On Scheduling Chains of Jobs on One Processor with Limited Preemption

A scheduling rule is given for determining the processing order of tasks which have the precedence structure of chains. It is assumed that the service times follow known distributions, that they are all independent, that costs are accrued by tasks at a constant rate until their service requirements are satisfied, that all the tasks are available at time 0 and that the service is interruptible at task-specific sets of points. The rule consists of computing for each chain an “optimal assignment” for its tasks and a rank function which depends on this assignment. Choosing at each point in time the chain with the smallest rank produces an optimal schedule. It is proved that the “optimal assignments” have the desirable property that as long as a task does not exceed its allotted service time, no preemption should take place.