Optimal scheduling of tasks when service is subject to disruption: the preempt-repeat case

It has long been recognised that situations in which some key resource or service is to be allocated among jobs or customers competing for it are often subject to a range of uncertainties. Key amongst these concern the reliability of service itself. When the service being delivered to a job is disrupted by some failure of the service mechanism, it is reasonable to suppose that effort may subsequently be required to restore that job to its position before the breakdown occurred. We develop optimal index policies for service allocation for a range of semi-Markovian models which capture this key feature in a range of ways.