Journal ArticleDOI
On Deciding Stability of Constrained Homogeneous Random Walks and Queueing Systems
TLDR
In this paper, it was shown that the problem of computing a fluid limit of a queueing system or of a constrained homogeneous random walk in d + is undecidable.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.read more
Citations
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Control Techniques for Complex Networks
TL;DR: The workload model that is the basis of traditional analysis of the single queue becomes a foundation for workload relaxations used in the treatment of complex networks and Lyapunov functions and dynamic programming equations lead to the celebrated MaxWeight policy.
Journal ArticleDOI
Light tail asymptotics in multidimensional reflecting processes for queueing networks
TL;DR: In this paper, the authors consider the stationary distributions of reflecting processes on multidimensional nonnegative orthants and other related processes, provided they exist, and discuss their possible extensions.
Posted Content
Undecidable problems: a sampler
TL;DR: A survey of undecidable decision problems arising in various branches of mathemat- ics is given in this paper, where two senses in which undecidability is used are discussed.
Journal ArticleDOI
Instability in stochastic and fluid queueing networks
David Gamarnik,John J. Hasenbein +1 more
TL;DR: In this article, it was shown that for networks with two stations, if the fluid model is not weakly stable under the class of all non-idling policies, then a corresponding queueing network is not rate stable under a particular nonidling scheduling policy which makes the associated stochastic process transient.
References
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Formal Languages and Their Relation to Automata
TL;DR: The theory of formal languages as a coherent theory is presented and its relationship to automata theory is made explicit, including the Turing machine and certain advanced topics in language theory.
Journal ArticleDOI
On Positive Harris Recurrence of Multiclass Queueing Networks: A Unified Approach Via Fluid Limit Models
TL;DR: In this paper, it was shown that a queueing network is positive Harris recurrent if the corresponding fluid limit model eventually reaches zero and stays there regardless of the initial system configuration, and that single class networks, multiclass feedforward networks and first-buffer-first-served preemptive resume discipline in a reentrant line are positive Harris-rewarded under the usual traffic condition.
Journal ArticleDOI
What's Decidable about Hybrid Automata?
TL;DR: It is proved that the reachability problem is undecidable for timed automata augmented with a single stopwatch, and an (optimal) PSPACE reachability algorithm is given for the case of initialized rectangular automata.
Proceedings ArticleDOI
What's decidable about hybrid automata?
TL;DR: It is proved that the reachability problem is undecidable for timed automata augmented with a single stopwatch, and an (optimal) PSPACE reachability algorithm is given for the case of initialized rectangular automata.
Journal ArticleDOI
Distributed scheduling based on due dates and buffer priorities
S.H. Lu,P. R. Kumar +1 more
TL;DR: In this article, several distributed scheduling policies are analyzed for a large semiconductor manufacturing facility, where jobs of wafers, each with a desired due date, follow essentially the same route through the manufacturing system, returning several times to many of the service centers for the processing of successive layers.