Before revision:   We show that zero queueing delay for such parallel jobs can be achieved using  a variant of the  \ policy, the batch-filling policy, with a probe overhead d = \omega\left(\frac{1}{(1-\lambda)\log k}\right)  , where k is the number of tasks in each job  .
After revision:  This notion quantifies the effect of queueing on a job level for jobs consisting of multiple tasks, and thus deviates from the conventional zero queueing delay for single-task jobs in the literature. We show that zero queueing delay for such parallel jobs can be achieved using a variant of the  \ policy, the batch-filling policy, with a probe overhead d = \omega\left(\frac{1}{(1-\lambda)\log k}\right) , where k is the number of tasks in each job .