## 4 TSN Network-Wide Scheduling--Approaches Overview, Challenges, and Future Directions
### Challenges for Network-Wide Scheduling  
In this section, we discuss challenges that are inherent to network-wide scheduling. The questions we raise in this section are crucial to guarantee end-to-end QoS to the network streams, independently of their possible placement. Figure 6 summarizes the discussed challenges. Figure 6: Network-wide scheduling faces many challenges. They are mainly on the networking level. * _Problem modeling level:_ Regardless of the used methods to solve the problem, the dimensionality of the problem poses a challenge. In legacy Ethernet, forwarding traffic requires solving the routing problem and assigning flow priorities. This still holds in TSN networks but with the addition of the time dimension. As stated previously,there are generally two main approaches for scheduling: exact approach (i.e., mathematical formulation as an optimization problem with off-the-shelf solvers) or heuristic/metaheuristic design. Solving the network-wide scheduling problem has a high problem dimensionality due to the many constraints and decision variables when using exact methods. Ref. [8] shows that the number of constraints increases with the number of switches and quadratic with the number of frames. Therefore, large use cases with many streams to schedule may lead to excessive runtime of the solver in many cases (e.g., when using SMT solvers). One main problem is the existence of binary and/or integer variables that require combinatorial optimization methods to be applied. To reduce the dimensionality and, thus, the problem complexity, several works fix some of the variables, which reduces the runtime at the expense of solution optimality. For example, ref. [47] modeled the scheduling and routing problems jointly using a genetic algorithm. The challenge facing this approach is gene encoding. Solving routing with genetic algorithms consists of finding the mapping between a limited number of transmission windows and a limited number of ports. However, scheduling consists of finding the best instant to open the window, which could theoretically be anytime during the scheduling cycle. Therefore, encoding all possible times leads to an exploding size of the gene. Ref. [47] avoided this problem by finding the path using the genetic algorithm and inferring the schedule once the paths are fixed as the earliest time that the stream can traverse all the links in its path without interference. * _Application level:_
* Due to many mechanisms and standards, TSN is gaining attention from several industries with very divergent use cases. Each use case may require different mechanisms. Therefore, the standardization community is trying to define different profiles. A profile specifies the set of choices (i.e., features, default configuration values, etc.) to apply. Table 4 summarizes the current TSN profiles per application area. The divergence between the requirements of applications from different areas places the scheduling algorithms against the challenge of being generic enough to serve applications belonging to different areas while being specific enough to provide optimal schedules for all applications regardless of their divergent requirements. * A second challenge on the application level is related to the virtualization of end-hosts. With the introduction of virtual PLCs and NFV that could be deployed in a set of possible edge compute nodes having TSN stacks and hardware support, the end-host could be attached to different locations in the topology. This brings an additional degree of freedom that could increase the solution space but also complicates the scheduling further to the increased problem dimensionality. * _Multi-domain level:_ TSN Ethernet as a deterministic networking technology is not alone in the ultra-low latency ecosystem. Other technologies such as 5G, Deterministic Networks (DetNet), and wireless TSN are also gaining momentum. Industrial applications could involve any combination of these technologies in a large-scale hybrid network.