## 1 Introduction  
With the continuous development of network communication, many application scenarios such as industrial IoT, vehicular networks, and avionics networks have increasingly higher requirements for real-time and reliable transmission, while traditional Ethernet can no longer meet the requirements of applications. Consequently, a more optimal design of communication systems is needed to achieve deterministic and low end-to-end transmission delay for a massive amount of time-triggered traffic. Traditionally, industry networks adopted a dedicated field bus [1] to obtain deterministic guarantees for real-time data transmission. What is more, various real-time Ethernet technologies, such as EtherCAT [2] and TTEthernet [3] have been proposed to achieve hard real-time guarantees for Ethernet.  
In addition, the IEEE 802.1 TSN task group puts forward the concept of a time-sensitive network (TSN) [4; 5; 6], which intends to build a unified interface that can be used in various fields through standardization to support real-time transmission. TSN supports real-time applications with zero packet loss and bounded end-to-end latency. To achieve bounded delay and low jitter transmission, the TSN task group improves a series of standards [7] including IEEE 802.1 Qbv supporting time-aware shaper to schedule real-time data in a time-triggered mechanism, whereas TSN standards do not cover specific algorithms for routing and scheduling.  
The routing and scheduling problem has been proven to be an NP-hard problem, and there are generally directly solving scheduling and search-based scheduling algorithms to solve such problems. [PERSON] proposes two routing and scheduling algorithms based on heuristic algorithms, i.e., a genetic algorithm [8] and a heuristic list scheduler [9]. The NEH algorithm proposed in [10] is a well-established initialization heuristic in genetic algorithms. Additionally, [PERSON] discusses a design approach for a hybrid genetic algorithm proposed in [11] which can compete with the well-adapted NEH algorithm. However, all mentioned heuristic algorithms model and optimize routing and scheduling, respectively. Routing selection typically uses the shortest path first (SPF) and load balance first (LBF) algorithms.  
Satisfiability Modulo Theories (SMT) and integer linear programming (ILP) mathematical techniques can jointly solve the routing and scheduling problem to meet the timing requirements [12; 13; 14]. The most common optimization goals include the shortest path and reducing maximum load balancing to improve scheduling success [15; 16]. The path generated by these algorithms can only ensure a low end-to-end latency of newly added traffic while they cannot guarantee the success rate of added traffic and also cannot confirm whether they have a serious impact on scheduled traffic. Yu [17] adds a preprocessing stage based on [13] which removes unnecessary links and generates a subgraph of the network. Additionally, an improved topology pruning is introduced to reduce the scale of the scheduling problem [18]. Inspired by this approach, we introduce a flow preprocessing step before optimizing on the network side. Nevertheless, existing scheduling algorithms for TT traffic do not address the impact of route planning and time scheduling results on scheduling success, the number of schedulable flows, and the future capacity of the network to carry traffic when the differences between different traffic periods are too large [15; 19; 20].