Pricing, Bandwidth Allocation, and Service Competition in Heterogeneous Wireless Networks

Small-cells deployed in licensed spectrum can expand wireless service to low mobility users, which potentially reduces the demand for macro-cellular networks with wide-area coverage. Introducing such heterogeneity also makes network resource allocation more complicated. To understand these challenges and tradeoffs we present a two-tier heterogeneous wireless network model with two types of users: mobile users that can only connect to macro-cells; and fixed users that can associate with either macro-cells or small-cells. We study pricing strategies and bandwidth allocation across macro- and small-cells, assuming both monopoly and competitive Service Providers (SPs). For a monopoly SP, we characterize the revenue-maximizing prices and bandwidth allocations. We then consider a competitive scenario, and we show the existence of a unique Nash equilibrium. The possible Nash equilibria for different system parameters are sorted into four categories corresponding to whether or not different SPs assign bandwidth to the macro- and/or small-cells. We also study the allocations that maximize social welfare. For the competitive scenario, we characterize the conditions under which the optimal social welfare is obtained in equilibria as the number of SPs tends to infinity. Case study examples and numerical results illustrate the corresponding pricing and bandwidth allocations.