Advance reservation games

Advance reservation (AR) services form a pillar of several branches of the economy, including transportation, lodging, dining, and, more recently, cloud computing. In this work, we use game theory to analyze a slotted AR system in which customers differ in their lead times. For each given time slot, the number of customers requesting service is a random variable following a general probability distribution. Based on statistical information, the customers decide whether or not to make an advance reservation of server resources in future slots for a fee. We prove that only two types of equilibria are possible: either none of the customers makes AR or only customers with lead time greater than some threshold make AR. Our analysis further shows that the fee that maximizes the provider’s profit may lead to other equilibria, one of which yields zero profit. In order to prevent ending up with no profit, the provider can elect to advertise a lower fee yielding a guaranteed but smaller profit. We refer to the ratio of the maximum possible profit to the maximum guaranteed profit as the price of conservatism. When the number of customers is a Poisson random variable, we prove that the price of conservatism is one in the single-server case, but can be arbitrarily high in a many-server system.CNS-1117160 - National Science Foundationhttp://people.bu.edu/staro/ACM_ToMPECS_AR.pdfAccepted manuscrip

Propagation of Input Tail Uncertainty in Rare-Event Estimation: A Light versus Heavy Tail Dichotomy

We consider the estimation of small probabilities or other risk quantities associated with rare but catastrophic events. In the model-based literature, much of the focus has been devoted to efficient Monte Carlo computation or analytical approximation assuming the model is accurately specified. In this paper, we study a distinct direction on the propagation of model uncertainty and how it impacts the reliability of rare-event estimates. Specifically, we consider the basic setup of the exceedance of i.i.d. sum, and investigate how the lack of tail information of each input summand can affect the output probability. We argue that heavy-tailed problems are much more vulnerable to input uncertainty than light-tailed problems, reasoned through their large deviations behaviors and numerical evidence. We also investigate some approaches to quantify model errors in this problem using a combination of the bootstrap and extreme value theory, showing some positive outcomes but also uncovering some statistical challenges