On Job Scheduling with Preemption Penalties

Abstract

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

The work is partially supported by NSF grants of China no. 70525004, 70702030 and 60736027, and Doctoral Fund of Ministry of Education of China (no. 20070698053).