Periodicity in the transient regime of exhaustive polling systems

DOI10.1214/105051606000000376zbMath1121.60098arXivmath/0702252OpenAlexW2088223949MaRDI QIDQ997406

Serguei Popov, Stanislav Volkov, Mikhail V. Menshikov, Iain M. MacPhee

Publication date: 6 August 2007

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702252

zbMATH Keywords

greedy algorithmdynamical systemtransiencerandom walkpolling systemsalmost sure convergenceinterval exchange transformation

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Dynamical systems involving maps of the interval (37E05)

Related Items (4)

Polling systems with parameter regeneration, the general case ⋮ Dynamics of piecewise contractions of the interval ⋮ Multitype branching processes with immigration in random environment, and polling systems ⋮ Emergence and dynamics of short food supply chains

Cites Work

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• Markov chains and stochastic stability
• Critical random walks on two-dimensional complexes with applications to polling systems
• Polling systems in the critical regime.
• Stability of polling systems with exhaustive service policies and state-dependent routing
• The Metric Theory of Interval Exchange Transformations I. Generic Spectral Properties
• Échanges d'intervalles affines conjugués à des linéaires
• Applied Probability and Queues
• Topics in the Constructive Theory of Countable Markov Chains
• Absolutely Continuous Invariant Measures for a Class of Affine Interval Exchange Maps
• On the Stability of Greedy Polling Systems with General Service Policies

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