Spatial-Temporal Learning-Based Distributed Routing for Dynamic LEO Satellite Networks Po-Heng Chou1,3 , Chiapin Wang2 , Shou-Yu Chen2 , and Hsiang-Ming Wang2 1
Research Center for Information Technology Innovation (CITI), Academia Sinica (AS), Taipei 11529, Taiwan Department of Electrical Engineering, National Taiwan Normal University (NTNU), Taipei 106308 Taiwan 3 Bradley Department of Electrical and Computer Engineering (ECE), Virginia Tech (VT), Alexandria, VA 22305, USA E-mails: [email protected], [email protected], [email protected], [email protected]
arXiv:2605.02413v1 [cs.NI] 4 May 2026
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Abstract—In this paper, we propose a spatial-temporal learning-based distributed routing framework for dynamic Low Earth Orbit (LEO) satellite networks, where graph attention networks (GAT) and long short-term memory (LSTM) are integrated within a deep Q-network (DQN)-based architecture to enable distributed and adaptive routing decisions based on local observations. The routing problem is formulated as a partially observable Markov decision process (POMDP) to address partial observability under dynamic topology and time-varying traffic. Simulation results show that the proposed method significantly outperforms conventional and learning-based routing schemes in terms of throughput, packet loss, queue length, and endto-end delay, while achieving proactive congestion avoidance with up to 23.26% queue reduction. In addition, the proposed approach maintains low computational overhead with negligible carbon emissions, demonstrating its efficiency from a Green AI perspective. Index Terms—LEO satellite networks, distributed routing, spatial-temporal learning, graph attention network (GAT), long short-term memory (LSTM), deep Q-network (DQN).
I. I NTRODUCTION Low Earth Orbit (LEO) satellite networks have emerged as a key enabler for next-generation global communication systems, providing low-latency, wide-area coverage and seamless connectivity for applications such as Internet of Things (IoT), remote sensing, and disaster recovery [1]. Compared to traditional geostationary systems, LEO constellations benefit from shorter propagation distances and flexible deployment, making them a fundamental component of 6G space–air– ground integrated networks (SAGINs) [2]. Despite these advantages, the highly dynamic topology of LEO satellite networks poses significant challenges for routing design. Continuous satellite movement and time-varying intersatellite links (ISLs) cause network connectivity to evolve rapidly, leading to frequent route disruptions and unstable transmission performance. Conventional routing approaches, such as shortest-path-based or static routing schemes, fail to adapt to such environments, resulting in increased delay, congestion, and packet loss [3]. Moreover, centralized routing strategies introduce excessive signaling overhead and suffer from scalability limitations in large-scale constellations [4]. To address these challenges, reinforcement learning (RL) [5] has been widely adopted for sequential decision-making in dynamic environments. RL enables agents to learn optimal This work was supported in part by the National Science and Technology Council (NSTC) of Taiwan under Grant 113-2926-I-001-502-G and 114-2221E-003-033.
policies through continuous interaction with the environment, making it well-suited for adaptive routing problems. Building upon this paradigm, deep reinforcement learning (DRL) [6] employs deep neural networks, such as deep Q-networks (DQN), to approximate value functions and policies, enabling scalable decision-making in high-dimensional state spaces. In addition, DQN has been applied to other LEO system optimization tasks beyond routing [7]. Recent studies have applied DRL to LEO routing optimization, where routing decisions are modeled as Markov decision processes (MDPs) or partially observable MDPs (POMDPs). These approaches allow satellites to learn adaptive routing strategies under dynamic topology and traffic conditions [8]. To further improve scalability, multi-agent reinforcement learning (MARL) frameworks have been introduced, enabling decentralized decision-making in large-scale satellite constellations [4], [9]. Furthermore, graph neural network (GNN)-enhanced DRL methods have been proposed to capture the underlying network topology, improving routing performance in non-Euclidean environments [10], [11]. However, such approaches primarily focus on spatial topology modeling and do not explicitly capture temporal traffic dynamics. Advanced variants integrating graph attention and evolutionary reinforcement learning further enhance adaptability in highly dynamic LEO scenarios [12]. Temporal graph-based routing methods have been proposed to capture dynamic topology evolution [13]. Beyond DRL-based routing, recent research highlights the importance of spatiotemporal modeling in LEO networks. Spatiotemporal traffic prediction techniques have been developed to estimate network states and guide routing decisions [14], [15]. Delay-aware routing schemes that incorporate traffic prediction have demonstrated improved performance under dynamic conditions [16]. These studies indicate that effective routing design requires jointly modeling spatial topology and temporal dynamics. However, existing approaches, such as [14], adopt a decoupled design that separates spatiotemporal traffic prediction from routing decision-making. While such designs can improve prediction accuracy, the lack of joint optimization limits their ability to adapt routing decisions to rapidly changing network conditions. In particular, when abrupt topology variations occur in dynamic LEO environments, the mismatch between predicted traffic patterns and real-time network states may lead to suboptimal routing decisions and degraded delay performance. In contrast, an end-to-
end learning framework enables joint adaptation to both traffic dynamics and topology variations, leading to more robust routing decisions. Despite these advances, several critical limitations remain. First, most existing approaches treat spatial topology and temporal dynamics separately, failing to capture their coupled effects in highly dynamic LEO environments. Second, conventional neural architectures, such as fully connected networks, are not well-suited for graph-structured satellite networks, leading to suboptimal feature representation. Third, centralized or partially centralized frameworks introduce significant communication overhead, limiting scalability in large-scale constellations. Recent advances in graph neural networks and sequence modeling provide promising solutions to these challenges. Graph attention networks (GATs) enable adaptive modeling of non-Euclidean structures by assigning importance weights to neighboring nodes, thereby enhancing spatial feature extraction [17]. Meanwhile, long short-term memory (LSTM) networks [18] effectively capture temporal dependencies in time-varying systems. The integration of these techniques enables unified spatiotemporal representation learning, which is particularly suitable for dynamic LEO environments. Motivated by these observations, we propose a spatialtemporal learning-based distributed routing framework for dynamic LEO satellite networks. Specifically, we integrate GAT for spatial topology modeling and LSTM for temporal dependency learning within a DRL-based decision framework, enabling each satellite to make adaptive routing decisions based on local observations. The routing problem is formulated as a POMDP, following prior DRL-based routing studies [8], allowing scalable and distributed operation under dynamic network conditions. The main contributions are summarized as follows: We propose a spatial-temporal learning-based routing framework that enables proactive congestion avoidance by jointly modeling topology dynamics and traffic evolution using GAT [17] and LSTM [18]. • A distributed DQN-based routing scheme is developed to enable decentralized decision-making based on local observations, improving scalability in large-scale LEO constellations. • The routing problem is formulated as a POMDP to capture partial observability and support adaptive policy learning in dynamic environments. • Simulation results show that the proposed method consistently outperforms conventional shortest-path routing [19], distributed routing [3], and learning-based approaches including DQN [8] and MARL [11] in terms of delay, throughput, and packet loss. • The proposed method achieves proactive congestion avoidance, reducing queue length by up to 23.26% and improving delay and reliability under dynamic traffic conditions, while incurring only minimal computational overhead and carbon footprint.
•
• Queue Length: ܳ ሺݐሻ State ࢙ ሺݐሻ: • Link Delay: ܦ ሺݐሻ • Topology Features: ࢞ ሺݐሻ
Dynamic LEO Satellite Network ࣡(t) = ࣰǡ ࣟሺݐሻ
࢙ ሺݐሻ
Update ܳఏ
Spatial-Temporal Routing Agent GAT + LSTM + DRL (Spatial, Temporal, Decision) ܽ = ݐarg max ܳఏ ࢙ ሺݐሻ, ܽ ܽ ሺݐሻ
Reward: ݎ = ݐ - αDelay+β Queue
Action ܽ ܰ א ݐ ݐ Next-hop Selection Packet Forwarding
Fig. 1: Illustration of the proposed spatial-temporal learningbased distributed routing framework, where each satellite performs local decision-making through GAT-LSTM-DQN integration. II. S YSTEM M ODEL A. System Overview Fig. 1 illustrates the overall framework of the proposed spatial-temporal learning-based distributed routing system. Each satellite operates as an independent agent that observes local states and determines routing actions through a learningbased decision process. The decision process integrates spatial feature extraction via GAT, temporal modeling via LSTM, and policy learning via DQN. Based on the constructed state, a routing agent determines the next-hop action ai (t) ∈ Ni (t). After executing the routing decision, packets are forwarded through the selected links, leading to updated network conditions. A reward signal ri (t) is then generated based on delay and congestion and fed back to update the routing policy. B. Network Model We consider a LEO satellite network consisting of N satellites. The network is modeled as a time-varying graph G(t) = (V, E(t)) [3], where V = {1, 2, . . . , N } is the set of satellites and E(t) ⊆ V × V represents the set of ISLs at time slot t. Satellite mobility causes the network topology to evolve over time. For each satellite i ∈ V, the set of neighboring satellites at time t is defined as Ni (t) = {j ∈ V | (i, j) ∈ E(t)}. Data packets are transmitted from a source node s ∈ V to a destination node d ∈ V through multi-hop routing over the graph G(t). C. Traffic and Queue Model We adopt a discrete-time packet transmission model. Let t ∈ {0, 1, 2, . . . } be the time slot index. At each time slot, packets arrive at satellite nodes and are stored in local buffers. The packet arrival process is modeled as a non-homogeneous Poisson process (NHPP), where the arrival rate λi (t) varies over time. To capture temporal periodicity, λi (t) is modeled as a periodic function, e.g., λi (t) = λ0 1 + sin(2πt/T ) , reflecting time-varying traffic patterns such as daily or orbital variations.
Let Qi (t) be the queue length (number of packets) at satellite i at time t. Let Ai (t) be the number of packet arrivals at node i during time slot t, and let µi (t) be the service rate (i.e., the number of packets that can be transmitted over outgoing links) of node i at time t. The queue evolves according to Qi (t + 1) = max{Qi (t) − µi (t), 0} + Ai (t)
(1)
F. Optimization Objective The objective is to learn a routing policy π(a|s) that maximizes the expected discounted cumulative reward "∞ # X t max E γ ri (t) , (5) π
t=0
where γ ∈ (0, 1) is the discount factor.
D. Delay Model The end-to-end delay consists of multiple components, including propagation delay, transmission delay, queuing delay, and processing delay. Specifically, the delay between satellites i and j at time t can be expressed as prop trans (t) + τij Dij (t) = τij (t) + τiqueue (t) + τiproc (t),
(2)
prop trans where τij (t) is the propagation delay, τij (t) is the transqueue (t) is the queuing delay, and τiproc (t) is mission delay, τi the processing delay.
E. POMDP Formulation The routing problem is formulated as a POMDP [8], defined by the tuple (S, A, P, R), where S, A, P, and R are the state space, action space, state transition probability, and reward function, respectively. State: At time t, each satellite i observes a local state si (t) ∈ S, defined as si (t) = Qi (t), {Dij (t)}j∈Ni (t) , xi (t) ∈ Rd (3) where xi (t) ∈ Rdx are topology-related features, such as relative position information or connectivity indicators of neighboring satellites. Since global network information is not fully observable, the problem is partially observable. Here, si (t) represents the observable state under partial observability. Action: The action ai (t) ∈ A is defined as selecting the next-hop node ai (t) ∈ Ni (t), where A = Ni (t) is the action space. State Transition: The state transition probability P(s′ |s, a) is governed by stochastic packet arrivals Ai (t), service rates µi (t), and time-varying topology E(t). Reward: The instantaneous reward ri (t) is defined according to the reward function R(s, a) to minimize delay and congestion ri (t) = − αDi,ai (t) (t) + βQi (t) (4) where Di,ai (t) (t) is the transmission delay to the selected nexthop node, and α, β > 0 are weighting coefficients [10]. This design emphasizes congestion avoidance over distance minimization by assigning a higher weight to the queueing term (i.e., β > α). Consequently, the routing agent is encouraged to sacrifice shorter paths in favor of less congested routes, thereby improving load balancing and reducing overall network delay. This design encourages the routing agent to anticipate future congestion and proactively avoid potential bottlenecks, rather than reacting only to instantaneous delay.
III. P ROPOSED S PATIAL -T EMPORAL L EARNING -BASED D ISTRIBUTED ROUTING S CHEME The temporal dynamics of traffic, as characterized by the NHPP-based arrival model in Sec. II, motivate the incorporation of sequence modeling techniques in the proposed framework. In this section, we present the proposed spatialtemporal learning-based distributed routing framework. Algorithm 1 summarizes the overall training and decision-making procedure of the proposed distributed routing framework, including spatial-temporal feature extraction, action selection, and policy update. Each satellite operates as an independent agent and performs the following procedure. A. Overview of the Proposed Framework At each time slot t, satellite i observes its local state si (t) and selects the next-hop node ai (t) based on a learned policy [5]. The decision-making process is realized through a spatial-temporal learning agent, which consists of three key components: a GAT for spatial feature extraction, an LSTM module for temporal dependency modeling, and a DQN module for policy optimization. The routing action is determined by selecting the next-hop node that maximizes the learned action-value function. B. Spatial Feature Extraction via GAT To capture the spatial correlations among neighboring satellites, we employ a GAT [17]. At each time slot, the local network structure around satellite i is represented as a graph defined by its neighboring set Ni (t). The input to the GAT is the topology-related feature vector xi (t) defined in Sec. II. For each neighbor j ∈ Ni (t), an attention coefficient is computed as exp σ wT [xi (t)∥xj (t)] , (6) αij (t) = P T k∈Ni (t) exp (σ (w [xi (t)∥xk (t)])) where xi (t) is the input feature vector of satellite i, which is derived from the topology-related component of the state si (t), w is a learnable weight vector, σ(·) is a nonlinear activation function, and ∥ is concatenation. The aggregated spatial feature is then given by X zi (t) = αij (t)xj (t), (7) j∈Ni (t)
which represents the aggregated spatial feature of satellite i.
C. Temporal Dependency Modeling via LSTM To capture the temporal dynamics of network states, we incorporate an LSTM module [18]. The spatial feature zi (t) is fed into the LSTM to model temporal dependencies. The hidden state is updated as (t)
(t−1)
hi = LSTM(zi (t), hi
),
(8)
(t)
where hi is the hidden representation at time t. This enables the agent to capture historical congestion patterns and link variations. Such temporal modeling is particularly important in LEO networks, where time-varying traffic arrivals, as modeled by the NHPP in Sec. II, introduce temporal correlations that cannot be captured by purely spatial methods. This design explicitly leverages the temporal correlation introduced by the NHPP-based traffic model, enabling the agent to learn periodic traffic patterns. D. DRL-Based Routing Decision Based on the learned representation, a DQN [6] is employed to estimate the action-value function. The Q-function is de(t) fined as Qθ (hi , a), which evaluates the expected cumulative (t) reward based on the learned representation hi . The optimal action is selected as (t)
ai (t) = arg max Qθ (hi , a). a∈Ni (t)
(9)
The network is trained to minimize the temporal-difference (TD) error. The target value is given by (t+1)
yi (t) = ri (t) + γ max Qθ− (hi ′ a
, a′ ),
(10)
Algorithm 1: Proposed GAT-LSTM-DQN-Based Distributed Routing Algorithm Input: Online network parameters θ and target network parameters θ− ; Replay buffer D; discount factor γ; Exploration parameters (ϵ0 , ϵmin , Kdecay ); Target network update frequency C. Output: Learned routing policy (t) (t) π(hi ) = arg maxa∈Ni (t) Q(hi , a; θ). 1 Initialize online network Q(h, a; θ), target network Q(h, a; θ− ), and replay buffer D; 2 for each episode do 3 Initialize network environment and local state si (0) for each satellite i ∈ V; 4 for each time slot t do 5 Update exploration rate ϵt = max(ϵmin , ϵ0 e−t/Kdecay ); 6 for each satellite i ∈ V do 7 Construct local state si (t) and extract topology-related feature xi (t); 8 Compute spatial feature zi (t) via GAT and (t) (t−1) update hi = LSTM(zi (t), hi ); 9 if U(0, 1) < ϵt then 10 Select a random next-hop action ai (t) ∈ Ni (t); 11 else 12 Select action (t) ai (t) = arg maxa∈Ni (t) Q(hi , a; θ); 13
where θ− are the parameters of the target network. E. Distributed Routing Mechanism The proposed framework operates in a fully distributed manner. Each satellite independently constructs its local state, performs feature extraction, and determines routing actions without requiring global network information. This distributed design significantly improves scalability and adaptability in dynamic LEO satellite networks. As shown in Algorithm 1, the proposed framework integrates GAT-based spatial modeling, LSTM-based temporal learning, and DQN-based decision-making into a unified pipeline, enabling each satellite to perform proactive and adaptive routing decisions based on local observations. IV. S IMULATION R ESULTS A. Simulation Setup We evaluate the proposed spatial-temporal learning-based distributed routing scheme in a dynamic LEO satellite network with periodically varying traffic loads. Following the simulation setting in the thesis implementation, the considered constellation contains 45 satellites interconnected by ISLs, and the traffic load is varied from 120 Mbps to 240 Mbps to examine the routing performance under light, moderate, and heavy congestion conditions. The key simulation parameters
14
15
16
17 18
Execute action ai (t), observe reward ri (t) = − αDi,ai (t) (t) + βQi (t) and next state si (t + 1); (t+1) Compute hi from si (t + 1) and store (t) (t+1) transition (hi , ai (t), ri (t), hi ) in D; Sample a mini-batch from D and compute (t+1) ′ yi (t) = ri (t) + γ maxa′ Qθ− (hi , a ); Update θ by minimizing 2 (t) yi (t) − Q(hi , ai (t); θ) ; if t mod C = 0 then Update target network: θ− ← θ;
are summarized in Table I and Table II, and the traffic follows the NHPP-based model described in Sec. II. The simulation parameters are selected based on realistic LEO network settings and are aligned with prior work in the literature [11]. To validate the effectiveness of the proposed method, we compare it with the following four routing schemes: • Dijkstra [19]: a topology-adaptive shortest-path routing algorithm; • GraphPR [11]: a GNN-enhanced multi-agent reinforcement learning-based distributed routing scheme; • DQN-IR [8]: a single-agent deep reinforcement learningbased routing method;
20
TABLE I: Simulation Parameters of the LEO Satellite Network
10 0 10 20 40
TABLE II: Hyperparameters of the Proposed Framework Value 4 64 128 1300 1 × 10−4 0.99 100,000 128 200 steps 1.0 0.01 0.995
0
200
400
3 U R S R V H G * U D S K 3 5 ' 4 1 , 5 ) ' 5 0 $ 5 / ' L M N V W U D
7 U D I I L F / R D G 0 E S V
(a) System throughput •
FDR-MARL [3]: a multi-agent reinforcement learningbased distributed routing scheme.
B. Training Convergence Analysis We first examine the training convergence behavior of the proposed method. Fig. 2 compares the reward evolution of the proposed GAT-LSTM scheme with the learning-based baselines. The proposed method exhibits faster convergence and more stable reward trajectories than the compared methods. This demonstrates that spatial-temporal modeling improves learning stability under dynamic conditions. C. Throughput and Delay Analysis Fig. 3 shows the system throughput and end-to-end delay under different traffic loads. As the network load increases, all methods suffer performance degradation due to intensified congestion and queue accumulation. However, the proposed method consistently outperforms the baseline schemes. In terms of throughput, the proposed method maintains the highest throughput across all traffic conditions. At a traffic load of 240 Mbps, it achieves approximately 210 Mbps throughput, outperforming all baseline methods under the same condition. This result indicates that the proposed routing framework can better distribute packets across available paths and avoid severe bottleneck formation. In terms of end-to-end delay, the proposed method achieves the lowest latency among all compared methods. At a traffic load of 240 Mbps, the delay is reduced to approximately 498 ms, which is significantly lower than that of the baseline methods. This improvement is primarily attributed to the proactive congestion avoidance enabled by the temporal modeling.
600 800 Episode
Fig. 2: Training reward convergence comparison of different routing algorithms.
6 \ V W H P 7 K U R X J K S X W 0 E S V
Hyperparameters Number of GAT attention heads GAT hidden dimension LSTM hidden dimension Maximum training episodes Learning rate Discount factor γ Replay buffer size Batch size Target update frequency Initial ϵ Minimum ϵ ϵ decay
1. DQN-IR 2. FDR-MARL 3. GraphPR 4. Proposed 1000 1200
30
$ Y H U D J H ' H O L Y H U \ P V
Value 45 70◦ 570 km 23.28 GHz 25 MHz 300 Mbps 120 / 180 / 240 Mbps 1500 Bytes 640 30
Average Reward
Parameters Number of satellites Orbital inclination Orbital altitude Carrier frequency Channel bandwidth ISL capacity Traffic load Packet size Maximum queue size Maximum hop count (TTL)
7 U D I I L F / R D G 0 E S V
(b) End-to-end delay
Fig. 3: Performance comparison under different traffic loads: (a) system throughput and (b) end-to-end delay. D. Packet Loss and Queue Length Analysis Fig. 4 compares the packet loss rate and average queue length under different traffic loads. In terms of packet loss, the proposed method achieves the lowest packet loss rate among all compared methods. At high traffic load (240 Mbps), the packet loss rate is reduced to below 46.81%, compared with higher loss observed in baseline methods. This improvement is mainly attributed to proactive congestion avoidance. In terms of queue length, the proposed method maintains the shortest average queue length across all traffic conditions. The queue length is reduced by up to 23.26% compared with baseline methods under heavy traffic load. This indicates that the proposed framework effectively prevents congestion buildup. E. Green AI and Computational Efficiency Analysis In addition to routing performance, we further evaluate the proposed framework from a Green AI perspective by analyzing its computational overhead and associated carbon footprint. Following the carbon emission quantification framework in [20], the carbon emission is estimated as CO2 eq = E × C, where E is the energy consumption (kWh) and C is the carbon intensity of electricity generation. We consider a typical on-board edge AI processor with a thermal design power (TDP) of 30 W (0.03 kW) and adopt a carbon intensity of 495 g CO2 /kWh. The computational
$ Y H U D J H 4 X H X L Q J / H Q J W K
3 D F N H W / R V V 5 D W H
3 U R S R V H G * U D S K 3 5 ' 4 1 , 5 ) ' 5 0 $ 5 / ' L M N V W U D
7 U D I I L F / R D G 0 E S V
(a) Packet loss rate
7 U D I I L F / R D G 0 E S V
(b) Average queue length
Fig. 4: Performance comparison under different traffic loads: (a) packet loss rate and (b) average queue length. TABLE III: Computational Cost and Carbon Footprint Comparison (10,000 Routing Decisions) Method FDR-MARL [3] DQN-IR [8] GraphPR [11] Proposed
Time Complexity O(LH 2 ) O(LH 2 ) O(|V|F 2 + |E|F ) 2 )) O(T (|V|F 2 + Hlstm
Time (ms) 0.56 0.58 1.32 2.70
Energy (kWh) 4.67 × 10−5 4.83 × 10−5 1.10 × 10−4 2.25 × 10−4
CO2 (g) 0.023 0.024 0.054 0.111
complexity, inference time, energy consumption, and carbon emission for processing 10,000 routing decisions are summarized in Table III. As shown in Table III, the proposed GAT-LSTM-DQN based routing framework incurs higher computational complexity and inference time due to the joint spatial and temporal modeling. However, the absolute energy consumption and carbon emission remain extremely low. Specifically, processing 10,000 routing decisions only consumes 2.25 × 10−4 kWh, corresponding to approximately 0.111 g of CO2 emissions. This energy cost is negligible in practical systems and is equivalent to powering a 10 W LED bulb for approximately 81 seconds. Therefore, the proposed framework aligns with Green AI principles by achieving superior performance with minimal additional carbon footprint, demonstrating an effective trade-off between computational overhead and system-level efficiency. V. C ONCLUSION This paper proposed a spatial-temporal learning-based distributed routing framework for dynamic LEO satellite networks. By integrating GAT and LSTM within a DQN-based architecture, the proposed method enables proactive congestion avoidance based on local observations. Simulation results showed that the proposed approach significantly improves throughput, packet loss, queue length, and end-to-end delay compared with conventional and learning-based routing schemes, while maintaining low computational overhead and negligible carbon emissions. Future work will extend this framework to QoS-aware routing, heterogeneous traffic scenarios, and cooperative multi-agent learning in large-scale LEO constellations. R EFERENCES [1] G. Chen, T. Liao, S. Meng, and S. Wu, “Heterogeneous multi-layer constellation for future satellite internet: Framework, optimization, and evolution vision,” IEEE Wireless Commun., Jan. 2026.
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