# Priority Pricing for Efficient Resource Usage of Mobile Internet Access
## 1 Introduction  
Radio-frequency spectrum resources are finite and scarce, but their demand is increasing exponentially every year [1]. Although today's fast wireless communication technologies enable us to enjoy various newly-devised services, these services are causing more congestion in wireless networks. To resolve this problem, studies have been conducted on the efficient use of wireless resources [2]. Pricing is one of the techniques used to effectively control network resource usage and manage user demands [3]. Pricing network services has been an issue of continuous debate since the early stages of Internet commercialization. Historically, the flat-ee scheme in which users are charged a fixed monthly fee irrespective of usage has been the predominant pricing structure for wired Internet access services, as both service providers and consumers prefer simple pricing to usage-sensitive pricing [1, 4]. However, pricing schemes other than the flat-ee scheme have begun to emerge in some domains, such as with wireless Internet access. In wireless networks, the bandwidth is too scarce and expensive to tolerate the potential waste of resources, which is typically associated with flat-fee pricing [5]. The evolution of mobile devices (e.g., smartphones and IoT devices) has caused traffic to explode, and the congestion of wireless networks is becoming more serious, jeopardizing the provision of stable quality of service (QoS). Wireless carriers have already dropped their unlimited flat-fee policy, and currently offer various pricing policies that combine fixed charging up to a certain data cap, and usage-based charging beyond that cap. Internet applications have different levels of QoS requirements, such as delay, latency, and goodput. The coexistence of applications with high QoS (such as automatic driving or VR interaction) with those with low QoS (such as emails) requires wireless networks to handle the corresponding traffic differently. The IETF differentiated service [6, 7, 8] is the currently preferred Internet QoS architecture. Traffic is differentiated based on the traffic class information in the IP packet headers and is served according to some formof priority-based scheduling. The architecture of current mobile network QoS is more complicated. According to the characteristics of user equipment (UE) and its services, various priority classes are necessary in the mobile network. For example, 5G mobile networks specify three service types: guaranteed bit rate (GBR) service, non-GBR service, and delay-critical GBR service, along with QoS classes defined by resource type, priority level, packet delay budget, packet error rate, maximum data burst volume, and averaging window [9]. Currently, many wireless providers have announced their plans to implement a priority pricing policy (i.e., different pricing for different traffic classes). The single-price scheme is the simplest form of priority pricing. In usage-based charging, a certain price is charged for a certain amount of data (e.g., Mbytes). Under usage-based charging, either the single-price scheme or priority-pricing scheme, determining the price(s) is a crucial issue. This study focuses on optimal price selection for \"priority pricing\" [3,10,11]; that is, finding the prices that maximize a certain system objective. Other pricing schemes have been studied: smart-market pricing [12,13], Paris-metro pricing [14,15], responsive pricing [16], edge pricing [17,18], proportional fairness pricing [19], and distributed majorization pricing [20]. Along with priority pricing, all of these schemes assume that the users are inherently price-sensitive and that the service provider can use prices to influence the behaviors of the users as a means of congestion control. Under priority pricing, the service provider offers a choice of {service level, price} pairs, and the users, who know the values of their jobs, select the service levels that they would like to use. A user chooses the service level depending on the QoS requirements as well as the service price.