A Novel Dynamic Pricing Approach for Preemptible Cloud Services

Dynamic pricing for preemptible cloud services (DPPCS) is highly demanded to effectively utilize the excess capacity in cloud computing. However, the dynamic nature of excess capacity exhibits high non-stationarity, which is characterized by multi-temporal stochastic patterns with time-varying statistical properties. The non-stationarity results in the DPPCS problem being a Non-Stationary Markov Decision Process (NSMDP) with unknown transition probabilities. Moreover, DPPCS is constrained by a certain maximum preemption rate, further complicating the DPPCS problem as a Constrained NSMDP (CNSMDP). We transform the CNSMDP into a piecewise Lagrangian dual model, which converts the CNSMDP into an unconstrained optimization problem. To solve the above problem, we propose a novel Q-Learning approach for DPPCS. We first present estimation methods for the unknown environment parameters, including a detection method for identifying temporal pattern changes, and a diffusion approximation method for estimating the actual preemption rate. Then, we introduce a Lagrange multiplier updating method, which can strike a balance between revenue and the preemption rate in the reward function. Building upon the above methods, we develop a Constrained Non-Stationary Q-Learning (CNSQL) algorithm for DPPCS, which dynamically adjusts its learning process to adapt to the multi-temporal patterns. Through simulated experiments, we demonstrate the effectiveness of our proposed approach compared to state-of-the-art algorithms. It performs well in improving revenue generated from excess capacity while maintaining the actual preemption rate within the specified constraint.