A framework for scheduling with online availability

With the increasing popularity of large-scale distributed computing networks, a new aspect has to be considered for scheduling problems: machines may not be available permanently, but may be withdrawn and reappear later. We give several results for completion time based objectives: 1. we show that scheduling independent jobs on identical machines with online failures to minimize the sum of completion times is (8/7 - epsilon)-inapproximable, 2. we give a nontrivial sufficient condition on machine failure under which the SRPT (shortest remaining processing time) heuristic yields optimal results for this setting, and 3. we present meta-algorithms that convert approximation algorithms for offline scheduling problems with completion time based objective on identical machines to approximation algorithms for the corresponding preemptive online problem on identical machines with discrete or continuous time. Interestingly, the expected approximation rate becomes worse by a factor that only depends on the probability of unavailability.