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THE OPTIMALITY OF TWO PRICES: MAXIMIZING REVENUE IN A STOCHASTIC COMMUNICATION SYSTEM

ABSTRACT This paper considers the problem of pricing and transmission scheduling for an Access Point (AP) in a wireless network, where the AP provides service to a set of mobile users. The goal of the AP is to maximize its own time-average profit. We first obtain the optimum time-average profit of the AP and prove the “Optimality of Two Prices” theorem. We then develop an online scheme that jointly solves the pricing and transmission scheduling problem in a dynamic environment. The scheme uses an admission price and a business decision as tools to regulate the incoming traffic and to maximize revenue. We show the scheme can achieve any average profit that is arbitrarily close to the optimum, with a tradeoff in average delay. This holds for general Markovian dynamics for channel and user state variation, and does not require a-priori knowledge of the Markov model. The model and methodology developed in this paper are general and apply to other stochastic settings where a single party tries to maximize its time-average profit. Index Terms Wireless Mesh Network, Pricing, Queueing, Dynamic Control, Lyapunov analysis, Optimization

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