Time-varying resource allocation allows users to define their own unique resource requirement plans during different time periods. This mode of allocation can increase the flexibility of resource usage and reduce resource usage costs for users. Moreover, combining this approach with an auction mechanism can enable resource providers to obtain greater social welfare and benefits; therefore, such resource allocation has become a hot topic in cloud computing. This paper addresses the problem of time-varying batch virtual machine (VM) allocation and pricing in the cloud. Specifically, (1) we propose a novel integer programming model for the time-varying batch VM allocation problem, and (2) we design two truthful auction mechanisms to solve the allocation and pricing problem in a competitive environment. The optimal mechanism includes a dynamic programming (DP)-based resource allocation algorithm and a Vickrey–Clarke–Groves (VCG)-based payment price algorithm. Meanwhile, we also design a greedy mechanism that includes a dominant-resource-based allocation algorithm and a dichotomy-based payment price algorithm. We prove the economic characteristics, including truthfulness and individual rationality, of the above two mechanisms. Furthermore, we prove the approximation ratio of the allocation algorithm in the greedy mechanism. Compared to state-of-the-art research, our approach is characterized by high social welfare, a high served user ratio and a short execution time.

时变资源分配允许用户在不同时间段定义自己独特的资源需求计划。这种分配方式可以增加资源使用的灵活性，降低用户的资源使用成本。而且，将这种方式与拍卖机制相结合，可以使资源提供者获得更大的社会福利和利益；因此，这样的资源分配成为云计算的热门话题。本文解决了云中随时间变化的批处理虚拟机 (VM) 分配和定价的问题。具体来说，（1）我们为时变批量 VM 分配问题提出了一种新颖的整数规划模型，（2）我们设计了两种真实的拍卖机制来解决竞争环境中的分配和定价问题。最优机制包括基于动态规划 (DP) 的资源分配算法和基于 Vickrey-Clarke-Groves (VCG) 的支付价格算法。同时，我们还设计了一种贪婪机制，包括基于优势资源的分配算法和基于二分法的支付价格算法。我们证明了上述两种机制的经济特征，包括真实性和个体理性。此外，我们证明了贪婪机制中分配算法的逼近率。与最先进的研究相比，我们的方法具有社会福利高、服务用户比例高和执行时间短的特点。我们还设计了一种贪婪机制，包括基于优势资源的分配算法和基于二分法的支付价格算法。我们证明了上述两种机制的经济特征，包括真实性和个体理性。此外，我们证明了贪婪机制中分配算法的逼近率。与最先进的研究相比，我们的方法具有社会福利高、服务用户比例高和执行时间短的特点。我们还设计了一种贪婪机制，包括基于优势资源的分配算法和基于二分法的支付价格算法。我们证明了上述两种机制的经济特征，包括真实性和个体理性。此外，我们证明了贪婪机制中分配算法的逼近率。与最先进的研究相比，我们的方法具有社会福利高、服务用户比例高和执行时间短的特点。