Stability of non-Markovian polling systems
type: Item
instance of: scholarly article
title: Stability of non-Markovian polling systems
zbMATH Open document ID: 0851.60089
DOI: 10.1007/BF01158575
author: Laurent Massoulié
published in: Queueing Systems
publication date: 1996-03-05T00:00:00Z
review text: The paper considers polling systems where the arrivals at each station are stationary ergodic processes \((G/G)\), not necessarily mutually independent. The server switches from station to station in a Markovian fashion and each queue is attended according to a specific policy. Under certain conditions, a stationary regime is constructed in a recursive way, using a monotonicity property of the system. It is also shown that this stationary regime is the smallest in the stochastic ordering sense. The policies considered are of the gated type and satisfy a monotonicity condition. First deterministic policies are considered and later it is explained how the reasoning can be extended to random policies.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 851505
zbMATH Keywords: polling systems
zbMATH Keywords: stationary ergodic processes
zbMATH Keywords: monotonicity property
zbMATH Keywords: stochastic ordering
MaRDI profile type: Publication
cites work: Polling on a space with general arrival and service time distribution
cites work: Performance bounds and pathwise stability for generalized vacation and polling systems
cites work: Stability, monotonicity and invariant quantities in general polling systems
cites work: Q4289657
cites work: On the saturation rule for the stability of queues
cites work: Ergodicity of a polling network
cites work: Q4692356
cites work: An introduction to the theory of point processes
cites work: Generalizations of the stochastic decomposition results for single server queues with vacations
cites work: Comparison theorems and ergodic properties of polling systems.
cites work: Monotonicity and stability of periodic polling models
cites work: Stability of token passing rings
cites work: A continuous polling system with general service times
cites work: Sur les mesures de Palm de deux processus ponctuels stationnaires
cites work: Polling systems and multitype branching processes
cites work: Bivariate distributions with given marginals
cites work: Conditions of existence of steady-state modes in cyclic queueing systems
full work available at URL: https://doi.org/10.1007/bf01158575
OpenAlex ID: W2134102328
description: scientific article; zbMATH DE number 851505