Pricing Fresh Data

We introduce the concept of fresh data trading, in which a destination user requests, and pays for, fresh data updates from a source provider, and data freshness is captured by the age of information (AoI) metric. Keeping data fresh relies on costly frequent data updates by the source, which motivates the source to price fresh data. In this work, the destination incurs an age-related cost, modeled as a general increasing function of the AoI. The source designs a pricing mechanism to maximize its profit, while the destination chooses a data update schedule to trade off its payments to the source and its age-related cost. Depending on different real-time applications and scenarios, we study both a finite-horizon model and an infinite-horizon model with time discounting. The key challenge of designing the optimal pricing scheme lies in the destination's time-interdependent valuations, due to the nature of AoI, and the infinite-dimensional dynamic optimization. To this end, we exploit three different dimensions in designing pricing by studying three pricing schemes: a time-dependent pricing scheme, in which the price for each update depends on when it is requested; a quantity-based pricing scheme, in which the price of each update depends on how many updates have been previously requested; and a simple subscription-based pricing scheme, in which the price per update is constant but the source charges an additional subscription fee. Our analysis reveals that (1) the optimal subscription-based pricing maximizes the source's profit among all possible pricing schemes under both finite-horizon and infinite-horizon models; (2) the optimal quantity-based pricing scheme is only optimal with a finite horizon; and (3) the time-dependent pricing scheme, under the infinite-horizon model with significant time discounting, is asymptotically optimal. Numerical results show that the profit-maximizing pricing schemes can also lead to significant reductions in AoI and social costs, and that a moderate degree of time discounting is enough to achieve a close-to-optimal time-dependent pricing scheme.