Improving Upon the generalized c-mu rule: a Whittle approach

Scheduling a stream of jobs whose holding cost changes over time is a classic and practical problem. Specifically, each job is associated with a holding cost (penalty), where a job's instantaneous holding cost is some increasing function of its current age (the time it has spent in the system since its arrival) and its class. The goal is to schedule the jobs to minimize the time-average total holding cost across all jobs.