This track, to be performed by the applicant, is concerned with state feedback control of general deterministic networks and builds on the applicants first results ([#References|references]).
The approach as introduced in ([#References|references]) seems to be applicable to arbitrary switching networks with setup times, for arbitrary given feasible network behaviors, while taking into account buffer constraints. However, only convergence towards behavior similar to that of the desired periodic orbit can be guaranteed. That is, it might be that some buffers always contain a fixed number of additional jobs, compared to the desired periodic orbit. Therefore, first the approach as introduced in ([#References|references]) should be modified to overcome the above mentioned shortcomings. This will be joint work with the group of prof. Leonov (St. Petersburg University, Russia).
Jobs moving from one server to the next often involve a non-negligible transportation delay. As a next step, the approach can be extended to networks with transportation delays between servers. This will be joint work with the group of prof. Helbing (TU Dresden, Germany), including applications to traffic light control.
Furthermore, the current approach leads to only one possible feedback. In practice this is undesirable. A class of feedbacks needs to be derived and depending on desired transient performance an appropriate feedback needs to be selected from this class. Typically, controllers have gains which can be used for tuning performance. Another constraint on the controller design might be the time between two successive series of service of a job type. The next step is to extend the approach to accommodate for tuning. This will be joint work with dr. Robertson (LTH Lund, Sweden), including application to the control of internet servers.
Related to this is the problem of deriving optimal network behavior. Since of all possible feasible desired behaviors, optimal network behavior is the most interesting one to make the system converge to. This issue will be addressed with the Combinatorial Optimization group of prof. Woeginger (Mathematics and Computer Science, TU/e), in particular with dr. Hurkens and dr. Sitters.
When considering buffer constraints, not only the desired behavior plays a role. Buffer constraints can make it impossible to reach the desired behavior from the current state, as illustrated in ([#References|references]). This reachability question is the next question to address.
Finally, the influence of different parameters is studied. What happens if parameters are different than assumed during controller design? So what if some arrival rates, processing rates, setup times, and/or transportation delays are different? What happens for time varying arrival rates? Under what conditions does the proposed feedback still yield reasonably good results?