The Power of Migration for Online Slack Scheduling

We investigate the power of migration in online scheduling for parallel identical machines. Our objective is to maximize the total processing time of accepted jobs. Once we decide to accept a job, we have to complete it before its deadline d that satisfies d ≥ (1 + ε) · p + r, where p is the processing time, r the submission time and the slack ε > 0 a system parameter. Typically, the hard case arises for small slack ε 1, i.e. for near-tight deadlines. Without migration, a greedy acceptance policy is known to be an optimal deterministic online algorithm with a competitive factor of 1+ε ε (DasGupta and Palis, APPROX 2000). Our first contribution is to show that migrations do not improve the competitive ratio of the greedy acceptance policy, i.e. the competitive ratio remains 1+ε ε for any number of machines. Our main contribution is a deterministic online algorithm with almost tight competitive ratio on any number of machines. For a single machine, the competitive factor matches the optimal bound of 1+ε ε of the greedy acceptance policy. The competitive ratio improves with an increasing number of machines. It approaches (1+ε) · ln 1+ε ε as the number of machines converges to infinity. This is an exponential improvement over the greedy acceptance policy for small ε. Moreover, we show a matching lower bound on the competitive ratio for deterministic algorithms on any number of machines. 1998 ACM Subject Classification F.1.2 Online Computation