Optimal transmission policies for two-user multiple access broadcast using dynamic team theory

Optimal transmission policies for a two-user multiple access broadcast channel with binary feedback are investigated. The system is modeled as a dynamic team. Conditioned on the channel feedback, the past history of buffer states is redundant to each user. Once this redundant data is removed, the information structure, although non-classical, satisfies the sufficient conditions of Mahajan, Nayyar, and Teneketzis, 2008 for a dynamic team problem to be tractable. Using the idea of a virtual coordinator of Mahajan, Nayyar, and Teneketzis, a dynamic programming decomposition is presented. This dynamic program is defined over a countable state space and a finite action space. When the arrival rates of both users are symmetric, an optimal policy is identified by solving the dynamic program analytically. This policy matches the optimal window protocol proposed by Hluchyj and Gallager, 1981. Thus, this paper presents the an example of a non-trivial dynamic team with non-linear dynamics where an exact analytic solution is obtained.