We consider a wireless provider who caters to two
classes of customers, namely primary and secondary users.
Primary users have long term contracts while secondary users
are admitted and priced according to current availability of
excess spectrum. Secondary users accept an advertised price
with a certain probability defined by an underlying demand
function. We analyze the problem of maximizing profit gained by
admission of secondary users. Previous studies in the field usually
assume that the demand function is known and that the call
length distribution is also known and exponentially distributed.
In this paper, we analyze more realistic settings where both of
these quantities are unknown. Our main contribution is to derive
near-optimal pricing strategies under such settings. We focus on
occupancy-based pricing policies, which depend only on the total
number of ongoing calls in the system. We first show that such
policies are insensitive to call length distribution except through
the mean. Next, we introduce a new on-line, occupancy-based
pricing algorithm, called Measurement-based Threshold Pricing
(MTP) that operates by measuring the reaction of secondary
users to a specific price and does not require the demand function
to be known. MTP optimizes a profit function that depends
on price only. We prove that while the profit function can be
multimodal, MTP converges to one of the local optima as fast as if
the function were unimodal. Lastly, we provide numerical studies
demonstrating the near-optimal performance of occupancy-based
policies for diverse sets of call length distributions and demand
functions and the quick convergence of MTP to near-optimal
on-line profit.
