## 1 Introduction
In the LEO satellite constellation scenario, the unpredictable jitter in inter-satellite wireless link latency, which is far more complex than the predictable jitter in wired links, introduces  
Figure 1: The difference between traditional network routing and parallel subnetwork routing. deviations in gate openings between satellite nodes, posing significant challenges for the deterministic transmission of time-sensitive data. By the end of 2024, there was significant development in time-sensitive business transmission technologies based on Low Earth Orbit satellite constellations. For instance, Huawei has introduced the \"Direct Satellite Connection for Mobile Phones\" service, enabling users to access time-critical video and audio services directly through their mobile devices. SpaceX has also launched the \"Star Shield\" service, utilizing the Starlink constellation to rapidly access and transmit battlefield and security information. Based on scenarios and emerging TSN technology for time-sensitive business transmission, the research work of this paper is as follows:  
1. Establish a routing and scheduling model named parallel subnetworks--FJSP--Reinforcement Learning Scheduling, abbreviated as \"PSFRS\", for time-sensitive business transmission in the scenario of optical interconnect parallel subnetworks. The objective is to minimize the multi-hop transmission delay for time-sensitive businesses, reduce resource consumption for satellite transmission, and adhere to constraints, such as the maximum number of simultaneous transmissions per satellite, the maximum number of hops for packet transmission, packet transmission interruption constraints, and the absence of priority constraints for time-sensitive business. Considering the characteristics of packet transmission in the objective function and constraints, we formulate the routing and scheduling strategy problem to achieve controllable multi-hop transmission delay in Low Earth Orbit satellite constellations. This problem involves multiple objective functions and coupled variables, making it challenging to obtain analytical solutions. 2. Address the potential queuing issues that may arise between subnetworks after reconfiguration in the optical interconnect parallel subnetwork. We utilize the controllability of delay in a single satellite using CQF gate scheduling in time-sensitive business transmission technology to extend the local end-to-end delay optimization problem to a global routing delay optimization problem. Consequently, the routing and scheduling problem in Low Earth Orbit satellite constellations transforms into a classic Flexible Job Scheduling Problem (FJSP). This transformation significantly enhances the feasibility of utilizing optical interconnect parallel subnetworks for time-sensitive business transmission and introduces a new approach for employing CQF gate scheduling for transmission in Low Earth Orbit satellite constellations. 3. Given the characteristic of optional selection for each hop in the routing of time-sensitive business transmission, we employ Q-learning-based reinforcement learning to solve the problems. This solution aligns with the requirements of routing and scheduling for time-sensitive business transmission in Low Earth Orbit constellations. Compared to traditional algorithms, this approach offers a superior solution to the NP-hard problem. 4. Building upon the previous work of the Optical Communication team at Shanghai University, simulations were conducted using existing simulation platforms and the specialized TSN simulation tool OMNET++ to validate the proposed models and routing scheduling strategies in time-sensitive business transmissions. The experiments focused on testing key metrics, such as algorithm complexity, constellation task burden, and end-to-end latency.