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.

中文翻译：

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异构无线网络中的定价，带宽分配和服务竞争

在许可频谱中部署的小型小区可以将无线服务扩展到低移动性用户，这有可能减少对具有广域覆盖范围的宏蜂窝网络的需求。引入这种异构性也使网络资源分配更加复杂。为了理解这些挑战和权衡，我们提出了一种具有两种类型用户的两层异构无线网络模型：只能连接到宏小区的移动用户；以及可以与宏小区或小型小区关联的固定用户。我们假设垄断和竞争性服务提供商（SP）都研究了宏蜂窝和小型蜂窝的定价策略和带宽分配。对于垄断SP，我们描绘了收益最大化的价格和带宽分配。然后，我们考虑竞争情况，并且我们展示了一个独特的纳什均衡的存在。针对不同系统参数的可能的纳什均衡被分为四类，分别对应于不同的SP是否为宏小区和/或小小区分配带宽。我们还研究了最大化社会福利的分配。对于竞争场景，我们描述了随着SP数量趋于无穷大而在均衡状态下获得最佳社会福利的条件。案例研究示例和数值结果说明了相应的定价和带宽分配。我们描述了随着SP的数量趋于无穷大而在均衡状态下获得最佳社会福利的条件。案例研究示例和数值结果说明了相应的定价和带宽分配。我们描述了随着SP的数量趋于无穷大而在均衡状态下获得最佳社会福利的条件。案例研究示例和数值结果说明了相应的定价和带宽分配。