Optimal Pricing Schemes for Public Wireless Networks

We consider a public wireless network with one access point (AP) and several users. The wireless network is setup by a service provider (SP) to enable Internet connections in public areas such as parks, libraries, and cafes. The service provider establishes appropriate pricing schemes to charge the users in order to cover its own cost in the setup and maintenance of the public wireless network. According to their demand and the prices, users choose the best pricing schemes for themselves. We can regard this public network as a three-layer network, with the three layers as the technology layer, the application layer, and the economic layer. In the next three subsections, we will describe these three layers and their interaction in details. Since the arrival and departure of users can take place at any time instant, we use a continuous-time model to describe the system. We denote t as the index of time. According to their arrival and departure processes and utility functions, the users are inherently categorized into K types, where the user type is indexed by k. We define the total number of type-k users, no matter in service or not, as Nk. Note that the type is the inherent property of a user, which is the user’s private information. However, since the users of the same type will choose the same payment plan, the service provider can partially observe the type of a user by the payment plan that user subscribes to. In other words, the service provider categorizes the users by their payment plans. We call this categorization as the user’s payment type. We assume that there are L payment plans. Then we can define the mapping from the inherent type k of a user to its payment type l as