Network Calculus-Based Latency for Time-Triggered Traffic under Flexible Window-Overlapping Scheduling (FWOS) in a Time-Sensitive Network (TSN)  
[PERSON]  
1 Department of Computer and Communication Engineering, Universita Putra Malaysia,  
Sendang 43400, Malaysia; [EMAIL_ADDRESS] (A.S.); [EMAIL_ADDRESS] (F.H.) [PERSON]  
1 Department of Computer and Communication Engineering, Universita Putra Malaysia,  
Sendang 43400, Malaysia; [EMAIL_ADDRESS] (A.S.); [EMAIL_ADDRESS] (F.H.) [PERSON]  
1 Department of Computer and Communication Engineering, Universita Putra Malaysia,  
Sendang 43400, Malaysia; [EMAIL_ADDRESS] (A.S.); [EMAIL_ADDRESS] (F.H.) [PERSON]  
1 Department of Computer and Communication Engineering, Universita Putra Malaysia,  
Sendang 43400, Malaysia; [EMAIL_ADDRESS] (A.S.); [EMAIL_ADDRESS] (F.H.) Footnote 1: email: {1,3,4}  
Footnote 2: email: {1,3,4}  
Footnote 3: email: {1,3,4}  
Footnote 4: email: {1,3,4  
for urgent traffic. These features have attracted many researchers and companies to the TSN framework for their interests [2]. Basically, the TSN framework serves mixed-criticality applications under three different traffic categories: time-triggered (TT), Audio/Video Bridging (AVB), and best effort (BE). The TT traffic represents the highest-priority class that requires a guaranteed zero jitter delay and a tightly bounded end-to-end latency. TT flows are configured by using the time-aware shaping (TAS) mechanism in the gate control list (GCL) schedule, as defined in IEEE 802.1 Qbv [3]. The AVB traffic represents the second-highest priority class that is configured by using the credit-based shaping (CBS) mechanism to meet the deterministic end-to-end latency requirement, as presented in IEEE 802.1 Qav [4]. The BE type represents the lowest-priority class, with no guaranteed timing requirements. Implementing an appropriate GCL timing table for TT traffic in all selected switches while ensuring critical time streams' latency requirements is a complex and crucial problem. The complexity arises not only from the difficulties to satisfy TT demands but also because the other critical time flows, i.e., the AVB, must be considered. Excluding the soft real-time traffic from the predefined schedule (GCL) and allowing the TT flows to preempt them (as defined in IEEE 802.1 Qbu [5]) may cause them to miss their latency deadlines, as many researchers have argued [6; 7; 8; 9]. For these reasons, proper GCL designs are essential to guarantee safe latencies for all critical time flows. Different scheduling solutions have been proposed to ensure latency requirements for hard real-time flows and enhance AVB latency performance at the same time. As the GCL implementation is window based, each priority class has to transmit related traffic through the assigned windows. Different window patterns have been proposed to enhance the overall system performance, as discussed in Section 2. Most of the relevant researchers in the literature, e.g., in [10; 11; 12; 13], have suggested allowing TT open windows to interfere with each other, leading to more available bandwidth for unscheduled transmissions. Although the researchers in [11; 12] have improved the overall solution space, no one has optimized how much TT windows can be overlapped without missing TT requirements. Accordingly, this paper focuses on presenting an optimal formal solution for the scheduling problem based on TT open windows' overlapping assumption. In this paper, we present a complete end-to-end latency analysis for TT traffic based on the variable overlapping ratio (OR) between TT open windows in the predefined GCL. The GCL schedule is designed for all selected nodes, considering the relative positional relationship between window offsets for adjacent nodes. The GCLs are implemented according to three overlapping metrics: the priority of the overlapped window, the position of overlapping, and the overlapping ratio (OR).