Stochastic recursive equations with applications to queues with dependent vacations

We focus on a special class of nonlinear multidimensional stochastic recursive equations in which the coefficients are stationary ergodic (not necessarily independent). Under appropriate conditions, an explicit ergodic stationary solution for these equations is obtained and the convergence to this stationary regime is established. We use these results to analyze several queueing models with vacations. We obtain explicit solutions for several performance measures for the case of general non-independent vacation processes. We finally extend some of these results to polling systems with general vacations.