A Markov chain model of a polling system with parameter regeneration

DOI10.1214/105051607000000212zbMath1151.60045arXivmath/0701226OpenAlexW3100458640MaRDI QIDQ2475027

Mikhail V. Menshikov, Serguei Popov, Iain M. MacPhee, Dimitri Petritis

Publication date: 20 March 2008

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

Full work available at URL: https://arxiv.org/abs/math/0701226

zbMATH Keywords

stabilityLyapunov functionsrecurrencepolling systemtime-inhomogeneous Markov chainsparameter regeneration

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10)

Related Items (6)

Polling systems with parameter regeneration, the general case ⋮ Detecting Markov chain instability: a Monte Carlo approach ⋮ Multitype branching processes with immigration in random environment, and polling systems ⋮ On a 2-class polling model with reneging and \(k_i\)-limited service ⋮ A Markov chain model of a polling system with parameter regeneration ⋮ Random Fluid Limit of an Overloaded Polling Model

Cites Work

• Markov chains and stochastic stability
• Criteria for the recurrence or transience of stochastic process. I
• Random walks in two-dimensional complexes
• 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
• A Markov chain model of a polling system with parameter regeneration
• Criteria for stochastic processes. II: Passage-time moments
• Passage-time moments for nonnegative stochastic processes and an application to reflected random walks in a quadrant
• Topics in the Constructive Theory of Countable Markov Chains
• Unnamed Item

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