## On Deciding Stability of Constrained Homogeneous Random Walks and Queueing Systems (2000)

Venue: | Mathematics of Operations Research |

Citations: | 6 - 5 self |

### BibTeX

@INPROCEEDINGS{Gamarnik00ondeciding,

author = {David Gamarnik},

title = {On Deciding Stability of Constrained Homogeneous Random Walks and Queueing Systems},

booktitle = {Mathematics of Operations Research},

year = {2000},

pages = {2002}

}

### OpenURL

### Abstract

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 first 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.

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Citation Context ...ated that this condition is not sufficient for stability. The results were obtained primarily in the context of stochastic networks ([5],[6],[10],[20],[24]), deterministic fluid networks ([2],[6],[7],=-=[8]-=-,[9]), deterministic adversarial networks ([1],[4],[12],[14]). One of the earliest result in the area were obtained by Rybko and Stolyar [24] and Lu and Kumar [20]. They showed that a simple priority ... |