Polling Systems with Job Failures and with Station Failures

We consider a polling system with Exhaustive service policy subject to job failures or to station failures. Each of the N stations (nodes) comprising the system is, in isolation, an M/G/1type queue. Failures at each node follow a Poisson process. A job failure causes the job to be rejected from the system, while a station failure (breakdown) causes the server to switch over to the next node. The case with job failures is transformed into a classical polling model. However, the case with station failures does not yield a solution when analyzed via the station occupancy approach. We therefore bring into use interpolation theory, never employed before in polling systems, and obtain explicit (approximated) solutions of key performance measures.