Verification of parametric concurrent systems with prioritised FIFO resource management

We consider the problem of parametric verification over a class of systems of processes competing for access to shared resources. We suppose the access to the resources to be controlled according to a FIFO-based policy with a possibility of distinguishing low-priority and high-priority resource requests. We propose a model of the concerned systems based on extended automata with queues. Over this model, we address verification of properties expressed in LTL X enriched with global process quantification and interpreted on finite as well as fair behaviours of the given systems. In addition, we examine parametric verification of process deadlockability too. By reducing the parametric verification problems to finite-state model checking, we establish several decidability results for different classes of the considered properties and systems (including the special case of systems with the pure FIFO resource management). Furthermore, we show that parametric verification against formulae with local process quantification is undecidable in the given context.