Before revision:  We then further show that the job response time converges to the maximum of independent task response times, in a proper sense. This gives the first asymptotically tight analytical characterization of the response time of a multi-task parallel job. To complement the asymptotic independence result, we also show that when k^{(n) =\Theta(n), any number of multiple queues are not asymptotically independent.
After revision:  We then further show that the job response time converges to the maximum of independent task =\Theta(n), any number of multiple queues are not asymptotically independent.