## 1 Introduction
The schematic difference between traditional satellite constellation routing and routing via parallel subnetworks is shown in Figure 1. The blue horizontal and vertical dashed arrows are the orbit of the satellite. Suppose there are two satellites A and B to transmit routing information. Clearly, after subdividing into parallel subnetworks, if time-sensitive services are being transmitted simultaneously within the same time frame, following traditional Dijkstra algorithms for routing within the subnetwork will inevitably lead to exceeding the time limit due to excessive hop counts, which does not meet the transmission requirements of time-sensitive services. Therefore, developing routing scheduling strategies to avoid queuing or worse scenarios for multiple time-sensitive service transmissions within the same time frame is a topic worthy of research. To ensure controlled latency, Time-Sensitive Networking (TSN) appears to be the most promising solution currently. TSN is an extension of traditional Ethernet, enhancing it with features like time synchronization mechanisms, credit-based traffic shaping mechanisms, time-based shaping mechanisms, gate control lists, and stream reservation while remaining fully compatible with traditional Ethernet. TSN and its extension into the wireless domain, such as 5G-TSN and WIFI-TSN, aim to provide deterministic communication for wireless mobile robotic arms and devices in cross-domain networks. The IEEE 802.1 [7] TSN Task Group (TG) is dedicated to developing a set of TSN standards, including sub-standards within IEEE 802.1 Ethernet. Therefore, TSN offers various sub-standards with diverse shaping and scheduling mechanisms, providing different levels of Quality of Service (QoS), such as Time-Aware Shaper (TAS), Asynchronous Traffic Shaper (ATS), and Credit-Based Shaper [8]. Among these mechanisms, TAS scheduling has been extensively researched over the years. TAS, through precise opening and closing of gates for Time-Triggered (TT) traffic types, offers time guarantees and zero jitters, facilitated by a gate mechanism known as Gate Control List (GCL). However, generating GCL for TAS is an NP-hard problem, with complexity increasing with network size and traffic volume. Therefore, various shaping mechanisms, like CBS, ATS, and CQF, have been proposed to alleviate TAS workload in mixed-criticality networks. Like TAS, CQF is also based on GCL. CQF is gaining popularity due to its simple GCL operations and direct computation of maximum and minimum jitter. While CQF does not provide the fine-grained scheduling of TAS, it offers a simple scheduling configuration with bounded delay and jitter. Hence, in mixed-criticality networks with diverse QoS requirements, selecting appropriate scheduling and shaping algorithms is becoming increasingly necessary. Furthermore, research on integrating TSN technology into Low Earth Orbit (LEO) satellite constellation scenarios has only recently begun to emerge in the past few years. Existing studies on the IEEE 802.1 Qbv gate scheduling mechanism primarily focus on wired networks, often assuming link delays as slow-changing or fixed values. References [9; 10] propose gate scheduling models, but these models do not consider offsets in gate slots between neighboring nodes, assuming gate slot alignment. Reference [11] introduces a non-overlapping gate list window mechanism to enhance business curve rates and eliminate traffic congestion in TSN. Reference [12] considers the relative position relationships of gate slots between adjacent nodes, presenting a window-based flexible gate list scheduling model that reduces the latency jitter requirements for business flows. However, references [11; 12] do not address scheduling strategies for time-sensitive service transmission as the number of satellites increases in LEO satellite constellations.