Online bounded-batch scheduling to minimize total weighted completion time on parallel machines

We consider the online bounded-batch scheduling to minimize total weighted completion time on parallel machines. In the problem, a set of n independent jobs arriving online over time has to be scheduled on m given machines, where the information of each job including its processing time and weight is not known in advance. Each machine can process up to b (b<n) jobs simultaneously as a batch. The processing time of a batch is the time required for processing the longest job in the batch. We present 4(1+ϵ)-competitive online algorithms on uniform machines when m is fixed and on identical machines when m is a part of input, respectively. Experimentation results show that the algorithm for identical machines (which covers the setting of uniform machines) is efficient.