Polling systems with breakdowns and repairs

This work analyzes various polling systems with both random breakdowns and repairs. A few works in the literature investigated polling networks with failing nodes, but none has treated the associated repair process or the combined effect of breakdowns and repairs on such systems. We consider three service mechanisms: Gated, Exhaustive and Globally Gated. For each service regime we study several variations, differing from each other by (i) whether the arrival process to a queue being repaired continues or stops during the repair process, and (ii) whether the failure is observed immediately when it occurs or only at the end of a service duration. For each of the 12 models studied we provide analyses regarding the system state at polling instants (law of motion, probability generating functions, first- and second-order moments) and derive expressions for several performance measures, such as (distribution and mean of) number of customers at the different queues, their waiting and sojourn times, server's cycle times, etc. We derive stability conditions for the various models and express all results in a unified generalized form.