Scheduling heterogeneous processors isn't as easy as you think

We consider preemptive online scheduling algorithms to minimize the total weighted/unweighted flow time plus energy for speed-scalable heterogeneous multiprocessors. We show that the well-known priority scheduling algorithms Highest Density First, Weighted Shortest Elapsed Time First, and Weighted Late Arrival Processor Sharing, are not O(1)-speed O(1)-competitive for the objective of weighted flow even in the special case of fixed variable speed processors (aka the related machines setting). This illustrates that scheduling heterogeneous multiprocessors is a different, and algorithmically more challenging problem, than scheduling homogeneous multiprocessors. We then show that a variation of the non-clairvoyant algorithm Late Arrival Processor Sharing coupled with a non-obvious speed scaling algorithm is scalable for the objective of unweighted flow plus energy on speedscalable multiprocessors. This is the first provably scalable non-clairvoyant algorithm on heterogeneous multiprocessors, even in the related machines setting, for the objective of total (unweighted) flow time. ∗Computer Science Department, Carnegie Mellon University, Pittsburgh, PA 15213, USA. [email protected]. Supported in part by NSF awards CCF-0964474 and CCF-1016799. †Department of Computer Science, University of Illinois, 201 N. Goodwin Ave., Urbana, IL 61801. [email protected]. Partially supported by NSF grants CCF-1016684. ‡Computer Science Department, Carnegie Mellon University, Pittsburgh, PA 15213, USA. [email protected] . Supported in part by NSF awards CCF-0964474 and CCF-1016799, and an IBM Graduate Student fellowship. §Department of Computer Science, University of Illinois, 201 N. Goodwin Ave., Urbana, IL 61801. [email protected]. Partially supported by CCF-1016684. ¶Computer Science Department, University of Pittsburgh, Pittsburgh, PA 15260, USA. [email protected]. Supported in part by NSF grants CCF-0830558 and CCF-1115575, and an IBM Faculty Award.