Meeting deadlines: How much speed suffices?

Abstract

We consider the online problem of scheduling real-time jobs with hard deadlines on m parallel machines. Each job has a processing time and a deadline, and the objective is to schedule jobs so that they complete before their deadline. It is known that even when the instance is feasible it may not be possible to meet all deadlines when jobs arrive online over time. We therefore consider the setting when the algorithm has available machines with speed s > 1. We present a new online algorithm that finds a feasible schedule on machines of speed e/(e - 1) ≈ 1.58 for any instance that is feasible on unit speed machines. This improves on the previously best known result which requires a speed of 2 - 2/(m + 1). Our algorithm only uses the relative order of job deadlines and is oblivious of the actual deadline values. It was shown earlier that the minimum speed required for such algorithms is e/(e - 1), and thus, our analysis is tight. We also show that our new algorithm outperforms two other well-known algorithms by giving the first lower bounds on their minimum speed requirement. © 2011 Springer-Verlag.