Monopolistic pricing models for revenue management are widely used in practice to set prices of multiple products with uncertain demand arrivals. The literature often assumes deterministic time of serving each demand and that the distribution of uncertainty is fully known. In this paper, we consider a new class of revenue management problems inspired by emerging applications such as cloud computing and city parking, where we dynamically determine prices for multiple products sharing limited resource and aim to maximize the expected revenue over a finite horizon. Random demand of each product arrives in each period, modeled by a function of the arrival time, product type, and price. Unlike the traditional monopolistic pricing, here each demand stays in the system for uncertain time. Both demand and service time follow ambiguous distributions, and we formulate robust deterministic approximation models to construct efficient heuristic fixed-price pricing policies. We conduct numerical studies by testing cloud computing service pricing instances based on data published by the Amazon Web Services (AWS) and demonstrate the efficacy of our approach for managing revenue and risk under various distributions of demand and service time.