  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.
