  We consider the problem of partitioning a spectrum band into M channels of
equal bandwidth, and then further assigning these M channels into P licensed
channels and M-P unlicensed channels. Licensed channels can be accessed both
for licensed and opportunistic use following a tiered structure which has a
higher priority for licensed use. Unlicensed channels can be accessed only for
opportunistic use. We address the following question in this paper. Given a
market setup, what values of M and P maximize the net spectrum utilization of
the spectrum band? While this problem is of fundamental nature, it is highly
relevant practically, e.g., in the context of partitioning the recently
proposed Citizens Broadband Radio Service band. If M is too high or too low, it
may decrease spectrum utilization due to limited channel capacity or due to
wastage of channel capacity, respectively. If P is too high (low), it will not
incentivize the wireless operators who are primarily interested in unlicensed
channels (licensed channels) to join the market. These tradeoffs are captured
in our optimization problem which manifests itself as a two-stage Stackelberg
game. We design an algorithm to solve the Stackelberg game and hence find the
optimal M and P. The algorithm design also involves an efficient Monte Carlo
integrator to evaluate the expected value of the involved random variables like
spectrum utilization and operators' revenue. We also benchmark our algorithms
using numerical simulations.
