problem aimed at minimizing the data transmission delay by optimally selecting the inter-satellite and TSE–satellite links.
- Characterization on TSIN topology: The updating time of the topology structure is assumed to be a fixed time interval in existing models, which introduces significant difficulties in balancing the network overhead and accurate transmission delay. To tackle this issue, we propose a space–time topology graph to represent the data transmission process in dynamic TSIN, where the link resources in both the spatial and temporal dimensions are quantified. In particular, we derive the optimal time updating interval of the topology relationship, with which the effectiveness and accuracy of obtaining the hybrid path can be balanced.
- Decomposition solution: The inter-satellite link and terrestrial–satellite link connection are time-varying and intermittent in TSIN, which makes the optimal data transmission path planning a challenging issue. By exploiting the space–time topology structure, we propose a satellite link selection algorithm to resolve the optimum inter-satellite link connection problem. Then, a hybrid routing algorithm based on a bipartite graph is proposed to determine the optimal TSE–satellite communication link connection, which can solve the subproblems with smaller sizes.

## 2. Related Work

#### 2.1. Satellite Routing Schemes

#### 2.2. Hybrid Terrestrial–Satellite Routing Schemes

## 3. System Model

#### 3.1. Scenario Description

- -
- Inter-satellite link (ISL): the link between satellites, the distance of which would change rapidly with the highly moving constellations.
- -
- TSE-satellite link (TSL): the link between a TSE and a satellite. Since a satellite can cover different TSEs for a different time, the TSL is time-varying.
- -
- Inter-terrestrial link (ITL): the link between terrestrial nodes. As the terrestrial network service equipments are usually static, the ITL distance is invariant.

#### 3.2. Space–Time Topology Model

#### 3.3. Problem Formulation

## 4. Link-State Aware Hybrid Routing Scheme

#### 4.1. Time Interval Optimization

#### 4.2. Link-State Aware Hybrid Routing Algorithm

#### 4.2.1. Time Interval Optimization-Based ISL Selection Algorithm

Algorithm 1 Time Interval Optimization-based Satellite Routing |

Input: Space-Time graph ${G}_{s}({V}_{s},{E}_{ss})$, source satellite ${v}_{0}\in {\mathsf{\Phi}}_{s}$, TTL of data packet, start time t, data packet size $x({v}_{i}^{t},{v}_{j}^{t},k)$ Output: Router Table ${R}_{s}$ 1: Initialize: Update router table and searched set ${\mathsf{\Phi}}_{d}$ by executing Algorithm 1 Let source set ${\mathsf{\Phi}}_{0}=\{{s}_{0},{N}_{s}\}$ Set termination time ${t}_{n}=t+TTL$ Optimal set ${V}_{opt}=\{T\left({v}_{i}^{t}\right),p\left({v}_{i}^{t}\right)|{v}_{i}^{t}\in {V}_{s}\}=\varnothing $ 2: If ${N}_{0}==\varnothing $ then3: Return ${R}_{s}$ 4: End5: While $({V}_{opt}\ne \varnothing )$ do6: foreach ${v}_{i}^{t}\in {\mathsf{\Phi}}_{0}$ do7: If ${v}_{i}^{t}\in {\mathsf{\Phi}}_{d}$ then8: Continue loop in line 6 9: End10: ${\mathsf{\Phi}}_{d}={\mathsf{\Phi}}_{d}\cup \left\{{v}_{i}^{t}\right\}$ 11: Neighbor$\left({v}_{0}^{t}\right)\leftarrow $ Find all non-empty neighbor set of ${v}_{i}^{t}$ 12: Update ${V}_{opt}$ by executing Algorithm 1 13: End for14: Extract ${v}_{min}^{t}$ which has minimum delay ${T}_{min}$ from ${V}_{opt}$ 15: Add ${v}_{min}^{t}$ into ${\mathsf{\Phi}}_{0}$ 16: Add $\{{T}_{min},{p}_{min}\}$ into ${R}_{s}$ 17: Return ${R}_{s}$ |

Algorithm 2 Link Delay Maintenance |

Input: Source satellite ${v}_{0}\in {\mathsf{\Phi}}_{s}$, start time t, terminal time ${t}_{n}=t+\mathsf{\Delta}\tau $, data packet size $\vartheta ({v}_{i}^{t},{v}_{j}^{t},k)$, neighbor set $Neighbor\left({v}_{i}^{t}\right)$ Output: The optimal set ${V}_{opt}$ 1: Foreach ${v}_{j}^{t}\in Neighbor\left({v}_{i}^{t}\right)$2: If ${v}_{j}^{t}\in {\mathsf{\Phi}}_{0}$ then3: Continue loop in line 1 4: End5: If $T\left({v}_{j}^{t}\right)\ge {t}_{n}$6: Continue loop in line 1 7: End8: $T\left({v}_{i}^{t}\right)=T\left({v}_{j}^{t}\right)+T({v}_{i}^{t},{v}_{j}^{t})$ 9: If $T\left({v}_{i}^{t}\right)\le {V}_{opt}\left({v}_{i}^{t}\right)$ then10: $p\left({v}_{i}^{t}\right)=p\left({v}_{j}^{t}\right)$ , put $E({v}_{i}^{t},{v}_{j}^{t})$ into $p\left({v}_{i}^{t}\right)$; 11: Replace ${V}_{opt}\left({v}_{i}^{t}\right)$ with $\{T\left({v}_{i}^{t}\right),p\left({v}_{i}^{t}\right)\}$ ; 12: End13: End14: Return ${V}_{opt}$ |

#### 4.2.2. Hybrid Routing Algorithm Based on Bipartite Graph

Algorithm 3 KM-based Link Selection |

Input: Bipartite graph, the minimum matching $H\left(t\right)$ of ${G}^{0}\left(t\right)$ Output: link selection in t-th ${R}_{t}$ 1: Initialize: $l\left({v}_{i}^{t}\right)$2: Foreach ${G}_{l}\left(t\right)\in {G}^{{}^{\prime}}\left(t\right)$ do3: If $H\left(t\right)\notin {R}_{t}$ then4: $P=\left\{{v}_{j}^{t}\right\},Q=\varnothing $, ${N}_{p}={G}^{{}^{\prime}}\left(t\right)\cup \left\{P\right\}$ 5: If ${N}_{p}\ne Q$6: Continue loop in line 2 7: End8: If ${N}_{p}=Q$ then9: $\mathsf{\Delta}=\underset{u,v}{min}\{l\left({v}_{i}^{t}\right)|l\left({v}_{i}^{t}\right)+l\left({v}_{j}^{t}\right)-w({v}_{i}^{t},{v}_{j}^{t}),{v}_{i}^{t}\in P,{v}_{j}^{t}\in {V}_{2}-Q\}$ 10: ${l}^{{}^{\prime}}\left({v}_{i}^{t}\right)=\left\{\begin{array}{c}l\left({v}_{i}^{t}\right)-\mathsf{\Delta},{v}_{i}^{t}\in P\hfill \\ l\left({v}_{i}^{t}\right)+\mathsf{\Delta},{v}_{i}^{t}\in Q\hfill \\ l\left({v}_{i}^{t}\right),otherwise\hfill \end{array}\right.$ 11: End12: End13: Extract $H\left(t\right)$ in $R\left(t\right)$ 14: End15: Return ${R}_{t}$ |

Algorithm 4 KM-based Link-state Aware Terrestrial-Satellite Hybrid Routing algorithm |

Input:Network topology; Output: Link planning of hybrid routing ${R}_{h}$ 1: Initialize: Update ${R}_{s}$ by executing Algorithm 2 2: If $t\le D$ then3: Construct bipartite graph of ${G}^{{}^{\prime}}\left(t\right)$ 4: Calculate link metric of ${G}^{{}^{\prime}}\left(t\right)$ according to (24) 5: Calculate the minimum weight match of ${G}^{{}^{\prime}}\left(t\right)$ by using Algorithm3, Extract hybrid path planning in t-th $R\left(t\right)$ 6: Write in link connection planning ${R}_{h}$ 7: Update data volume of link according (25) 8: $t\leftarrow t+1$ 9: End10: Return ${R}_{h}$ |

#### 4.3. Complexity Analysis

## 5. Simulation and Analysis

#### 5.1. Simulation Setup

#### 5.2. Satellite Routing Performance

#### 5.2.1. Transmission Delay

#### 5.2.2. Packet Drop Rate and Network Throughput

#### 5.3. Terrestrial–Satellite Routing Performance

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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Routing Schemes | Core Idea | Limitations | |
---|---|---|---|

Satellite routing schemes | Routing algorithm based on virtual topology [18,19] | The system period is divided into equal-length snapshots, and the route of each snapshot is calculated offline | The routing table needs to be frequently synchronized |

Routing algorithm based on virtual node [20,21] | Virtual nodes are set to represent physical satellites, and the shortest distance route between virtual nodes is calculated | The link congestion and failure would deteriorate throughput performance | |

Routing algorithm based on load balancing [22,23,24,25,26] | Based on the traffic state information, the route is adjusted dynamically according to the real-time state at intermediate nodes to avoid congestion | The intermittent problem of link connection caused by dynamic topology has not been solved | |

Hybrid terrestrial -satellite routing schemes | Relay routing [13,14] | Satellites act as relay forwarding nodes, which are interconnected through ground stations | The scalability of satellite networks is limited |

Extended terrestrial routing [15,17] | Terrestrial routing algorithms are extended to the satellite networks | Dynamic topology leads to frequent path updates | |

SDN-based routing [27,28,29] | The control center collects the link information of the whole network and calculates the route | The time-varying topology of satellites increases the computation overhead | |

Graph-based routing [30,31,32,33,34,35,36,37,38] | Communication link planning algorithm is designed according to the scheduled contact graph | The frequent changes of inter-satellite link and terrestrial-satellite link selection is missing |

Notations | Definitions |
---|---|

S | The set of satellites ${s}_{i}$ |

G | The set of TSEs ${g}_{i}$ |

$UT$ | The set of UTs $U{T}_{i}$ |

D | The total number of time intervals in path plan |

$\mathsf{\Delta}\tau $ | The duration of each time interval |

$G\left(t\right)$ | The directed graph composed of T layers |

V | The vertices set of G |

$E\left(t\right)$ | The links set of G |

${E}_{l}\left(t\right)$ | The links set of spatial link |

${E}_{b}\left(t\right)$ | The links set of temporal link |

$d({v}_{i}^{t},{v}_{j}^{t})$ | The distance of link $({v}_{i}^{t},{v}_{j}^{t})$ |

${v}_{P}$ | The transmission speed of radio signal |

$r({v}_{i}^{t},{v}_{j}^{t})$ | The capacity of link $({v}_{i}^{t},{v}_{j}^{t})$ |

${b}_{i}^{t}\left(k\right)$ | The data volume in storage of ${v}_{i}^{}$ for $U{T}_{k}$ during the t-th time interval |

$\vartheta ({v}_{i}^{t},{v}_{j}^{t},k)$ | The capacity of link $({v}_{i}^{t},{v}_{j}^{t})$ for $U{T}_{k}$ data |

$\omega ({v}_{i}^{t},{v}_{j}^{t})$ | The connection state of link $({v}_{i}^{t},{v}_{i}^{t})$ |

${T}_{p}({v}_{i}^{t},{v}_{j}^{t})$ | The propagation delay |

${T}_{q}({v}_{i}^{t},{v}_{j}^{t})$ | The queuing delay |

${T}_{w}({v}_{i}^{t},{v}_{j}^{t})$ | The transmission delay |

${E}_{gu}\left(t\right)$ | The communication opportunities for UTs to TSE in each time interval |

${E}_{sg}\left(t\right)$ | The communication opportunities for satellite to TSE in each time interval |

${E}_{ss}\left(t\right)$ | The communication opportunities for satellite to satellite in each time interval |

$C({v}_{i}^{t},{v}_{j}^{t})$ | The maximum capacity of $({v}_{i}^{t},{v}_{j}^{t})$ |

${r}_{min}$ | The minimum rate requirement of data transmission |

Constellation | Iridium | Hongyun |
---|---|---|

No. of planes | 6 | 13 |

No. of satellites per plane | 11 | 12 |

Orbital inclination | ${86}^{\circ}$ | $86.{5}^{\circ}$ |

Orbital height | 788 km | 1000 km |

Intraplane ISLs length | 4032.9 km | 3790 km |

Intraplane ISLs propagation delay | 13.5 ms | 12.6 ms |

Longest interplane ISLs distance | 4370 km | 2366 km |

Longest interplane ISLs propagation delay | 14.5 ms | 7.89 ms |

Shortest interplane ISLs distance | 1680 km | 1426 km |

Shortest interplane ISLs propagation delay | 5.6 ms | 4.75 ms |

Parameters | Values |
---|---|

Orbital altitude | 1000 km |

$\theta $ | 87.4${}^{\circ}$ |

N | 13 |

M | 12 |

Minimum elevation angle | 10${}^{\circ}$ |

Phase offset between interplane satellites | 360/12/2 = 15${}^{\circ}$ |

Bandwidth of ISL | 15 Mbps |

Bandwidth of ground link | 15 Mbps |

Queue type | FIFO |

Buffer queue size | 100 packets |

Packet sizes | 1500 byte |

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## Share and Cite

**MDPI and ACS Style**

Xu, H.; Shi, Z.; Liu, M.; Zhang, N.; Yan, Y.; Han, G. Link-State Aware Hybrid Routing in the Terrestrial–Satellite Integrated Network. *Sensors* **2022**, *22*, 9124.
https://doi.org/10.3390/s22239124

**AMA Style**

Xu H, Shi Z, Liu M, Zhang N, Yan Y, Han G. Link-State Aware Hybrid Routing in the Terrestrial–Satellite Integrated Network. *Sensors*. 2022; 22(23):9124.
https://doi.org/10.3390/s22239124

**Chicago/Turabian Style**

Xu, Huihui, Zhangsong Shi, Mingliu Liu, Ning Zhang, Yanjun Yan, and Guangjie Han. 2022. "Link-State Aware Hybrid Routing in the Terrestrial–Satellite Integrated Network" *Sensors* 22, no. 23: 9124.
https://doi.org/10.3390/s22239124