On Deciding Stability of Constrained Homogeneous Random Walks and Queueing Systems

Authors:
David Gamarnik
Affiliations:
-
Venue:
Mathematics of Operations Research
Year:
2002

Citing 0
Cited 3

Computing stationary probability distributions and large deviation rates for constrained random walks.: the undecidability results.

ACM SIGMETRICS Performance Evaluation Review
Weak instability in stochastic and fluid queueing networks

ACM SIGMETRICS Performance Evaluation Review - Special issue on the fifth workshop on MAthematical performance Modeling and Analysis (MAMA 2003)
Stochastic Bandwidth Packing Process: Stability Conditions via Lyapunov Function Technique

Queueing Systems: Theory and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

We investigate stability of scheduling policies in queueing systems. To this day no algorithmic characterization exists for checking stability of a given policy in a given queueing system. In this paper we introduce a certaingeneralized priority policy and prove that the stability of this policy is algorithmically undecidable. We also prove that stability of a homogeneous random walk in d + is undecidable. Finally, we show that the problem of computing a fluid limit of a queueing system or of a constrained homogeneous random walk is undecidable. To the best of our knowledge these are the first undecidability results in the area of stability of queueing systems and random walks in d +. We conjecture that stability of common policies like First-In-First-Out and priority policy is also an undecidable problem.