Abstract
We study asymmetric polling systems where: (i) the incoming workflow processes follow general Levy-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 Poincare 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 Poincare map are derived. The forward orbit of the map?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.
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