We investigate stability of some scheduling policies in queueing systems. To the day no algorithmic characterization exists for checking stability of a given policy in a given queueing system. In this paper we propose a certain generalized priority policy and prove that the stability of this policy is algorithmically undecidable. We also prove that stability of a homogeneous random walk in Z d + is undecidable. To the best of our knowledge this is the rst undecidability result in the area of stability of queueing systems and random walks in Z d + . We conjecture that stability of other common policies like First-In-First-Out and priority policy is also an undecidable problem.
It was established by the author REF that, in general, stability of such random walks in Z d + is not a decidable property.
On Deciding Stability of Constrained Homogeneous Random Walks and Queueing Systems
Mathematics of Operations Research
Mathematics Computer Science