Analysis of polling systems
Queueing analysis of polling models: progress in 1990-1994
Frontiers in queueing
Decomposition results for general polling systems and their applications
Queueing Systems: Theory and Applications
Exact Analysis of the State-Dependent Polling Model
Queueing Systems: Theory and Applications
Analysis and Control of Poling Systems
Performance Evaluation of Computer and Communication Systems, Joint Tutorial Papers of Performance '93 and Sigmetrics '93
Queueing Systems: Theory and Applications
The M/G/∞ system revisited: finiteness, summability, long range dependence, and reverse engineering
Queueing Systems: Theory and Applications
On a queuing model with service interruptions
Probability in the Engineering and Informational Sciences
Marginal queue length approximations for a two-layered network with correlated queues
Queueing Systems: Theory and Applications
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We study asymmetric polling systems where: (i) the incoming workflow processes follow general Lévy-subordinator statistics; and, (ii) the server attends the channels according to the gated service regime, and incurs random inter-dependentswitchover times when moving from one channel to the other. The analysis follows a dynamical-systems approach: a stochastic Poincaré map, governing the one-cycle dynamics of the polling system is introduced, and its statistical characteristics are studied. Explicit formulae regarding the evolution of the mean, covariance, and Laplace transform of the Poincaré map are derived. The forward orbit of the map驴s transform -- a nonlinear deterministic dynamical system in Laplace space -- fully characterizes the stochastic dynamics of the polling system. This enables us to explore the long-term behavior of the system: we prove convergence to a (unique) steady-state equilibrium, prove the equilibrium is stationary, and compute its statistical characteristics.