On Job Scheduling with Preemption Penalties

This paper studies the problem of online job scheduling in a model with preemption penalty introduced by Zheng et al. [11]. In such a model with preemption penalty parameter rho, the scheduler has to pay a penalty of rho times the weight of each aborted job. We consider two cases according to the scheduler's knowledge of Delta (ratio of length between longest and shortest jobs). In the first case where the exact value of Delta is known at the beginning, we re-investigate the WAL algorithm of Zheng et al. and prove that it is ((1 + rho)Delta + o(Delta))-competitive for sufficiently large Delta. In particular, when rho = 1, the previous competitive ratio of 3 Delta + o(Delta) proved in [11] is improved to 2 Delta + o(Delta). In the second case where the online strategy only knows beforehand that Delta >= k(3) (rho + 1)(3) for some parameter k > 1, a (k(1+rho)/k-1 Delta + o(Delta))-competitive deterministic strategy is presented. For large Delta, the competitive ratio approaches that of WAL as k increases.