Better Algorithm for Order On-Line Scheduling on Uniform Machines

Ordinal On-Line Scheduling on Two Uniform Machines

Scheduling uniform machines on-line requires nondecreasing speed ratios

We consider the following on-line scheduling problem. We have to schedule n independent jobs, where n is unknown, on m uniform parallel machines so as to minimize the makespan; preemption is allowed. Each job becomes available at its release date, and this release date is not known beforehand; its processing requirement becomes known at its arrival. We show that if only a finite number of preem...

Scheduling on Uniform Nonsimultaneous Parallel Machines

We consider the problem of scheduling on uniform processors which may not start processing at the same time with the purpose of minimizing the maximum completion time. We give a variant of the Multifit algorithm which generates schedules which end within 1.382 times the optimal maximum completion time for the general problem, and within √ 6/2 times the optimal maximum completion time for proble...

On-Line Scheduling on Uniform Multiprocessors

Each processor in a uniform multiprocessor machine is characterized by a speed or computing capacity, with the interpretation that a job executing on a processor with speed for time units completes units of execution. The on-line scheduling of hard-real-time systems, in which all jobs must complete by specified deadlines, on uniform multiprocessor machines is considered. It is known that online...

A note on hierarchical scheduling on two uniform machines

This paper studies online hierarchical scheduling on two uniform machines with the objective to minimize makespan. Machines are provided with different capability, i.e., the one with speed s can schedule all jobs, while the other one with speed 1 can only process partial jobs. Optimal algorithms for any 0 < s <∞ are given in the paper. For 0 < s < 1, it has a competitive ratio of min{1 + s,1 + ...