On the state liveness of some classes of guidepath-based transport systems and its computational complexity

Abstract

Guidepath-based transport systems is a pertinent abstraction for the traffic that is generated in many contemporary applications, ranging from industrial material handling and robotics, to computer game animations and the qubit transport systems employed in quantum computing. A particular problem that must be effectively addressed for the systematic operation of these systems, is the preservation of their “liveness”, i.e., the preservation of the ability of the system agents to complete their current assignments and engage successfully in similar assignments in the future operation of the system. This paper provides a systematic and comprehensive characterization of the notion of “liveness” for the entire spectrum of the aforementioned transport systems, and it further investigates the implications of this characterization for the deployment of maximally permissive liveness-enforcing supervision for the underlying traffic. It is shown that the computational complexity of the sought supervisors is contingent upon certain structural and operational attributes of the considered transport systems, that define, thus, a useful taxonomy for these environments. The paper proposes effective and efficient liveness-enforcing supervisors for each member of this taxonomy. Furthermore, the concluding part of the paper indicates how the obtained results can be integrated in a broader control framework for the considered transport systems that will also address time-related performance considerations for these environments, like the maximization of their throughput.