Online deadline scheduling with preemption penalties

This paper presents a study of the problem of online deadline scheduling under the preemption penalty model of Zheng, Xu, and Zhang (2007). In that model, each preemption incurs a penalty of rho times the weight of the preempted job, where rho >= 0 is the preemption penalty parameter. The objective is to maximise the total weight of jobs completed on time minus the total penalty. When the scheduler knows the ratio of longest to shortest job length, Delta, we show that the WAL algorithm of Zheng et al. (2007) is ((1 + rho)Delta + o(Delta))-competitive for sufficiently large Delta. This improves the bound shown in Zheng et al. (2007). When the scheduler only knows that Delta >= (k(1 + rho))(3) for some k > 1, we propose a ((k(1 + rho)Delta/(k - 1)) + o(Delta))-competitive algorithm. When rho = 0, we give an optimal, O(Delta/log Delta)-competitive algorithm that, unlike previous algorithms, does not require knowledge of Delta. This settles an open problem mentioned in Ting (2008). (C) 2011 Elsevier Ltd. All rights reserved.