We study a general online combinatorial auction problem in algorithmic mechanism design. A provider allocates multiple types of capacity-limited resources to customers that arrive in a sequential and arbitrary manner. Each customer has a private valuation function on bundles of resources that she can purchase (e.g., a combination of different resources such as CPU and RAM in cloud computing). The provider charges payment from customers who purchase a bundle of resources and incurs an increasing supply cost with respect to the totality of resources allocated. The goal is to maximize the social welfare, namely, the total valuation of customers for their purchased bundles, minus the total supply cost of the provider for all the resources that have been allocated. We adopt the competitive analysis framework and provide posted-price mechanisms with optimal competitive ratios. Our pricing mechanism is optimal in the sense that no other online algorithms can achieve a better competitive ratio. We validate the theoretic results via empirical studies of online resource allocation in cloud computing. Our numerical results demonstrate that the proposed pricing mechanism is competitive and robust against system uncertainties and outperforms existing benchmarks.

翻译：我们研究算法机制设计中一类通用的在线组合拍卖问题。服务提供商将多种容量受限的资源分配给按序任意到达的客户。每位客户对可购买的资源组合（例如云计算中CPU与RAM等不同资源的组合）拥有私有估值函数。提供商向购买资源组合的客户收取费用，并产生随已分配资源总量递增的供应成本。目标是最大化社会福利，即客户对其所购资源组合的总估值减去提供商为所有已分配资源产生的总供应成本。我们采用竞争分析框架，提出具有最优竞争比的标价机制。该定价机制的最优性体现在：没有任何其他在线算法能实现更优的竞争比。我们通过云计算中在线资源分配的实证研究验证了理论结果，数值实验表明所提出的定价机制具有竞争性和鲁棒性，能够抵御系统不确定性，且优于现有基准方案。