Optimal solution to a team problem with information delays: an application in flow control for communication networks

We consider a network of a number of best-effort type sources, viewed as decision makers (DM's) of a team, sharing a bottleneck node. Each source (or DM) has access to differently delayed versions of the same information about the status of the network and decides on his own rate of transmission. We seek the best decision functions for each DM that minimize a certain quadratic performance index under the given information pattern. We first exploit the special information structure of the problem by bringing in some additional variables to formulate it in the form of a standard discrete-time Linear-Quadratic-Gaussian (LQG) problem. Then, the solution of the original problem is obtained as that of the equivalent LQG problem. Finally, we present an example to illustrate the solution.