  We consider a system consisting of a single transmitter/receiver pair and $N$
channels over which they may communicate. Packets randomly arrive to the
transmitter's queue and wait to be successfully sent to the receiver. The
transmitter may attempt a frame transmission on one channel at a time, where
each frame includes a packet if one is in the queue. For each channel, an
attempted transmission is successful with an unknown probability. The
transmitter's objective is to quickly identify the best channel to minimize the
number of packets in the queue over $T$ time slots. To analyze system
performance, we introduce queue length regret, which is the expected difference
between the total queue length of a learning policy and a controller that knows
the rates, a priori. One approach to designing a transmission policy would be
to apply algorithms from the literature that solve the closely-related
stochastic multi-armed bandit problem. These policies would focus on maximizing
the number of successful frame transmissions over time. However, we show that
these methods have $\Omega(\log{T})$ queue length regret. On the other hand, we
show that there exists a set of queue-length based policies that can obtain
order optimal $O(1)$ queue length regret. We use our theoretical analysis to
devise heuristic methods that are shown to perform well in simulation.
