Dynamic pricing of preemptive service for elastic demand

We consider a service provider that accommodates two classes of users: primary users (PUs) and secondary users (SUs). SU demand is elastic to price whereas PU demand is inelastic. When a PU arrives to the system and finds all channels busy, it preempts an SU unless there are no SUs in the system. Call durations are exponentially distributed and their means are identical. We study the optimal pricing policy of SUs by using dynamic programming to maximize the total expected discounted profit over finite and infinite horizons, and the average profit. Our main contribution is to show that although the system is modeled as a two-dimensional Markov chain, the optimal pricing policy depends only on the total number of users in the system (PUs and SUs), i.e. the total occupancy. We also demonstrate that optimal prices are increasing with the total occupancy. Finally, we describe applications of these results to the special case of admission control and show that the optimal pricing policy structure of the original system is not preserved for systems with elastic PUs.