Online Resource Allocation Under Partially Predictable Demand

For online resource allocation problems, we propose a new demand arrival model where the sequence of arrivals contains both an adversarial component and a stochastic one. Our model requires no demand forecasting; however, because of the presence of the stochastic component, we can partially predict future demand as the sequence of arrivals unfolds. Under the proposed model, we study the problem of the online allocation of a single resource to two types of customers and design online algorithms that outperform existing ones. Our algorithms are adjustable to the relative size of the stochastic component; our analysis reveals that as the portion of the stochastic component grows, the loss due to making online decisions decreases. This highlights the value of (even partial) predictability in online resource allocation. We impose no conditions on how the resource capacity scales with the maximum number of customers. However, we show that using an adaptive algorithm-which makes online decisions based on observed data-is particularly beneficial when capacity scales linearly with the number of customers. Our work serves as a first step in bridging the long-standing gap between the two well-studied approaches to the design and analysis of online algorithms based on (1) adversarial models and (2) stochastic ones. Using novel algorithm design, we demonstrate that even if the arrival sequence contains an adversarial component, we can take advantage of the limited information that the data reveal to improve allocation decisions. We also study the classical secretary problem under our proposed arrival model, and we show that randomizing over multiple stopping rules may increase the probability of success.

Automated summary

In this study, a new demand arrival model combining both adversarial and stochastic components was proposed for online resource allocation problems. The proposed online algorithms designed under this model outperform existing ones and are adjustable to the size of the stochastic component. The research highlights the value of predictability and adaptive algorithms in online resource allocation, bridging the gap between adversarial and stochastic approaches.