Dynamic Pricing for Controlling Age of Information

Abstract

Fueled by the rapid development of communication networks and sensors in portable devices, today many mobile users are invited by content providers to sense and send back real-time useful information (e.g., traffic observations and sensor data) to keep the freshness of the providers' content updates. However, due to the sampling cost in sensing and transmission, an individual may not have the incentive to contribute the realtime information to help a content provider reduce the age of information (AoI). Accordingly, we propose dynamic pricing for the provider to offer age-dependent monetary returns and encourage users to sample information at different rates over time. This dynamic pricing design problem needs to balance the monetary payments to users and the AoI evolution over time, and is challenging to solve especially under the incomplete information about users' arrivals and their private sampling costs. For analysis tractability, we linearize the nonlinear AoI evolution in the constrained dynamic programming problem, by approximating the dynamic AoI reduction as a time-average term and solving the approximate dynamic pricing in closed-form. Then, we estimate this approximate term based on Brouwer's fixed-point theorem. Finally, we provide the steady-state analysis of the optimized approximate dynamic pricing scheme for an infinite time horizon, and show that the pricing scheme can be further simplified to an ε-optimal version without recursive computing over time.

Taming Time-Varying Information Asymmetry in Fresh Status Acquisition

“…Zhang et al in [14] focus on AoI pricing problem, and compare time-dependent pricing and quantity-based pricing. Wang et al [15] consider a dynamic pricing problem, where the platform offers agedependent reward and encourages PoIs to upload their status at different rates. Li et al in [16] design a linear age-based reward and characterize the system efficiency in terms of price of anarchy.…”

Regulating Competition in Age of Information Under Network Externalities

“…If δ th j+1 ≤ δ < δ th j , where j ∈ {1, · · · , N −1}, platform k ∈ {j +1, · · · , N } will still follow the social optimizer λ * * k yet platform i ∈ {1, · · · , j} with smaller costs will deviate, requiring us to design newλ i (δ) as a function of δ to replace λ * * i for such platforms. By ensuring the long-term (15) without deviation just equal to (14) with the best deviation, where…”

“…As in many of the AoI literature (e.g., [11], [26], [27]), we assume in each platform's crowdsourcing pool, the sampling from each sensor source over time follows a Poisson process, and the total sampling to platform i observations as superposition also follows Poisson process with mean rate λ i . Platform i can control mean rate λ i by providing proper incentive compensation to the crowdsourcing pool as in [14] and [16], and its average sampling cost is c i λ i with unit compensation cost c i .…”

Optimizing Age Penalty in Time-Varying Networks with Markovian and Error-Prone Channel State

“…The simple point-to-point system model has been studied in [ 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 ]. When update packets are generated by external sources and are queued in a buffer before transmission, queuing theory can be used to analyze the performance of such system, see, e.g., in, [ 3 , 4 , 5 , 6 , 7 , 8 ]. In [ 3 ], it is shown that the optimum packet generation rate of a first-come-first-served (FCFS) system should achieve a trade-off between throughput and delay.…”

“…In [ 3 ], it is shown that the optimum packet generation rate of a first-come-first-served (FCFS) system should achieve a trade-off between throughput and delay. In [ 8 ], dynamic pricing is used as an incentive to balance the AoI evolution and the monetary payments to the users. Other studies [ 9 , 10 , 11 ] consider the generate-at-will system without a queue.…”