# Analysis of 5G Channel Access for Collaboration with TSN Concluding at a 5G Scheduling Mechanism
## 5 Analysis of the Channel Access Prioritization of Packets
### Mapping of Scheduling Decisions  
The transmitting behavior of UEs and gNB needs to be organized through a time grid known to all participants of the radio channel. The access to the radio channel is organized by a central instance, the MAC scheduler of the gNB. The scheduling decisions are updated and communicated in a time-discrete manner according to the TTI grid. In the case of dynamic scheduling, decisions about the amount of radio resources granted for the downlink and uplink of each UE are made at every TTI, affecting one Transport Block per UE (and MIMO layer). Therefore, the decision regarding which traffic classes are served channel access is made once per TTI as well. Because of the flexible Subcarrier Spacing and scheduling formats, the duration of a TTI in 5G can reach from 1000 \(\upmu\)s (15 kHz SCS and slot-based scheduling) to 8.93 \(\upmu\)s (240 kHz SCS and mini-slot scheduling over two OFDM symbols) [15].  
The TSN standard, 802.1 Qbv [22], describes the time parameter for the duration of a single GCL slot in the unit of nanoseconds, a much smaller order of magnitude than the smallest possible TTI in 5G. Therefore, in relation to the 5G TTI grid, decisions about the channel access of packets belonging to different traffic classes in TSN are taken nearly continuously based on the traffic class affiliation of a packet and the current point in time.  
This leads to the conclusion that the continuous conditions \(g_{i,j}(t)\) derived from the GCLs need to be mapped to a discrete set of scheduling conditions \(c_{ij}(\
u)\):  
\[c_{i,j}(\
u)=g_{i,j}(\
u\cdot T_{TTI})\quad,\
u\in\mathbf{N} \tag{3}\]This kind of sampling results in additional restrictions according to the composition of GCLs. The duration of the time interval that describes a single slot of a GCL has to be at least one TTI in order to be regarded in the set of scheduling conditions with certainty:  
\[t_{2}^{i,j}-t_{1}^{i,j}>T_{TTI}\quad\forall i,j \tag{4}\]  
In the event that \(T_{GCL}\) or a multiple thereof corresponds to the temporal grid of the TTI, the GCL requirements can be mapped to a finite set of scheduling conditions \(\vec{c}_{i,j}\). The vector \(\vec{c}_{i,j}\) corresponds to one or multiple GCL periods \(\vec{g}_{i,j}(t)\). If the mapping is supposed to take place only once in the lifetime of a TSN stream, the overall duration of the GCL must be either a multiple or a whole divisor of 0.5 ms, as the grid of radio frames in the Next Generation Radio Access Network (NG-RAN) aligns every 0.5 ms independent of the active subcarrier spacing [30]. If this condition cannot be met, the temporal relation between the GCL requirements and the executed scheduling decisions is constantly shifting. Therefore, the mapping from \(g_{i,j}(t)\) to \(\vec{c}_{i,j}\) needs to be updated on a regular basis. The more often this update is executed, the smaller the dimension of \(\vec{c}_{i,j}\), and vice versa. At this point, a trade-off between the less frequent transmission of a larger control channel payload and the more frequent transmission of a smaller control channel payload has to be made.