Before revision:  Specifically, we aim to approximate the length of the largest of the N queues in the network. From a practical point of view, this has interesting applications, such as modeling the delays in a large supply chain. We present a fluid limit and a steady-state result for the maximum queue length , as N\to\infty.
After revision:  Specifically, we present a fluid limit and a steady-state result for the maximum queue length , as N\to\infty.