The paper considers a decentralized stochastic team problem with a partially-nested information pattern, that arises in the context of flow control. Basically, we consider a network with a number of users having access to differently delayed versions of the same information, with each one deciding on his own rate of transmission, but participating in a common cost quantifying the outcome of their joint actions. This leads to a Linear-Quadratic-Gaussian (LQG) team problem, with partially nested information. We study the derivation of the optimal solution in a two user network and show that the solution exists in both finite and infinitehorizon cases. The controller, which turns out to be certainty-equivalent, is constructed recursively using a dynamic programming type approach. We also present an algorithm to construct the optimal solution for the most general case with multiple (more than two) users. Finally, we present various simulation results to illustrate the performance of the optimal controller under different scenarios.