## 5 TSN Scheduling Problem Formulation
### TSN Scheduling Optimization Objectives
Bandwidth waste may happen for several reasons, e.g., if two HTS windows are scheduled after each other but the gap between the closure of the first and the opening of the second is so small that it does not allow the transmission of any LTS or BE frame. Bandwidth wastage could also happen due to frequent guard-bands. However, guard-bands, when required by the HTS streams, can not be avoided except between two streams of the same type that could be scheduled back to back without the need for a guard-band. In that case, precautions against jitter should be taken. Consequently, minimizing the number of guard-bands is not a relevant objective. In summary, this second group of objectives is not crucial to model the schedulability of HTS streams, although it could be beneficial in specific scenarios. One of the most important objectives of TSN is to provide guarantees in terms of bounded latency to streams, which requires eliminating nondeterminism from the network mainly caused by variable queuing delay leading to high jitter. Different aspects contribute to nondeterminism including synchronization errors, imprecise bridge delays considered during scheduling or frequent configuration updates, and the inconsistency that could bring to the network. While it is difficult to eliminate all of those problems, determinism can be improved by minimizing jitter. This could be performed at every hop inside the delivery path or at the last hop by making sure that the worst-case latency of an HTS stream should be smaller than the required maximum latency. Managing the jitter at the last hop could be achieved by making sure that the stream is always delivered with the worst-case latency by increasing its queuing delay at the last hop when needed (e.g., by exclusively allocating a queue at the last hop as in [116]). Consequently, the management of the queues becomes easier. However, the complexity of this approach is expected to increase with the number of HTS streams in the network since the jitter is not controlled in the network except for the last hop, which also would negatively impact the worst-case latency for all streams. The main goal of this discussion is the importance of determinism for the TSN scheduling problem. Only five papers (see Figure 3) of the analyzed literature treated jitter minimization as a central objective of their work. This could be explained by the fact that many use cases do not need a very high level of determinism and that they can tolerate, to a certain extent, some randomness which renders jitter minimization not very relevant. However, if the use case does not require determinism, then it would be more convenient (i.e., less configuration effort without performance loss) to use CQF than TAS. Nevertheless, Tables 12 and 13 show that only seven papers use shapers other than TAS. In conclusion, we believe the choice of the right shaper is very important and that in the case that TAS is selected, maximizing determinism should be the primary objective of the work. Nevertheless, this primary objective could be combined with other objectives, or constraints could be added that guarantee the feasibility of the solution.