Online Batch Scheduling for Flow Objectives

Batch scheduling gives a powerful way of increasing the throughput by aggregating multiple homogeneous jobs. It has applications in large scale manufacturing as well as in server scheduling. In batch scheduling, when explained in the setting of server scheduling, the server can process requests of the same type up to a certain number simultaneously. Batch scheduling can be seen as capacitated broadcast scheduling, a popular model considered in scheduling theory. In this paper, we consider an online batch scheduling model. For this model we address flow time objectives for the first time and give positive results for average flow time, the k-norms of flow time and maximum flow time. For average flow time and the the k-norms of flow time we show algorithms that are O(1)-competitive with a small constant amount of resource augmentation. For maximum flow time we show a 2-competitive algorithm and this is the best possible competitive ratio for any online algorithm. ∗Department of Computer Science, Duke University, Durham NC 27708-0129. [email protected]. Partially supported by NSF grant CCF-1008065. †Toyota Technological Institute, Chicago IL, 60637, USA. [email protected]