On Optimality of Second-Highest Policy for Opportunistic Multichannel Access

We consider an opportunistic communication system in which one transmitter communicates with one receiver by one of $N$ two-state Markov channels. The transmitter probes a channel before access. In particular, the transmitter does not access the probed channel if it is found to be in a bad state. Taking into account the probing cost, the transmitter will transmit over the chosen channel for a fixed time interval after probing. To maximize the throughput of the transmitter, we propose the second-highest probing policy, i.e., probing the second-best channel in terms of available probabilities of those channels. Further, we present three sets of conditions to guarantee the optimality of the policy for three scenarios, respectively. The conditions show that the optimality of the policy is tightly coupled with initial belief vector and non-trivial eigenvalue of two-state transition matrix. In addition, we extend the optimality of the policy to two related scenarios from the standpoint of exploitation versus exploration.