Power allocation over two identical Gilbert-Elliott channels

We study the problem of power allocation over two identical Gilbert-Elliot communication channels. Our goal is to maximize the expected discounted number of bits transmitted over an infinite time horizon. This is achieved by choosing among three possible strategies: (1) betting on channel 1 by allocating all the power to this channel, which results in high data rate if channel 1 happens to be in good state, and zero bits transmitted if channel 1 is in bad state (even if channel 2 is in good state) (2) betting on channel 2 by allocating all the power to the second channel, and (3) a balanced strategy whereby each channel is allocated half the total power, with the effect that each channel can transmit a low data rate if it is in good state. We assume that each channel's state is only revealed upon transmission of data on that channel. We model this problem as a partially observable Markov decision processes (MDP), and derive key threshold properties of the optimal policy. Further, we show that by formulating and solving a relevant linear program the thresholds can be determined numerically when system parameters are known.