Circling Reduction Algorithm for Cloud Edge Traffic Allocation Under the 95th Percentile Billing

In cloud ecosystems, managing bandwidth costs is pivotal for both operational efficiency and service quality. This paper tackles the cloud-edge traffic allocation problem, particularly optimizing for the 95th percentile billing scheme, which is widely employed across various cloud computing scenarios by Internet Service Providers but has yet to be efficiently addressed. We introduce a mathematical model for this issue, confirm its NP-hard complexity, and reformulate it as a mixed-integer programming (MIP). The intricacy of the problem is further magnified by the scale of the cloud ecosystem, involving numerous data centers, client groups, and long billing cycles. Based on a structural analysis of our MIP model, we propose a two-stage solution strategy that retains optimality. We introduce the Circling Reduction Algorithm (CRA), a polynomial-time algorithm based on a rigorously derived lower bound for the objective value, to efficiently determine the binary variables in the first stage, while the remaining linear programming problem in the second stage can be easily resolved. Using the CRA, we develop algorithms for both offline and online traffic allocation scenarios and validate them on real-world datasets from the cloud provider under study. In offline scenarios, our method delivers up to 66.34% cost savings compared to a commercial solver, while also significantly improving computational speed. Additionally, it achieves an average of 14% cost reduction over the current solution of the studied cloud provider. For online scenarios, we achieve an average cost-saving of 8.64% while staying within a 9% gap of the theoretical optimum.