Admission control and pricing of secondary users in preemptive communication networks
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We investigate the optimal admission control and optimal pricing policies enforced by a network service provider that accommodates calls of two classes of users: primary users (PUs) and secondary users (SUs). PUs have preemptive priority over SUs, that is when a primary user (PU) arrives to the system and finds all the channels busy, it preempts an SU if there exists any. Call durations are exponentially distributed and their means are identical. In the first part of this thesis, we study the optimal admission control policy of SUs to maximize the average profit. In the second part, we investigate the properties of the optimal pricing policy that maximizes the average profit in the same setting. In the first part, we apply admission control on the SUs only. Using dynamic programming (DP), we find the optimal admission control policies that maximize the total expected discounted profit over finite and infinite horizons as well as the average profit. Our primary contribution is to prove that the optimal admission control of the SUs depends only on the total number of users in the system (i.e. it does not depend on the number of PUs and SUs in the system individually) and is of threshold type. Therefore, although the system is modeled as a two-dimensional Markov chain, our findings allow simple and efficient computation of the optimal control policy. In the second part, we a8sume that SU demand is elastic to price whereas PU demand is inelastic. We study the optimal pricing policy of SUs to maximize the average profit. We introduce a DP formulation of the problem to determine the optimal pricing policy that maximizes the total expected discounted profit over the finite horizon. Our main contribution is to show that the optimal pricing policy depends only on the total number of users in the system (PUs and SUs) , i.e. the total occupancy. We extend this result to the infinite horizon. We also demonstrate that optimal prices increase with the total occupancy. Finally, we show that the optimal pricing policy structure of the original system is not preserved for systems with elastic PUs.
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