Improved Competitive Analysis of Online Scheduling Deadline-Sensitive Jobs

We consider the following scheduling problem. There is a single machine and the jobs will arrive for completion online. Each job j is preemptive and, upon its arrival at time aj , its other characteristics are immediately revealed to the machine: the deadline dj , the workload Dj and the value vj . The objective is to maximize the aggregate value of jobs completed by their deadlines. Using the minimum of dj−aj Dj over all jobs as the slackness s, a non-committed and a committed online scheduling algorithm A and AC is proposed in [Lucier et al., SPAA’13; Azar et al., EC’15], achieving competitive ratios of crA(s) = 2 + O( 1 ( 3 √ s−1)2 ) and crAC (s) = crA(s·ω(1−ω)) ω(1−ω) respectively, where ω ∈ (0, 1) and s ≥ 1 ω(1−ω) . In this paper, without recourse to the dual fitting technique used in the above works, we propose a simpler and more intuitive analytical framework for A and AC , improving crA(s) to 1 +O( 1 ( 3 √ s−1)2 ) and therefore improving crAC (s) by 1 ω(1−ω) . As stated in [Lucier et al., SPAA’13; Azar et al. EC’15], it is justifiable in scenarios like the online batch processing for cloud computing that s is large, hence the item O( 1 ( 3 √ s−1)2 ) in crA(s) can be ignored. Under the above assumption, our analysis brings very significant improvements: from 2 to 1 and from 2 ω(1−ω) to 1 ω(1−ω) for crA(s) and crAC (s) respectively.