Optimal Channel Probing and Transmission Scheduling in a Multichannel System

In this study we consider the problem of optimal channel selection policies for a transmitter in a multichannel wireless system where a channel can be in one of multiple states. Each channel state is associated with a probability of transmission success. In such systems, the sender typically has partial information concerning the channel states, but can deduct more information by probing individual channels, e.g. by sending control packets in the channels. On the other hand, while probing can help the sender determine the best channel to use, it consumes valuable resources. The main goal of this work is to derive optimal strategies for determining which channels to probe (in what sequence) and which channel to use for transmission. Our primary interest in this study is to derive key structural properties of the optimal strategy. In particular, we show that it exhibits a threshold structure and can be described by an index policy. We further show that the optimal strategy can only take on one of three structural forms. In addition, we explicitly derive optimal strategies for some practical channel models, and provide conditions under which some commonly used strategies are optimal. Using these properties, we present a two step lookahead policy and show that it is optimal for a number of special cases of practical interest.