Before revision:  Upon arrival, each jobchooses k^{(n) under the condition k^{(n)} = o(n^{1/4}) , the steady state response times at any k^{(n) greatly generalizes the asymptotic-independence type of results in the literature where asymptotic independence is shown only for a fixed constant number of queues.
After revision:  Upon arrival, each jobchooses k^{(n) under the condition k^{(n)} = o(n^{1/4}) . This greatly generalizes the asymptotic-independence type of results in the literature where asymptotic independence is shown only for a fixed constant number of queues.