## 4 FWOS System Model and Design Decisions  
TSN switching considers two dependent traffic isolation mechanisms, i.e., spatial and temporal isolations, to differentiate between ingress flows. Spatial isolation is applied in each switch by selecting incoming frames to one of eight priority queues served by various forwarding constraints at the egress port. Temporal isolation is provided in the gate control list (GCL) schedules. The GCL is an off-line timetable specifying the open and close events for all associated gates. To protect TT flows from unscheduled traffic transmissions, the preemption technique is applied by allowing the TT flows to interrupt the transmission of non-expressed flows. Against other TT transmissions, complete isolation between TT windows in the GCL timings undoubtedly provides targeted deterministic latency behavior for scheduled (TT) traffic, as proposed in [6]. Nevertheless, complete window isolation wastes the available bandwidth for unscheduled traffic and may not guarantee the determinism for soft critical time traffic (AVB). There are two ways to process scheduled and unscheduled traffic in a TSN, back-to-back and porosity configurations, as depicted in Figure 3, respectively. In both structures, flexible overlapping between scheduled open windows saves more available bandwidth for unscheduled flows. The overlapping can occur from either one edge or two window edges (opening and closing). The more the TT windows overlap, the more the available time intervals for unscheduled traffic increase. It cannot be neglected that flexible overlapping schedules negatively affect the performance of scheduled traffic. Thus, essential evaluations of timing are necessary to cover all overlapping situations. In this work, we are interested in evaluating the performance of the time-aware shaping (TAS) technique under the flexible window-overlapping scheduling (FWOS) algorithm. This model allows TT windows to interfere with one another without missing the TT queues' latency deadlines. Hence, only the hard real-time flows (TT flows) are considered here for latency calculations, assuming that the set of all TT flows is denoted as \(\mathcal{S}\). Each TT flow (\(s_{m}\in\mathcal{S}\)), where \(m\) is the priority of the flow, consists of a set of frames \((\mathcal{F}_{m})\). Each node \(h\) is designed to select the ingress frame to one of \(N_{q}^{h}\) TT priority queues (\(Q_{1}^{h}\), \(\ldots\), \(Q_{N_{q}}^{h}\)), where \(Q_{1}^{h}\) and \(Q_{N_{q}}^{h}\) represent the highest- and lowest-priority queues, respectively. Each \(Q_{m}^{h}\) frame is selected to the egress port by its gate \((G_{m}^{h})\) with the open-window length \(W_{m}^{h}\) and the period \(T_{m}^{h}\). Note that the presented scheduling model is proposed assuming guaranteed synchronization for all selected switches. For performance evaluation, we consider \(Q_{h}^{h}\) as a targeted queue with an open-window duration of \(W_{k}^{h}\), where \(1\leq k\leq N_{q}\). The \(Q_{k}^{h}\) window may overlap with any \(Q_{m}^{h}\) window, as shown in Figure 4, and the overlapping ratio (OR) between them in the \(i\)-th cycle represents  
Figure 3: Configurations of the time-triggered (TT) schedule under both full isolated windows and flexible overlapping windows: (**a**) back-to-back configuration and (**b**) porosity configuration. the length of the time interval \((L_{k,m}^{h,i})\), when both windows are simultaneously open, divided by the total length of the \(Q_{k}^{h}\) window, \(W_{k}^{h,i}\), as  
\[OR_{k,m}^{h,i}=\frac{L_{k,m}^{h,i}}{W_{k}^{h,i}} \tag{1}\]  
As presented in Figure 4, the OR varies from 0 to 1, covering all the expected overlapping conditions.