On-line multi-threaded scheduling

On-line scheduling problems are studied with jobs organized in a number of sequences called threads. Each job becomes available as soon as a scheduling decision is made on all preceding jobs in the same thread. We consider two different on-line paradigms. The first one models a sort of batch process: a schedule is constructed, in an on-line way, which is to be executed later. The other one models a real-time planning situation: jobs are immediately executed at the moment they are assigned to a machine. The classical objective functions of minimizing makespan and minimizing average completion time of the jobs are studied. We establish a fairly complete set of results for these problems. One of the highlights is that List Scheduling is a best possible algorithm for the makespan problem under the real-time model if the number of machines does not exceed the number of threads by more than 1. Another one is a polynomial time best possible algorithm for minimizing the average completion time on a single machine under both on-line paradigms.