Before revision:  In this model, we say a policy leads to zero (asymptotic) queueing delay if the job delay under the policy approaches the delay given by the max of service times of its tasks , as if tasks entered service right upon arrival.
After revision:  In this model, we propose a new notion of zero (asymptotic) queueing delay if the job delay under the policy approaches the delay given by the max of service times of its tasks , as if tasks entered service right upon arrival.