Closed polling models with failing nodes

Closed polling systems with station breakdowns, under the Gated, Exhaustive or Globally Gated services regimes, are studied and analyzed. Multi-dimensional sets of probability generating functions of the system's state are derived. They are further utilized to obtain an approximate solution for the mean number of jobs residing in the system's various queues at polling instants. The analysis is then concentrated on the case of Cyclic Bernoulli Polling. Explicit formulae for the mean number of jobs, as well as for the expected cycle duration and system utilization, are derived. Comparison of the throughputs of the three regimes concludes the paper.