The μc-rule is a policy for deciding order of service in a queue where there is a per-second cost for waiting: priority goes to the task whose ratio of cost-rate to mean service time is largest. The μc-rule is of interest because it is simple and because it is optimal in a variety of single-server systems. It seems not, in general, to be optimal in systems where the process of arrivals is state-dependent-in particular, in systems with flow control. The paper describes here a setting in which a specialization of the μc-rule (Shortest Jobs First) is optimal when flow control and order of service are optimized together.
