On random walks arising in queueing systems: Ergodicity and transience via quadratic forms as Lyapounov functions. I

DOI10.1007/BF01149191zbMath0687.60083MaRDI QIDQ1263172

Guy Fayolle

Publication date: 1989

Published in: Queueing Systems (Search for Journal in Brave)

zbMATH Keywords

supermartingalesquadratic formsLyapunov functionslinear inequalitiescriteria for transience and ergodicity

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22)

Related Items (6)

The rate of convergence of a homogeneous Markov chain arising from two-queue networks ⋮ Reflecting random walks in curvilinear wedges ⋮ Stability of token passing rings ⋮ Tail Asymptotics of the Stationary Distribution of a Two-Dimensional Reflecting Random Walk with Unbounded Upward Jumps ⋮ On the Stability of Greedy Polling Systems with General Service Policies ⋮ On partially homogeneous nearest-neighbour random walks in the quarter plane and their application in the analysis of two-dimensional queues with limited state-dependency

Cites Work

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• Criteria for the recurrence or transience of stochastic process. I
• Brownian motion in a wedge with oblique reflection
• The solution of certain two-dimensional Markov models
• Criteria for classifying general Markov chains
• On the Stochastic Matrices Associated with Certain Queuing Processes

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