Mobile data traffic has been steadily rising in the past years. This has generated a significant interest in the deployment of incentive mechanisms to reduce peak-time congestion. Typically, the design of these mechanisms requires information about user demand and sensitivity to prices. Such information is naturally imperfect. In this paper, we propose a fixed-budget rebate mechanism that gives each user a reward proportional to his percentage contribution to the aggregate reduction in peak-time demand. For comparison, we also study a time-of-day pricing mechanism that gives each user a fixed reward per unit reduction of his peak-time demand. To evaluate the two mechanisms, we introduce a game-theoretic model that captures the public good nature of decongestion. For each mechanism, we demonstrate that the socially optimal level of decongestion is achievable for a specific choice of the mechanism's parameter. We then investigate how imperfect information about user demand affects the mechanisms' effectiveness. From our results, the fixed-budget rebate pricing is more robust when the users' sensitivity to congestion is "sufficiently" convex. This feature of the fixed-budget rebate mechanism is attractive for many situations of interest and is driven by its closed-loop property, i.e., the unit reward decreases as the peak-time demand decreases.
@cite_22: 
@cite_33: Usage-based pricing of offered traffic to a data network can be an effective technique for congestion control. To gain insight into the benefits usage-based pricing offers, the authors propose and study a simple model in which many users wish to transmit packets to a single-server queue. Based on the announced price per packet and the available quality of service (QoS) (e.g., mean delay), each user independently decides whether or not to transmit. Given statistical assumptions about the incoming traffic streams and the QoS as a function of offered load, the equilibrium relationship between price and QoS is determined by a fixed-point equation. The relationships among price, QoS, revenue, and server capacity are illustrated numerically, assuming a particular type of random user population. These examples indicate that adjusting the price to maximize revenue results in an efficient use of service capacity with an associated small mean delay.
@cite_7: 
@cite_28: Network congestion is a fundamental problem facing Internet users today. A network where users are selfish, and thus reluctant to defer to other users, may result in the famous "tragedy of the commons", where, in the absence of controls, a shared resource is overconsumed by individuals who consider only their personal costs and not the cost to society as a whole. In terms of the Internet, the "tragedy" could be viewed as congestive collapse, resulting from overconsumption of the shared network resource. It is important to distinguish congestion pricing from other forms of network pricing. Charging network users for the congestion they cause can lead to more efficient network utilization by forcing them to take social costs into account. In a congestion-pricing framework, the congestion charge would replace usage and QoS charges. Users would pay their ISPs a subscription charge to cover fixed costs and a congestion charge only when appropriate. This pricing scheme is feasible because, in the absence of congestion, the marginal cost of a network link is practically zero. Congestion pricing can also benefit network operators. By indicating the level of congestion and the user tolerance of it in their networks, congestion pricing can inform operators about when to re-provision and increase network capacity.
@cite_21: 
@cite_32: We consider a network where each user is charged a fixed price per unit of bandwidth used, but where there is no congestion-dependent pricing. However, the transmission rate of each user is assumed to be a function of network congestion (like TCP), and the price per unit bandwidth. We are interested in answering the following question: how should the network choose the price to maximize its overall revenue? To obtain a tractable solution, we consider a single link accessed by many users where the capacity is increased in proportion to the number of users. We show the following result: as the number of users increases, the optimal price per unit bandwidth charged by the service provider may increase or decrease depending upon the bandwidth of the link. However, for all values of the link capacity, the service provider's revenue per unit bandwidth increases and the overall performance of each user (measured in terms of a function of its throughput, the network congestion and the cost incurred by the user for bandwidth usage) improves. Since the revenue per unit bandwidth increases, it provides an incentive for the service provider to increase the available bandwidth in proportion to the number of users.
@cite_6: 
@cite_2: 
@cite_13: Consider a system that is modeled as an M M 1 queueing system with multiple user classes. Each class is characterized by its delay cost per unit of time, its expected service time and its demand function. This paper derives a pricing mechanism which is optimal and incentive-compatible in the sense that the arrival rates and execution priorities jointly maximize the expected net value of the system while being determined, on a decentralized basis, by individual users. A closed-form expression for the resulting price structure is presented and studied.
@cite_17: In the communication network pricing literature, it is the linear pricing schemes that have been largely adopted as the means of controlling network usage or generating profits for network service providers. This paper extends the framework to nonlinear pricing and investigates optimal nonlinear pricing policy design for a monopolistic service provider. The problem is formulated as an incentive-design problem, and incentive (pricing) policies are obtained for a many-users regime, which enable the service provider to approach arbitrarily close to Pareto- optimal solutions. Under the assumption that the service provider knows the true user types, analytical and numerical results indicate a profit improvement exceeding 38 over linear pricing by the introduction of nonlinear pricing. We also consider the scenario where the service provider has incomplete information on user types. A comparative study of the results for complete information and incomplete information is carried out as well, with numerical results pointing to 25 -40 loss of profit by the service provider due to incompleteness of information on the user types.
Many pricing mechanisms have been proposed to manage quality of services (QoS) in networks, see e.g., surveys @cite_28 @cite_2 @cite_22 . For instance, in @cite_33 , Honig and Steiglitz propose a usage-based pricing mechanism, and analyze it using a model with delay-sensitive users. Their results show how to find the price that maximizes the provider's revenue by solving a fixed-point equation. A similar model is used in @cite_32 where Ba s ar and Srikant analyze the many-users limit. They show that, as the number of users increases, the provider's revenue per unit of bandwidth increases and conclude that this gives providers an incentive to increase their network capacity. In a number of papers, e.g., @cite_13 @cite_6 @cite_21 , pricing mechanisms based on multiple classes of customers with different priorities are proposed and analyzed in terms of equilibrium achieved and optimal price per class. In @cite_17 @cite_7 , Shen and Ba s ar investigate the performance of non-linear pricing in a model similar to @cite_32 and find an improvement of up to 38 contrast, in this paper, we investigate linear pricing mechanisms that leverage the time variability of user demand using a single priority class.