Job scheduling in cloud computing environments is a critical yet complex problem. Cloud computing user job requirements are highly dynamic and uncertain, while cloud computing resources are heterogeneous and constrained. This paper studies the online resource allocation problem for elastic computing jobs with soft deadlines in cloud computing environments. The main contributions include: 1) Integer linear programming modeling is used to design an auction time scheduling framework with three key modules - resource allocation, evaluation, and operation, which can dynamically allocate resources in closed loops. 2) Methods such as time-based single resource utilization evaluation and weighted average evaluation are proposed to evaluate resource usage efficiency. 3) Soft acceptance protocols are introduced to achieve elastic online resource allocation. 4) The time complexity of the proposed algorithms is analyzed and proven to be polynomial time, demonstrating efficiency. 5) Modular design makes the framework extensible. This paper provides a structured cloud computing auction framework as a reference for building practical cloud resource management systems. Future work may explore more complex models of random arrival and multi-dimensional resource constraints, evaluate algorithm performance on real cloud workloads, and further enhance system robustness, efficiency and fairness.

翻译：云计算环境中的作业调度是一个关键而复杂的问题。云计算用户作业需求高度动态且不确定，而云计算资源异构且受限。本文研究了云计算环境中具有软截止期限的弹性计算作业的在线资源分配问题。主要贡献包括：1）采用整数线性规划建模，设计了一个包含资源分配、评估和操作三个关键模块的拍卖时间调度框架，能够以闭环方式动态分配资源；2）提出了基于时间的单一资源利用率评估和加权平均评估等方法，用于评估资源使用效率；3）引入软接受协议以实现弹性在线资源分配；4）分析了所提出算法的时间复杂度，并证明其为多项式时间，从而体现了效率；5）模块化设计使该框架具有可扩展性。本文提供了一个结构化的云计算拍卖框架，作为构建实用云资源管理系统的参考。未来工作可探索随机到达和多维资源约束等更复杂的模型，在真实云负载上评估算法性能，并进一步增强系统的稳健性、效率和公平性。