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Low earth orbit (LEO) satellite communication networks require huge load capacity and information processing speed to carry global communication traffic. Inter-satellite links and the on-board processing are the key technologies to achieve this goal, but the new network architecture leads to great challenges on satellite routing. This paper designs a hybrid inter-satellite link with the same-orbit laser and the different-orbit microwave to increase the link capacity and adopts a CPU centralized scheduling to improve the utilization of computing resources. Then, this paper establishes minimum delay function by considering the inter-satellite transmission delay and the on-board processing delay. The transmission delay model bases on the orbital period, and the processing delay adopts the multi-services model, the limited-capacity single-service model, and the unlimited-capacity single-service model in the queuing theory to model the on-board CPU centralized scheduling, photoelectric converters, and electro-optical converters, respectively. Based on this model, this paper proposes an inter-satellite routing strategy with modified Q-routing algorithm. The modified algorithm uses Dijkstra algorithm to accelerate the convergence of Q-routing algorithm and retains the strong real-time performance of Q-routing algorithm. Simulations show that the delay of the modified algorithm is 83.3$$\%$$ % lower than that of the Dijkstra algorithm, and the larger the network and the traffic, the more obvious the advantage.

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