Clearing models for M/G/1 queues

Abstract

We consider M/G/1-type queueing systems with `disasters', occurring at certain random times and causing an instantaneous removal of the entire residual workload from the system. After such a clearing, the system is assumed to be ready to start working again immediately. We consider clearings at deterministic equidistant times, at random times and at crossings of some prespecified level, and derive the stationary distribution of the workload process for these clearing times and some of their combinations.