260 IEEE TRANSACTIONS ON NETWORK AND SERVICE MANAGEMENT, VOL. 15, NO. 1, MARCH 2018 Pricing the Volume-Based Data Services in Cellular Wireless Markets Behdad Heidarpour , Zbigniew Dziong, Senior Member, IEEE, Wing Cheong Lau, Senior Member, IEEE, and Shahin Vakilinia Abstract—Over the past few years, many major wireless providers restricted their unlimited data plans and replaced them with limited-size fixed-price data packages. While this could be perceived as a disadvantage for customers, it helps the cellular wireless providers to reduce the traffic intensity at their base stations and this leads to a better service quality and higher rates for concurrently connected users. Hence, there is a trade- off between the data volume and the data rates attributed to the users. To avoid the adverse effect of service inaccessibility, the cellular providers should carefully set the size and pricing of their data packages. Toward this end, the providers need a model that, together with proper market information, would allow to set the best prices for volume-based data and estimate the accept- able quantity of subscribers and their average data rate. In this paper, we propose such a model that quantifies the relationship between pricing and various market/system parameters such as data volume size, user budget, data rate, and service blocking probability. In particular, we formulate a set of revenue opti- mization problems for different spectrum assignment criteria like shared-carrier and dynamic sub-carrier allocation. Finally, several realistic scenarios are investigated in which the optimal network parameters are computed. Index Terms—Wireless networks, data plans, pricing, network economics, cellular provider, data rate. I. I NTRODUCTION W ITH rapid growth of wireless markets in past twenty years, providers have been evaluating different pric- ing schemes to maximize their revenue. In particular, the providers of packet-switching networks have considered many ways regarding pricing criteria to achieve a higher amount of net income. These schemes are highly diversified from sim- ple flat-rate [1] to dynamic pricing methods [2]. Schemes that consider Service Level Agreement (SLA) are not common for the end-users in data networks, yet they are essential in mid- level and high-level inter-provider contract based methods. Manuscript received April 12, 2017; revised September 29, 2017; accepted October 19, 2017. Date of publication October 30, 2017; date of current ver- sion March 9, 2018. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC). The associate editor coordinating the review of this paper and approving it for publication was K. C. Almeroth. (Corresponding author: Behdad Heidarpour.) B. Heidarpour and Z. Dziong are with the Département de Génie Électrique, École de Technologie Supérieure (University of Quebec), Montreal, QC H3C 1K3, Canada (e-mail: behdad.heidarpour@gmail.com). W. C. Lau is with the Department of Information Engineering, The Chinese University of Hong Kong, Hong Kong. S. Vakilinia is with the Laboratory for Multimedia Communication in Telepresence, École de Technologie Supérieure (University of Quebec), Montreal, QC H3C 1K3, Canada. Digital Object Identifier 10.1109/TNSM.2017.2768240 Smart pricing methods [3], such as time-dependent pricing schemes [4], in which the provider sets the price based on congestion hours, or other network parameters, are studied in several works but they are not widely accepted by the wireless providers. This is not only due to the operational complexity of such dynamic pricing schemes but also due to the difficulties in managing customer expectations and edu- cating them on complicated interaction between user behavior and pricing. Before 2012, it was common among major players in the cellular wireless market (such as Verizon, AT&T, and Sprint) to offer low-price unlimited data plans. However, nowadays their pricing schemes are dominated by plans with a cap on data volume and calling minutes. In this approach, instead of unrestricted access to the data service, the sub- scriber pays a certain price to use up to a specified amount of data alongside the voice service for a particular dura- tion. For example, the subscribers pay for one, two or more Gigabytes of data at a particular price. The available data in the package is being renovated mostly in monthly periods and the user-provider contract usually stays unchanged for over one or two years. We refer the readers to [5] and [6] for the examples of U.S. wireless carriers and [7], [8] for Canadian providers. Other than the North-American market, the volume-based pricing is widely adopted by providers around the world. E.g., French provider, Orange, [9], Indian providers, Airtel [10] and BNSL [11], Brazilian Vivo [12], have data plans with caps ranging from 50 MB to 100 GB. In fact, one can find volume-based plans at some providers in almost all countries. The universal dominance of this pricing scheme motivates us to investigate its character- istics and optimality under different wireless technologies with shared, dedicated or dynamic spectrum allocation policies. We aim to find a model that can predict the revenue of providers with volume-based data plans. The key elements of our model are the market and network parameters such as data-volume size, price, data rate, service availability and user budget. The combination of these parameters affects user’s subscription behavior. Similar to many real markets, the voice and data services are assumed to be offered in separated packages. The set of data users is a subset of voice users which means that if a user wants to have a data subscription, it needs to join the voice network as well. In this way, we present the market in two stages; firstly, the voice users enter the market out of a set of potential 1932-4537 c  2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.