Non-clairvoyant Scheduling for Weighted Flow Time and Energy

We consider the online scheduling problem of minimizing total weighted flow time plus energy in the dynamic speed scaling model, where a processor can scale its speed dynamically between 0 and some maximum speed T . In the past few years this problem has been studied extensively under the clairvoyant setting, which requires the size of a job to be known at release time [1, 4, 5, 8, 15, 18–20]. For the non-clairvoyant setting, despite its practical importance, the progress is relatively limited. Only recently an online algorithm LAPS is known to be O(1)-competitive for minimizing (unweighted) flow time plus energy in the infinite speed model (i.e., T = ∞) [11, 12]. This paper makes two contributions to the non-clairvoyant scheduling. First, we resolve the open problem that the unweighted result of LAPS can be extended to the more realistic model with bounded maximum speed. Second, we show that another non-clairvoyant algorithm WRR is O(1)-competitive when weighted flow time is concerned. Note that WRR is not as efficient as LAPS for scheduling unweighted jobs as WRR has a much bigger constant hidden in its competitive ratio. ∗This is a corrected version of a paper with the same title in CATS 2010 [14]; in particular, Lemmas 2 and 4 of Section 3 and the ordering of jobs in the potential analysis of Section 4 were given incorrectly before and are fixed in this version. On the other hand, the conjecture, given in Section 5, about the generalization of LAPS to the weighted setting has recently been resolved [13]. †Research is partially supported by HKU Grant 21476018. ‡Research is partially supported by NSFC Grant 60970003. c © 2011 Sze-Hang Chan, Tak-Wah Lam, Lap-Kei Lee, Hing-Fung Ting, and Peng Zhang ©cc Licensed under a Creative Commons Attribution License DOI: 10.4086/cjtcs.2011.001 S.H. CHAN, T.W. LAM, L.K. LEE, H.F. TING, AND P. ZHANG